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Questioning the Foundations Essay Contest (2012)
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Is Quantum Theory As Fundamental As It Seems? by Michael James Goodband
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Author Michael James Goodband wrote on Aug. 2, 2012 @ 15:21 GMT
Essay AbstractThe success of quantum theory in describing the particle forces has been assumed to imply that quantum theory is fundamental. This assumption has been integral to the search for a unified physics theory, but what if it is wrong? Questioning why we needed quantum theory in the first place is directly answered by experiments revealing electrons to possess a wave property that cannot be derived in classical physics. What if this is exactly as it sounds?
Author BioMichael Goodband holds a physics degree from Cambridge University and a PhD in theoretical physics. His IT development work on agent-based evolutionary software systems encountered issues with causal closure in agent systems, sparking independent research. Author of "Agent Physics" (2012).
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Edwin Eugene Klingman wrote on Aug. 3, 2012 @ 02:01 GMT
Dear Michael James Goodband,
I found your essay fascinating, but, like my own essay, it must be read more than once to absorb what you are saying. I like the question you ask and your focus on the wave aspect of the electron and whether or not it's derivable in classical mechanics and the relevance of Godel's theorem to this. Also that his incompleteness proof applies only to theories over natural-numbers but not over real-numbers. I had missed that distinction.
Because you focus on particle creation as well as wave function quantum mechanics your essay goes beyond mine,
The Nature of the Wave Function. I deal with non-relativistic QM and weak field relativity, whereas you go to QFT and black holes. You cover a lot of ground. I will have to re-read your essay to grasp your points about network expansion as it relates to complete theories, although it does seem to be a unifying scheme. I invite you to read my essay and comment.
Good luck in the contest,
Edwin Eugene Klingman
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Michael James Goodband replied on Aug. 3, 2012 @ 17:57 GMT
Hi Edwin
Thanks for reading the essay and your comments. I have read your essay, which I found interesting, and have re-read it. Now that my essay has been posted and I am part of the contest, I will be commenting on the essays I have read.
The distinction between when Gödel's theorem applies struck me when the incompleteness conditions arose in a computer project and I considered the question, so what if a property is non-derivable? If a property can be observed, then it can be denoted and modelled in some mathematical theory; whether the theory makes any physical sense or not is a different matter. I then followed the logic of changing natural-number terms to real-number terms and was surprised to find that it easily gave many of the 'weird' characteristics of Quantum Theory. The proof that there is no hidden variable theory is trivial in this context. Such a change of representation does however raise the sort of questions about maths representation considered in Roger Schlafly's essay, where, like you, I have used the term physically-real to mean faithful mathematical representation. In these terms, the particle property is physically-real and the wave property is physically-real, but the two are mutually incompatible in classical physics. The only wave to get these two characteristics to coexist in the same term is to use a non-physically-real term, which is the wave-function.
I think that you were brave to go for the features of QT directly from GR. I arrived at GR by looking for the conditions required for the representation change to actually occur, and found that they do in a Kaluza-Klein theory. I just used topological and geometric conditions as they can be used to specify what must be true, without having to find the actual solutions. The condition of Planck's constant from the angular momentum bound of a rotating black hole on the Planck scale is a surprisingly simple condition, I would have expected it to be more complicated. This condition does imply that a black hole would have a mass shell and is devoid of space inside, which would provide a scenario of the Johann Weiser black hole essay.
Good luck in the contest,
Michael
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Alan Lowey wrote on Aug. 3, 2012 @ 18:03 GMT
Dear Michael,
Your knowledge of physics is way above my own so I can't fully comment on your impressively sounding essay. I *do* have an answer to the wave/particle duality nature of sub-atomic particles though, namely, the spinning Archimedes screw. If an electron is visualised as a travelling Archimedes screw which has motion through space, then this repesents the 'particle' nature. If the screw is spinning as well, then this represents the 'wave' nature of the electron. A force carrying particle can be similarly thought of as a spinning Archimedes screw due to it's ability to create a force of attraction, which would be a property of the smallest graviton for example. See attached.
All the best,
Alan
attachments:
Archimedesscrew.gif
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Author Michael James Goodband replied on Aug. 4, 2012 @ 11:45 GMT
Hi Alan
In Kaluza-Klein theories (KKT) the extra dimensions are shrunk into closed spaces, which for the case of electromagnetism basically gives the motion of light as being of the form of a spiral wave travelling along the surface of a closed tube. Such rotation around the closed dimension would give a visualisation of why a photon has spin in KKT.
The wave expansion about a particle-like compactified black hole given in my essay would physically correspond to the scenario of virtual-radiation about a particle creating a particle/anti-particle pair and then for the created anti-particle to annihilate the original particle. This gives a sort of alternation between a particle and the waves of its virtual-radiation field. The wave-particle duality comes from the time-scale of this alternation being as rapid as the Planck time, and so all interactions occur over the time scale of millions of such cycles. It is like drawing a particle and a wave on two pieces of card and then rapidly flicking between them, the net result is that you see both wave and particle at the same time. Whereas you can stop flicking the cards to see one of them at a time, the Planck time scale of the alternation means that there is no corresponding way of only seeing one at a time and so we see wave-particle duality.
This gives a scenario of an alternation between a particle with a virtual-radiation wave field, where the waves in KKT travel in a spiral fashion around a compactified tube. Accurate visualisations of higher dimensional scenarios are always slightly dubious, but you could argue that the average net effect seems to have elements of your visualisation.
Michael
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Alan Lowey replied on Aug. 4, 2012 @ 11:53 GMT
Hi Michael,
Thanks very much for the clarifications and the recognition of how the Archimedes screw visualisation *does* tie-in with modern theories. Much appreciated.
Alan
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Felix M Lev wrote on Aug. 3, 2012 @ 18:27 GMT
Dear Michael,
Congratulations with your interesting essay and good luck in the competition!
You raise a very important problem whether quantum theory can be substantiated in view of the Goedel theorem. The theorem is based on the fact that a set of natural numbers is infinite. As a consequence, standard quantum theory is based on standard mathematics with infinitely small, infinitely large etc. In my papers (see e.g. http://arxiv.org/abs/1011.1076 and references therein) I consider an approach when quantum theory is based not on complex numbers but on a Galois field. Since any Galois field is finite, no problem with the Goedel
incompleteness arises. Standard theory is formally a special case of a theory based on a Galois field in the the formal limit p->infty where p is the characteristic of the Galois field. You also raise a question whether gravity should be quantized. In my approach http://arxiv.org/abs/1104.4647 gravity is
not an interaction at all but simply a kinematical manifestation of de Sitter symmetry over a Galois field.
Felix
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Michael James Goodband replied on Aug. 4, 2012 @ 12:29 GMT
Dear Felix
Thanks for your positive comments and best of luck to you too!
You're absolutely right that Gödel's theorem has a critical dependence upon the natural-numbers being infinite, where for physical theories the natural-numbers arise as the cardinality of sets. Hence your finite Galois field avoids incompleteness issues. I note that your paper http://arxiv.org/abs/1011.1076 has to make the assumption that the universe is finite in order to get finite sets of particles. I also have to impose this finite universe condition to get a closed universe with the necessary topology to get a chiral twisted space that looks like the electroweak vacuum, and a spectrum of 12 topological monopoles that look like the 12 fundamental fermionic particles.
Despite our different approaches, we agree on this finite condition and we are not the only ones. In my case the finite condition of a closed universe gives topological monopole particles with a finite radius and no point singularity. Other essays have argued against point-like particles and singularities from a different basis. So with regards to possible 'meta'-principles asked for in the contest, a meta-principle of reality being finite - as in a closed universe and no singularities - is one that is being proposed from a number of different angles.
Michael
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Joe Fisher wrote on Aug. 4, 2012 @ 14:02 GMT
Dear Doctor Goodband,
Due to an abysmal lack of formal education on my part, although I valiantly tried my best to read your essay several times, I did not understand a word of it. While it might readily seem to be the height of ignorant impertinence for me to make any sort of comment about your essay, as a realist whose essay Sequence Consequence fully explains my position, I would like to pose this question to you. Just as it has been physically impossible for scientists to create a perfect vacuum in the laboratory, why are scientists so confident that they can effortlessly build a perfect dark chamber? Whether or not visible light is made up of a finite number of perfectly formed identical photons or exchangeable identical particles or identical waves seems immaterial. Whatever light is made up of it is still a physical entity and as such once it comes into existence, light cannot be totally eradicated it can only be altered. It is my contention that visible light does not have a speed of motion, it is always stationary. I truly believe that once visible light strikes a surface, it stays on that surface illuminating it. If the source of the light goes out, the visible light on the surface automatically assumes the darkened appearance of the surface, but it cannot physically move away or cease to exist.
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Jayakar Johnson Joseph wrote on Aug. 5, 2012 @ 08:00 GMT
Dear Michael James
I think Quantization is imperative to describe the infinite universe with finite expressions, in that the quantization of physical noumenon of nature needs adaptations for sensing the phenomena of nature.
With best wishes
Jayakar
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Joy Christian wrote on Aug. 5, 2012 @ 23:23 GMT
Hi Michael,
Your comments on the essay by Edwin Eugene Klingman led me to your own essay. You wrote on Edwin's blog:
"Models with causal linkage between the particle and wave property generally have problems with Bell-type analysis, or re-analysis. Quantum Theory has a very peculiar form of non-locality, with what can be called non-locality of identity which is confirmed by wave interference and quantum entanglement experiments. However, this is strangely not accompanied by non-locality of causation such that it could be practically used to send a signal faster than light. Unfortunately because your model has causal linkage between the wave and particle properties, when you obtain the non-locality of identity required for comparison with QT you also acquire non-locality of causation. So Joy Christian is right and the model as given in the essay does fall victim to the non-locality issue, as encountered via Bell-type analysis."
I have been trying to tell this to Edwin for some time now, but you have been able to say it much more clearly. Bell's analysis is not something that can be overcome that easily.
In any case, what I found interesting in your own essay is your comments about the four parallelizable spheres, S^0, S^1, S^3, and S^7, and their associated normed division algebras. In this context you may find my attached paper interesting (with a fuller account of my ideas in several chapters of
my book).
Best of luck for the essay competition,
Joy Christian
attachments:
5_1101.1958v1.pdf
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Michael James Goodband replied on Aug. 6, 2012 @ 11:24 GMT
Hi Joy,
Fascinating paper! It looks very much like you've got the other side of the story I have presented in the context of extended GR.
In my Agent Physics book - and in the review paper of the chapter presenting the theory http://www.mjgoodband.co.uk/papers/STUFT.pdf - I proposed the following meta-principle:
Physical causation will only be consistent and complete if it realises all the manifolds S0, S1, S3 and S7.
I assume that this applies to a real physical manifold - as in a real fabric of reality like the fabric concept of space-time - which when read off directly in the context of extended GR specifies a closed S3 universe with particle dimensions S7. Such a universe is necessarily cyclical S1 and to obtain the manifold S0 as physical objects requires topological monopoles - hence the given pattern S10 -> S3*S7 with the formation of a physical twist in the fabric of space which breaks the S7 symmetry in a suitable way. This gives monopoles and anti-monopoles - giving a realisation of S0 - which must be in a representation of the rotation group - with group manifold S3 - and particle symmetry representation of the manifold S7. The S1 representation would come from the monopoles having a wave property, which I have to add from observation as my derivation of QFT is based on the wave property being non-derivable.
Unless I'm much mistaken, it looks as though your work could be stated as the meta-principle:
Physically-real representation of reality (in the sense of ERP) will only be consistent and complete if it involves all the manifolds S0, S1, S3 and S7.
Would this be correct? Such a condition on mathematical representation would be the other side to the equivalent condition being applied to a real physical fabric of reality. However, the consequence of this restriction is that the symmetry breaking required to give topological monopoles must be of the form:
S7 = SU(4)/SU(3) -> (Spin(3) * SU(2) * U(1))/Z3
Which would imply that the local colour group HAS to be SO(3) and not SU(3). Once the significance of the manifolds S0, S1, S3 and S7 is recognised there doesn't seem to be a way of avoiding this conclusion. Does this seem correct to you?
Michael
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Joy Christian replied on Aug. 6, 2012 @ 13:46 GMT
Hi Michael,
You wrote: "Fascinating paper! It looks very much like you've got the other side of the story I have presented in the context of extended GR."
Yes, it does seem like our two respective approaches are flip sides of the same coin. I have arrived at the parallelized spheres via an analysis of EPR and Bell, whereas you have arrived at them (it seems) more from the particle physics side. But the conclusion seems inevitable:
"Physical causation will only be consistent and complete if it realises all the manifolds S0, S1, S3 and S7."
By the way, we are not the only ones who have recognized the significance of these manifolds for fundamental physics. Geoffrey Dixon, Rick Lockyer, and Michael Atiyah (to name just a few) also seem to share our conviction.
I also agree with your proposed meta-principle for my work, although I would use a slightly different language:
"Locally causal representation of reality (in the senses of EPR and Bell) can only be consistent and complete (in the sense of Einstein and EPR) if it is based on a parallelized 7-sphere, S^7, which contains S^3, S^1, and S^0 as nested submanifolds, in the manner of Hopf."
This is more mouthful than what you have suggested, but it describes what I am proposing more accurately.
I am not sure how to answer your other question:
"However, the consequence of this restriction is that the symmetry breaking required to give topological monopoles must be of the form:
S7 = SU(4)/SU(3) -> (Spin(3) * SU(2) * U(1))/Z3
Which would imply that the local colour group HAS to be SO(3) and not SU(3). Once the significance of the manifolds S0, S1, S3 and S7 is recognised there doesn't seem to be a way of avoiding this conclusion. Does this seem correct to you?"
I am not sure about this, mainly because I am not a particle physicist. What I am 100% sure about is the significance of the manifolds S^0, S^1, S^3, and S^7. If this implies what you think it implies, then I would put my last penny on it.
Best,
Joy
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Joy Christian replied on Aug. 6, 2012 @ 21:13 GMT
Michael,
For me the significance, or rather the inevitability of the manifolds S^0, S^1, S^3, and S^7 is necessitated by a rather innocent looking algebraic identity (cf. equation 1.53 of the attached paper). I am sure you are more than acquainted with this identity, but for a summary of my perspective on the matter please have a look at sections 1.4 and 1.5 of the attached paper.
Best,
Joy
attachments:
9_Origins.pdf
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Alejandro Rivero replied on Dec. 10, 2012 @ 15:53 GMT
I come to this thread after some comments at vixra; let me note that any discussion of S7 and, most important, (S3xS5)/U(1), should consider the work on 7 dimensional Kaluza Klein theories and very particularly the fact that the manifolds of later type have isometry group SU(3)xSU(2)xU(1), as Witten published in that age.So SU(3) is not lost, and it is somehow connected to so(6)~su(4) in 8 dimensions. The connection to the S7 is very retorted, via the branched covering of CP2 with S4 (or S4 on CP2, I never remember how it is).
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Jonathan J. Dickau replied on Dec. 11, 2012 @ 00:47 GMT
Interesting comment Alejandro,
I'm wondering which Witten papers they are, and also I am sad your comment gets hidden.
Regards,
Jonathan
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Edwin Eugene Klingman wrote on Aug. 6, 2012 @ 04:13 GMT
Hi Michael,
Thanks again for your comments on my thread. They definitely helped my 2nd reading of your essay.
Like Joy I had noted your mention of S0, S1, S3, and S7 as the only normed division algebras, a point that Joy has repeatedly remarked on. This time I was particularly fascinated by your view of black holes as Kaluza-Klein 'particles' with empty S2 interior and 'real physical surface' as event horizon, and no singularity.
You indicate also that you derive values close to the Standard Model "despite being derived solely within classical physics." I plan to look at that reference. In the first page or so you remark there is no means in classical mechanics for a single particle to travel as a wave. Of course my model is based on the particle always traveling 'with' a wave. It is this linked state that you seem to view as a causal linkage leading to Bell-type non-locality issues. With inherently unknowable phase the abstraction 'causal' may be stronger than is actually the case, as there is also a self-interacting aspect of the C-field that may or may not allow physically real solutions to be derivable. In other words I am uncertain, according to your definition, whether to consider my wave property of the particle 'derivable' or not. [By the way, I tried to get your book Agent Physics on Amazon, with no success. Any ideas?]
Another point I did not fully appreciate the first time I read your essay is this: "Conservation laws applying to charges of particles mean that no real-number valued variables could be the cause of changes in particles numbers [with implications for incompleteness proof]." And this time through I did like your conserved charge as a limit to black hole self-immolation.
The following section on Non-physically-real terms is a tough nut to crack. I read and understood the words, but it doesn't jell. Partly because I believe particles derive from physical processes, not symmetry. Perhaps I'll understand this better after reading your reference [15]. I do agree with you about physics unification without quantum mechanics being fundamental.
In studying your 'twist' in S7, it does not sound the same as Joy's torsional twist. Is it? I did not interpret your change in metric in the ergo-region to be equivalent to Joy's change in handedness, but do you believe your solution is isomorphic to his?
I hope to have a few new questions after another reading or so.
Best,
Edwin Eugene Klingman
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Edwin Eugene Klingman replied on Aug. 6, 2012 @ 06:59 GMT
Michael,
Nine pages is just not enough! I doubt that anyone can understand your essay with one or two readings. I would advise anyone who wishes to better understand what you are doing to read your reference [15].
Edwin Eugene Klingman
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Michael James Goodband replied on Aug. 6, 2012 @ 15:57 GMT
Edwin is probably right. There are two interlinked parts in my essay which are both quite involved, and have been discussed carefully as they suggest a model for physics unification. See
1) http://vixra.org/abs/1208.0010
2) [15] http://www.mjgoodband.co.uk/papers/QFT_KK.pdf
The first part is about the physical conditions under which Gödel's incompleteness theorem can apply...
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Edwin is probably right. There are two interlinked parts in my essay which are both quite involved, and have been discussed carefully as they suggest a model for physics unification. See
1) http://vixra.org/abs/1208.0010
2) [15] http://www.mjgoodband.co.uk/papers/QFT_KK.pdf
The first part is about the physical conditions under which Gödel's incompleteness theorem can apply to science theories constructed in strictly physically-real terms, and how this is not the end of the story as you can change the mathematical representation - to non-physically-real terms - to escape from Göde's proof. This is discussed in more general terms in a philosophy of science paper that I have posted on http://vixra.org/abs/1208.0010 to make it more available. The issues raised here are those of the relationship between physical reality and mathematical representation - as also discussed by Roger Schlafly and mentioned by others e.g. Dan Bruiger - especially how it can become problematic when a physical system forms a closed cycle of cause and effect. The problem here is specifically with the top-down causation part of the closed cycle, from effect back to cause - George Ellis discusses how we might be under-estimating all such top-down causation in science.
The second part of my essay is specifically identifying a scenario which realises the conditions needed for Gödel's incompleteness theorem to apply to a particle-like object within classical physics. This is specifically identified in a rotating black hole of the Planck scale, as the rotation drags space-time such that there-exists a region where any radiation in it would be of the form of the virtual-radiation of Quantum Theory. The calculation of the effect this virtual-radiation has in reducing the rest mass of the particle-like black hole is shown to be subject to Gödel's incompleteness theorem. The Planck mass of the object is reduced by the virtual-radiation field around it, but the reduced mass cannot be calculated in classical physics. Heuristic arguments imply that the mass reduction effect can be almost total, giving an almost massless particle-like black hole with a radius of the Planck length and angular momentum of ½ the Planck constant - such an object looks suspiciously like a real particle. I then assume that a non-derivable feature in this theory is that this object possesses a wave property, and use the change in mathematical representation discussed above to show that these objects would then be described by a Quantum Field Theory. Since QFT can be derived by a change in mathematical representation QFT cannot be fundamental; this is expanded upon in detail in [15] http://www.mjgoodband.co.uk/papers/QFT_KK.pdf.
The final part of the essay then discusses how this all adds up in being able to derive both General Relativity for space-time and a Quantum Field Theory for 12 topological monopoles with the same charges as the 12 fundamental particles, where the Lagrangian has the same mathematical form as that of the Standard Model. The points discussed above with Joy Christian about the spaces S0, S1, S3 and S7 being special, imply that the extended GR model of the essay - S10 unified field theory - is uniquely characterised for the assumption that the fabric of space is a real physical surface. The theory has 2 potential conflicts: it says that the local colour group HAS to be SO(3), not SU(3); and the universe HAS to closed (S3). If these are true, and the mathematical representation change is the origin of Quantum Theory that it appears to be, then S10 unified field theory would seem to be viable a candidate for physics unification.
Michael James Goodband
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Author Michael James Goodband replied on Aug. 7, 2012 @ 12:59 GMT
Edwin
I am glad that my comments were helpful.
On the issue of a black hole being a hollow S2 in my Kaluza-Klein theory, Johann Weiser presents results of numerical calculations in GR with a relativistic ideal gas model, which shows the metric of a black hole as being a hollow mass shell. The particles of the Weiser solutions all reside just outside the event horizon radius, the inside is hollow and there is no physical singularity at the centre. In section 3 of ref [15] http://www.mjgoodband.co.uk/papers/QFT_KK.pdf. I also give a simple thermodynamic analysis which yields the temperature and entropy expressions for a black hole, but without using the Quantum Theory of Hawking radiation.
My usage of the word 'twist' refers to a physical twist in the higher dimensional torus S3*S7 with 'outer circle' S3 of the spatial universe and 'inner circle' S7 of compactified dimensions associated with particle symmetries in KKT. In visual terms, imagine a ball of dough and poke a hole through it to get a doughnut or the torus S1*S1. This is the analogy of imagining the universe as a closed surface and then registering that the operative word in wormhole is 'hole' - a hole in a sphere gives a torus whatever the number of dimensions. However, a normal sphere is the odd one out of spheres S^N, as it is possible to poke a hole through all higher dimensional spheres to get a torus with a twist in it. For the doughnut we have to break the loop, twist one end relative to the other and stick it back together again. This is the sort of physical twist I mean, resulting from poking a wormhole through S10 to give the 'torus' S3*S7 with a twist in it - this twist has the properties of the electroweak vacuum, including giving a closed formula for the Weinberg angle (in the technical notes of the essay) which is within the experimental range.
Joy's torsion refers to the twisted structure of the fibre bundles S3 and S7. Wikipedia has a stab at giving a visualisation of the torsion of the S1 fibre in going around the S2 base-space of S3 on http://en.wikipedia.org/wiki/Hopf_bundle, but I can't say that it helps me much. With my QFT background I tend to visualise the topological monopole ('t Hooft-Polyakov monopole) you get when the S2 base-space and S1 fibre of S3 are in a sense unwrapped. A simple visualisation of this is given by imagining poking cocktail sticks into an orange and then slotting Hula-Hoops onto the sticks - the circle S1 of the Hula-Hoop gives the S1 fibre and the surface of the orange gives the S2. The change in orientation of the cocktail sticks going around the orange gives a sense of the fibre-bundle torsion, but this configuration has the symmetry of the sphere S2 whereas the torsion of the fibre-bundle gives S3.
Best,
Michael
Author Michael James Goodband replied on Aug. 7, 2012 @ 16:15 GMT
The Agent Physics book is available from UK Amazon, or I can supply it direct via the UK Amazon marketplace. The Amazon stock numbers are not correct; hopefully that will be sorted out soon.
Steve Dufourny Jedi replied on Sep. 30, 2012 @ 17:04 GMT
yes of course , and some monney after the nobel, of course of course. your strategy shows in fact your lack of skillings for the gnerality.
In fact you think really that you are going to share the nobel dear Hopf and Milnor. Let me laugh !!! or kill me.But there you are not scientists but murders, me I will be always a real searcher inventor of the therory of spherization. You shall not be in the books. Me yes, I have already spoke a lot before fqxI since more than 9 years. If you knew the number of persons knowing my theory in all countries of these planets. Kill me, it is better you know. You do not merit the nobel.
Regards
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Thomas Howard Ray wrote on Aug. 6, 2012 @ 17:36 GMT
Michael,
It's a breath of fresh air to see some serious understanding of modern topology, when these forums have been full of serious misunderstandings the last couple of years. Where were you when we needed you? :-)
Also, I for one very much appreciate your organization -- building from classical black hole relativity to quantum theory. Nice.
I don't think Joy Christian's mathematically complete framework has the problem of demanding a closed universe; parallelization of S^1, S^3, S^7 gives us a flat space to work in, so that conformal mapping guarantees angle preservation to infinity even in a curved space, and simple connectedness does the rest. I.e., because all real functions are continuous, and because the octonionic space of S^7 allows the geometric algebra to return all real values, the set of complete measurement results on S^3 constitutes a closed logical judgment on all the local physics, even in an open universe. (There's some peripheral discussion of this issue in my essay "The perfect first question," that I hope you get a chance to visit.) I'm not familiar with the term "particle space" that you apply to S^7; however, it seems to fit with my informal characterization of Christian's S^7 structure as "physical space" in concert with S^3 as "measure space."
Really, you've done a crackerjack job. Thanks for sharing and best wishes in the competition.
Tom
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Author Michael James Goodband wrote on Aug. 7, 2012 @ 18:47 GMT
Given the prior discussion of Joy Christian's work on FQXi I thought it might help to clarify how my S10 unified field theory arrives at the same conclusion: it is all about the Hopf spheres S0, S1, S3 and S7. This might initially look like yet another case of putting mathematics before physics - the cart before the horse - that many of the essay entrants have pointed at as being a problem with...
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Given the prior discussion of Joy Christian's work on FQXi I thought it might help to clarify how my S10 unified field theory arrives at the same conclusion: it is all about the Hopf spheres S0, S1, S3 and S7. This might initially look like yet another case of putting mathematics before physics - the cart before the horse - that many of the essay entrants have pointed at as being a problem with physics. However, I arrive at this conclusion from the physics side, where the crux is identifying the form of Quantum Theory as being that due to a change in mathematical representation from natural-number terms denoting particle numbers, to real-number terms denoting particle numbers, in order to escape Gödel's incompleteness theorem where the wave property of a particle is the non-derivable feature in classical physics. This would mean that the matter fields of Quantum Theory are not fundamental and so cannot be just introduced into a unified theory of physics - matter must originate by some other means. This suggests re-considering extensions to GR, but not to forget the physics!
The metric of GR is conceptually a grid laid out over a surface in order to define distance measurements. An example which grounds the physics is to imagine an inflated party balloon and drawing lines of latitude and longitude on the balloon with a felt tip pen. This grid defines a metric field for the surface which expands and contracts as the balloon inflates and deflates. The Einstein tensor gives how this metric field changes with the volume of the balloon, where the form of the Einstein tensor is based upon the physical assumptions that the space is both homogeneous and isotropic. Add the physical conditions that the space is finite but without a boundary, and spheres are the simplest surfaces meeting these conditions. Now to say that there is no space-time in GR is analogous to imagining that the balloon blinks out of existence leaving the ink of the pen lines hanging in thin air - a mathematical map without its physical territory!
So we leave the territory where it is, keep the physical conditions specifying spheres, and then remember that Kaluza and Klein successfully unified gravity and electromagnetism by extending the number of dimensions with a closed S1 dimension associated with the U(1) symmetry group of electromagnetism. The condition of space being a closed sphere S^N and the S1 group space of electromagnetism gives the key to particles, as any theory where a symmetric space S^N is broken in some way to give a space containing S1 will give rise to topological monopoles. Such particle-like objects would be of the form of a hole in the space, like an air bubble in water.
In the same way the U(1) electromagnetic group space S1 corresponds to a compactified dimension in the orginal Kaluza-Klein theory, the S3 group space of the SU(2) isospin group would also correspond to compactified dimensions. There is the apparent problem that the colour group SU(3) doesn't have a simple correspondence to some space, so we will just denote it X for now. If the operative 'hole' of a wormhole is inserted into some sphere S^N it will change the topology to that of a higher dimensional torus S^3*S^M where the form of the closed spatial universe is the sphere S3. The problem is then to solve for S^M to get the particles as topological defects and for the colour space X to be something sensible - the solution is S^7 for which the colour space X = S^3 corresponds to colour group SO(3). As the space of monopoles and anti-monopoles is S^0 = {-1, 1} the Hopf spheres S0, S1, S3 and S7 are all physically realised. So physics arrives at the mathematical condition, it is just then a lot simpler to say it as the meta-principle: it is all about the Hopf spheres!
The S3 is the physical space of a closed universe and S7 consists of the compactified dimensions of a Kaluza-Klein theory, which I refer to as the particle space as it gives the properties of the topological monopoles as particles. The S^3 closed universe is locally flat R^3 and has S^7 particle dimensions at every point x. However, to get the conditions for particles as topological monopoles, there must exist a non-trivial global map from S7 to the spatial S3 universe. In local terms in R^3, this means that the orientation of S7 changes between two spatial points x1 and x2; in GR this change would be denoted by the metric, whereas in the dimensionally reduced theory it would be called the Higgs field. This physical S^7 space at every point x in the locally flat R^3 space apears to give the point at which to start considering comparisons with Joy's work.
Michael James Goodband
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Author Michael James Goodband replied on Aug. 7, 2012 @ 18:56 GMT
I meant the fibres of the Hopf spheres. Sorry!
Joy Christian replied on Aug. 7, 2012 @ 21:57 GMT
Hi Michael,
Nice summary. As Tom says: Where were you when we needed you? :-)
The discussion of my work, both here at FQXi and elsewhere, is usually at a very superficial level. Most people seem to get stuck at the most basic EPR correlation, when I want to talk about local causality of any conceivable quantum correlations, no matter what the underling quantum state. This can *only* be done by recognizing the exceptional properties of the parallelized 7-sphere---especially its closed-ness under multiplication, as well as that of its fibres, S^3, S^1, and S^0.
This is perhaps *the* fundamental conceptual difference between our respective uses of these spheres. While I too arrived at them through physical considerations (by analysing the conceptual arguments of Einstein, EPR, and Bell), what I ended up with are the *parallelized* spheres, which are---so to speak---as flat as a sheet of paper. More precisely, their curvature tensors vanish identically, while torsions within them remaining non-zero. Thus the theory of gravity more appropriate in the context of my work is the teleparallel gravity, not the usual general relativity. It turns out that without parallelization local causality cannot be maintained for all conceivable quantum correlations, or even for the basic EPR correlation. Parallelization is the *only* way to meet Bell's challenge. Unfortunately this fact is not yet widely appreciated, even by some supporters of my work.
Best,
Joy
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Edwin Eugene Klingman replied on Aug. 8, 2012 @ 00:53 GMT
As the potential skunk at the picnic, and the possibly alluded to deluded 'supporter' and one who is minimally familiar with both of your work, it is not clear to me that a shared appreciation of S0, S1, S3, and S7 doth a marriage make. I too believe that these normed division algebras are important and, with Rick Lockyer's view of Octonions, see them as applying to my own work. Just sayin'.
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Joy Christian replied on Aug. 8, 2012 @ 05:46 GMT
Hi Edwin,
My comments were by no means an attack on you (there are supporters of my work outside FQXi and the cyberspace, including within the main-stream Bell community). But, yes, as I have said before, you are among those who have not yet understood my argument.
I have nothing against your own ideas as long as you acknowledge that your model is manifestly non-local and it can never be local. But you are unlikely to acknowledge this because you are unable to see the blatant non-locality of your model. I thought we had agreed to disagree about this.
In any case, both Michael's work and mine stand on its own. They neither need to be married, nor stand in conflict. At this stage I am as curious as Michael to witness some of the same broad conclusions emerging from two very different explorations.
Best,
Joy
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Edwin Eugene Klingman replied on Aug. 8, 2012 @ 06:32 GMT
Hi Joy,
That was tongue-in-cheek and not to be taken seriously, but I don't think that Michael's approach to normed division algebras bears much relation to yours. I believe that he and I see SO(3) as more appropriate to our theories than SU(3) but his theory and mine are very far apart in other ways. But you are correct, that it is interesting that normed division algebras are becoming significant in this fashion. And I do not think your theories are either married or in conflict. I really don't see much overlap except for the shared appreciation of this topology. My remark was spurred by Tom's "where were you?" with the implication that his use of Sn spheres would have helped your case. Perhaps, but I doubt it. Although there was a period about 18 months ago when you and others were arguing about the definitions of particular topologies when Michael would probably have been on your side. And he does agree with you that I haven't solved the non-locality problem.
I'll bow out of this discussion with the best wishes for your model and for Michael's theory. Both are very impressive. The problem with both is their complexity, requiring so much effort to comprehend. They are beautiful accomplishments. Congratulations to both of you. I truly admire you both for the obvious intellectual effort required to produce these works.
Best,
Edwin Eugene Klingman
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T H Ray replied on Aug. 8, 2012 @ 18:09 GMT
Joy wrote, " ... what I ended up with are the *parallelized* spheres, which are---so to speak---as flat as a sheet of paper. More precisely, their curvature tensors vanish identically, while torsions within them remaining non-zero."
This seminal point really isn't easy to grasp, but grasped it must be. I think what Michael says below, "The pre-condition of the S^7 -> S^3 map and the lack of an independent S^1 are both addressed by the unification principle" -- i.e., the "no preference" principle necessitated by general relativity (nice, Michael) -- nails down why Riemann curvature vanishes everywhere while torsion is preserved in the 2-dimensions of S^1 as a twist, which demands such a nonorientable surface embedded in the orientable measure space. Classical orientation entanglement is preserved, as in spinor theory.
I realize that Michael continues with S^3 X S^7 to S^10, but we don't need it for the present discussion, because the limit of parellizability is S^7. (I would comment, though, that an earlier topology paper of mine concluded that the 10-dimension limit is identical to the 4-dimension horizon but that is also, no pun intended, outside the scope of this discussion.)
Yeah, I'm shooting from the hip. It looks like something important is going to start percolating here very quickly, though.
Tom
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Steve Dufourny wrote on Aug. 8, 2012 @ 01:26 GMT
Hello Professor Mickael from UK,
Ok let's play, they need help :)
Your essay shows us a very good knowledge of several theories, existings.But I see several irrationalities. Why BH particules ? the derivations cannot give us a quantum BH, a BH is a sphere , with a volume, central to galaxies, with rotations. So indeed Godel is right, but his reasoning is subtle, indeed a lot of people confound the theorems of uncompleteness of Godel with the physical axiomatizations. the axiom of truth becomes an essential. Is it important to insert not coherent derivations or superimposings for a kind of confusions.
My perception is that a lot of persons utilize this uncompleteness of Godel to imply an, ocean of confusions. In fact, the coherences must be formalized with a kind of universal wisdom !!! Is it necessary to imply the confusions when the truth is so evident and simple? it is the question after all.
The Uncompleteness is simple in its pure meaning.
until soon and spherically yours of course.
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Author Michael James Goodband wrote on Aug. 8, 2012 @ 15:47 GMT
Hi Joy (Part 1),
I have been contemplating your work in the links you gave. My slip in saying the Hopf spheres I think was my subconscious trying to get my attention: with the particle/anti-particle space being S^0={-1,1} and the space of cyclic waves being S^1, the existence of wave-particle duality seems to be saying the fibre-bundle of the first Hopf sphere. This implies that the first...
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Hi Joy (Part 1),
I have been contemplating your work in the links you gave. My slip in saying the Hopf spheres I think was my subconscious trying to get my attention: with the particle/anti-particle space being S^0={-1,1} and the space of cyclic waves being S^1, the existence of wave-particle duality seems to be saying the fibre-bundle of the first Hopf sphere. This implies that the first Hopf sphere provides an underlying context for an analysis of Quantum Theory, such as yours.
I think that you short-changed yourself with the meta-principle you gave earlier. Although in mathematical terms the S^7 case (eqn 1.32 of your 9_Origins.pdf attachment) is more general than the S^3 case (eqn 1.28) as S^7 contains S^3 subspace, the assertion of S^7 ONLY precludes the possibility in physics that the two spaces have different origins such that the S^3 is not a physical subspace of S^7. A real sphere example is where the space of the particle symmetries is S^7 - as in my S10 unified field theory (STUFT for short) - and the space of the rotation group is S^3. The rotation group is not a subgroup of the particle symmetries and so BOTH S^3 and S^7 occur as they have a different origin. So the most general statement of your work is not solely in terms of S^7, but S^3 (1.28) AND S^7 (1.32). With the first Hopf sphere providing an underlying context for the wave-particle duality of Quantum Theory, your work would then seem to independently contain S0, S1, S3, S7 and not just as subspaces of S7 (as parallized spheres).
In the context of the spheres being real physical surfaces, the presence of BOTH S^7 and S^3 is critical as the homotopy group for the map S^7 -> S^3 shows that it just involves the S^4 base-space PI_7(S^3) = PI_4(S^3) = Z_2 and gives a chiral non-trivial vacuum looking for all the world like the electroweak vacuum and gives the correct value of the Weinberg angle just in geometric terms. This breaks the symmetry of the S^7 and gives a 3 by 4 table of topological monopoles looking like the particles.
In metric field terms, your eqn 1.53 together with the closure condition of eqn 1.55 specify the spheres S0, S1, S3, S7 as a collection of closed spaces. The principles of GR seem to be captured by the meta-principle: make no preference. This means no preferred speed, ie. the speed of light is always the same, no preferred location (homogeneity) and no preferred direction (isotropy) - these also say no boundary to the space. Applying this no preference condition to the 4 spheres, says all of them. With space being S^3 and the 'particle space' being S^7 the above map S^7 -> S^3 gives a non-trivial vacuum winding and topological monopoles and anti-monopoles with space S^0. The pre-condition of the S^7 -> S^3 map and the lack of an independent S^1 are both addressed by the unification principle: the S^3 of space and the S^7 'particle space' are unified in a sphere S^10 which then has a hole inserted to give S^3*S^7 with the above mapping. In GR, such a scenario would be cyclical between the unified S^10 phase and the 'broken' S^3 * S^7 phase, thus giving the independent occurrence of S^1 in a 10+1 dimensional extension to GR.
This gives the physically-real side I address in extended GR where spheres are spheres, particles are particles and waves are waves.
Michael
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Joy Christian replied on Aug. 9, 2012 @ 12:29 GMT
Hi Michael,
You have raised a number of interesting issues. I will number my responses to them for clarity.
(1) You wrote: "...the assertion of S^7 ONLY precludes the possibility in physics that the two spaces have different origins such that the S^3 is not a physical subspace of S^7."
The "S^7 only" assertion is not strictly necessary for my analysis to go through. However,...
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Hi Michael,
You have raised a number of interesting issues. I will number my responses to them for clarity.
(1) You wrote: "...the assertion of S^7 ONLY precludes the possibility in physics that the two spaces have different origins such that the S^3 is not a physical subspace of S^7."
The "S^7 only" assertion is not strictly necessary for my analysis to go through. However, from the point of view of quantum correlations, separation of S^3 from S^7 in the manner you have suggested seems to be unjustified. In my picture quantum correlations are correlations among events occurring within spacetime---or equivalently among the clicks of a network of detectors. As far as EPR type correlations are concerned these events can be viewed as occurring within S^3. But S^3 is definitely not enough to reproduce quantum correlations beyond those exhibited by the 2-level systems. For example, the correlations exhibited by the GHZ state can only be reproduced as events occurring within a parallelized 7-sphere. To be sure, the clicks we observe appear to us as occurring within R^3. So the "extra" dimensions of S^7 are certainly hidden from us in that sense, but these dimensions are not necessarily compactified as in your work. In fact I tend to view the correlations exhibited by states like GHZ as the *evidence* that the rotation group of the physical space is S^7, not S^3, with the latter being only a special case of S^7. Still, this does not seem to necessitate the "S^7 only" assertion.
(2) Like Tom, I very much like your meta-principle: "make no preference. This means no preferred speed, ie. the speed of light is always the same, no preferred location (homogeneity) and no preferred direction (isotropy) - these also say no boundary to the space." Absolutely marvellous!
(3) But the following separation is potentially in conflict with my analysis: "With space being S^3 and the 'particle space' being S^7..."
For the reasons explained above, in my analysis the separation of S^3 as "physical space" from S^7 as "particle space" is not justified. All measurement events are occurring within S^7, but we only see them as occurring within R^3. This, however, does not seem to be in conflict with your earlier statement that "physical S^7 space at every point x in the locally flat R^3 space appears to give the point at which to start considering comparisons with Joy's work."
(2) Much of what you say in your Part 2 below has to do with the 'flattening' you require to get QT fully consistent and complete. The flattening required for my analysis to go through has to do with "absolute parallelism", as in teleparallel gravity. Since both S^3 and S^7 are simply-connected manifolds, absolute parallelism is equivalent to their curvature tensors vanishing identically, with torsions within them remaining non-zero in general. This is automatically the case if we view S^3 and S^7 as sets of unit quaternions and octonions, respectively. The very algebra of quaternions and octonions then provides means to define orthonormal frames at each point of these manifolds. This however induces torsional twists within them, and it is these twists in the manifolds that are responsible for what we observe as strong quantum correlations. The latter have nothing to do with non-locality or entanglement per se, because the distant events within S^3 and S^7 are now causally linked by distant parallelism in a non-mysterious way. In other words, in my picture the correlations between distant events are no more mysterious than the innocent correlation between Dr. Bertlmann's socks discussed by Bell.
Best,
Joy
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Author Michael James Goodband replied on Aug. 9, 2012 @ 15:53 GMT
Hi Joy,
I will frame my point about separate occurrences of S3 and S7 in terms of the classic EPR scenario of correlated spin states between 2 particles, which without special characters I will denote as e^|e_ for electron spin up e^ and electron spin down e_ .
My point is that this is just quantum mechanics, think quantum field theory. Just as the emission of a photon converts e^ to e_ the emission of a W-boson converts an electron into an neutrino, an up quark into a down quark etc. and there are also inter-family conversion reactions. Such interactions mean that the most general EPR 2 particle scenario in QFT is *not* of the form A^|A_ but A^|B_ where particles A and B can be of any type; A=B is just a special case in QFT.
The observables to consider in the correlation analysis are both the spin eigenvalues of the rotation group SU(2) - group space S3 - and the particle types which are eigenvalues of some 'particle space'. I use this term in place of particle symmetry group, because grand unified theories assumed that it was going to be a group - a hidden assumption I could have raised in my essay - whereas my work says that it is the quotient group SU(4)/SU(3) isomorphic to S7. So there are 2 sets of observables with quantum correlations {^,_} and {A,B,...} where the values of the first set are the eigenvalues of the rotation group with space S3. In my case the second set contains eigenvalues of SU(4)/SU(3) ~ S7 (after the symmetry has been broken) and the S3 is clearly distinct from this S7.
Your analysis should also apply to the quantum correlations between the observables in each of the 2 sets {^,_} and {A,B,...} for the most general EPR 2 particle scenario A^|B_ in the Standard Model QFT. Ultimately my question is whether there is a way to use your analysis in reverse to place a constraint on the origin of these observables?
I.e. some argument of the form
Parallelised S3 => group space S3 for the observables {^, _}
Parallelised S7 => 'group space' S7 for the observables {A,B,...}
A straightforward argument doesn't seem to work, which is why I am asking :-)
Michael
Anonymous replied on Aug. 9, 2012 @ 20:05 GMT
Hi Michael,
You have framed your question very clearly. It reminds me of some passionate discussions I had last year on these pages with Ray B. Munroe, who is sadly no longer with us. He was a supporter of my use of 7-sphere, but he also saw things from the particle physics perspective and I had to explain my foundational perspective to him from scratch. Please allow me to do the same here,...
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Hi Michael,
You have framed your question very clearly. It reminds me of some passionate discussions I had last year on these pages with Ray B. Munroe, who is sadly no longer with us. He was a supporter of my use of 7-sphere, but he also saw things from the particle physics perspective and I had to explain my foundational perspective to him from scratch. Please allow me to do the same here, if not for you, at least for other readers who might to be interested.
The issue at heart is local causality. This concept has been crystallized by various people over the years, starting with Einstein in his special relativity, and culminating in Bell's analysis of the EPR scenario. Bell used some earlier ideas of von Neumann to frame the concept for any realistic theory, and made it independent of any specific theory of physics, including quantum theory or quantum field theory, and independent even of the specifics of special and general relativities. He thus provided a very general, very reasonable classical, local-realistic framework, which does not depend on the specifics of a given set of observables. It depends only on the yes/no questions the experimentalists may ask and answer. Thus, for example, for the classic EPR-Bohm scenario involving a joint observable AB for observing spin up and spin down at two remote ends of the experiment, he formulated local causality in terms of the following factorizability condition:
AB(a, b, L) = A(a, L) x B(b, L),
where A(a, L) is independent of the remote context b as well as the remote result B, and likewise B(b, L) is independent of the remote context a as well as the remote result A. That is it. As you can see, his formulation of local causality only involves the measurement results A = yes/no and B = yes/no, apart from the measurement contexts a and b (such as the directions of the local polarizers), and the common cause L, which is the "hidden" variable or a complete EPR state.
It should now be clear why the kind of details you have spelt out for more general scenarios involving particle productions etc are irrelevant for the central concerns of local causality. All that matters is how the yes/no answers to relevant questions are correlated, because any experiment in physics can always be reduced to a series of questions that can be answered in a "yes" or "no."
Nevertheless, let us look at things from your perspective. Let us consider a scenario where an EPR 2-particle state is not of the form P^|P_ (in a variant of your notation) but of the form P^|Q _, where Q =/= P. For you, then, there are two sets of observables with quantum correlations, {^,_} and {P,Q,...}, where the first set contains eigenvalues of the rotation group S3, and the second set contains eigenvalues of SU(4)/SU(3) ~ S7. The question then is: Is Bell's local-realistic analysis applicable to this situation? Yes, absolutely. Is my topological correction to Bell's analysis applicable to this situation? Again, yes, absolutely.
But here is a difficulty for you: Your set {^, _} is restricted to S3. It is, however, not possible in general to reproduce quantum correlations using my framework within S3 if the corresponding quantum systems have the spectrum of eigenvalues (or measurement results) more general than that of a 2-level system. So, ironically, there is no problem for the exotic set {P,Q,...}, for which the "group space" within your framework is S7, which is the most general available within my framework. It is the set {^, _} that will cause a locality problem for you, because, for a general quantum field, the spectrum of eigenvalues within {^, _} would be highly nontrivial. Within my framework, on the other hand, both {P,Q,...} and {^, _} fall under the same "group space" S7, and so there is no problem.
So my framework does put the following constraint on the observables: If one restricts to the group space S3, then the only quantum systems for which local causality can be maintained are the 2-level systems. For more general systems S7 is inevitable.
Best,
Joy
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Joy Christian replied on Aug. 9, 2012 @ 20:10 GMT
That was me above. I must have logged out.
Joy
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Eckard Blumschein replied on Aug. 10, 2012 @ 11:42 GMT
Dear Michael James Goodband,
I see a wide gap between you, Joy Christan, Thomas Ray, Lawrence Crowell and others on one hand and likewise qualified experts like Alain Kadin who do not restrict to a mathematical approach on the other hand. Edwin Eugene Klingman seem to be almost the only one who is anchored in both areas.
May I hope for your readiness to seriously deal with and even eventually accept interdisciplinary arguments and for your efforts to present your most important arguments as easily understandable as possible to those who are laymen in your branch of modern mathematics?
While I dislike the concept of transfinite cardinality, I agree on that the rational numbers are as countable as are the natural ones. They are said to have the same cardinality aleph_0. So it's amazing to me that the difference between them is as important as you are claiming.
You wrote: "the particle/anti-particle space being S^0={-1,1} and the space of cyclic waves being S^1". Did you discuss this with Kadin and Klingman?
I anticipate that you feel hurt by many statements in my essay. May I ask you for on open discussion before prejudice. My position roughly corresponds to that by Detlef D. Spalt who only published in German with one exception (La Continu de l'Analyse Classique dans la Perspective du Résultatisme et du Genésiologisme) and is perhaps unknown to you.
Regards,
Eckard
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T H Ray replied on Aug. 10, 2012 @ 12:23 GMT
" ... the particle/anti-particle space being S^0={-1,1} and the space of cyclic waves being S^1". Did you discuss this with Kadin and Klingman?"
Eckard, that's a very straightforward statement. The 1-dimension S^0 (which Bell-Aspect take as the measure space {-1, + 1} or {- oo, + oo} ) does not have enough degrees of freedom to accommodate the wave function. Joy recognized the contradiction here, because quantum mechanics cannot survive without a wave function -- and so assigns the function a probabilistic interpretation in the Hilbert space, dragging the notion of nonlocality along. No matter how many ways one slices it, the standard intepretation of quantum mechanics is not coherent without nonlocality.
By changing to a topological framework, nonlocality is obviated.
Tom
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Author Michael James Goodband replied on Aug. 10, 2012 @ 13:20 GMT
Hi Joy,
Thanks. I was getting the impression that the functional spaces of your analysis wasn't going to match up with the group spaces and particle symmetry spaces of particle physics. Although such a functional analysis appears non-contextual, the particle physics perspective spots that local causation over observables has the context of special relativity (SR). This brings with it features that look like they should be more than just coincidence, as the spinor representation of the Poincare group of SR is SU(2)*SU(2) where the group space of SU(2) is S3, and the spin eigenvalues form an S0 space. This structure is linked to local causation of fermionic objects in SR, and so forms the particle physics context for the analysis of correlations between observables. From the particle physics side, it is very hard to get past the idea that this isn't of significance - even if it really is irrelevant!
Best,
Michael
Joy Christian replied on Aug. 10, 2012 @ 15:24 GMT
Hi Michael,
If I understand your comments correctly, here is what I think is your worry:
What I have dealt with in my work is the issue of no-signalling non-locality of the orthodox quantum theory. I have used Bell's local-realistic framework which carefully separates this type of non-locality out from a possible signalling non-locality that would actually violate special-relativistic causality (as is well known, no-signalling non-locality does not). My analysis deals with both types of non-localities in a clear-cut manner, at least at a formal level. However, since I am using functional spaces like S3 and S7 in the context that is unusual from the particle physics perspective, it is unclear whether this would not lead to some signalling-type causality violations when my framework is eventually turned into a proper theory.
This is a justified concern. Eventually my framework will have to be properly relativized, or at least made compatible with some representation of the Poincare group. Fortunately there exists a mathematical framework for doing this. It is an extension of the algebra I have used in my work, known as the Spacetime Algebra. At the moment, however, relativizing my framework is not my primary concern. All I can say at the moment is that I think it can be done. We shall see.
Best,
Joy
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Author Michael James Goodband wrote on Aug. 8, 2012 @ 17:06 GMT
Joy (Part 2),
There is a critical dividing line between your work and mine which doesn't seem to have been fully appreciated yet: essentially my extended GR is on the physically-real side and your work is on the non-physically-real side - as in QT. Although the physically-real side of extended GR is consistent I prove that it is incomplete because the calculation of the mass reduction of the topological monopoles as Planck scale rotating black holes is subject to Gödel's incompleteness theorem. This both means that the reduced masses of the particle-like objects cannot be calculated from classical physics, and that the self-consistent dynamic state of the particle-like objects can possess a non-derivable feature.
Assuming that this feature is a wave property, Gödel's proof can be circumvented by changing from physically-real terms denoting the countable number of particles at specific points in space, to non-physically-real terms denoting them as real-number valued fields spread throughout space with a wave property, ie. a wave function. The mathematical conditions of Gödel's proof can then be used to prove no hidden variable theory and the mathematical conversion from wave function to particle number cannot be derived in classical physics - hence has 'weird' descriptions like 'collapse of the wave-function' which make little physical sense.
However, in the switch in integrals from physically-real terms to the non-physically-real term of the wave function there is a critical flatness condition. The problematic expansion is about a black hole, and the event horizon and ergo-region *cannot* be denoted by a continuous field term in space, so the replacement which derives QFT *only* holds in flat space away from the black hole. This firstly means that QFT *cannot* be unified with GR. But there is a further problem with this approximation of QFT, in that it excludes the ergo-region with its sign reversal of the metric term gtt that allows apparently non-local causation to make sense in physical causation terms. In an approximation that excludes this ergo-region, you *are* going to have a causation issue. The purpose of the representational change to the non-physically-real wave function and QT is to get a consistent and complete theory, but the represenational replacement doesn't even consider this causation issue.
It would seem that my flat space condition on the representational replacement was just the beginning of the 'flattening' required to get QT fully consistent and complete. There is going to have to be some condition in QT to resolve this causation issue, but I currently don't understand the parallelization of S0, S1,S3 and S7 well enough to understand how it does it.
Best,
Michael
T H Ray replied on Aug. 8, 2012 @ 18:15 GMT
Michael,
Quick reply, while I am still digesting ...
Truncate your theory to the S^7 limit, and I think you will find that Joy's framework satisifies both the completeness criterion for a physical theory (as described by EPR) and Godel completeness.
Tom
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Steve Dufourny replied on Aug. 9, 2012 @ 10:00 GMT
Hello,
I am surprised that several "said" responsible scientists are so irrational in their superimposings.probably it is due to a lack of generality, I don't know, or the bad strategies simply.In all case, I am surprised by this comportment. But Like I love Jesus Christ and Buddah , I pardon you all. I am understanding your strategy after all.It is simply logic your comportment.I know this Good team band. And I accept. I continue, I persevere like a real searcher. Like a real generalist, a real universalit. I just show you what are my sciences, in fact I am happy to give courses to these strategists.In fact it exists the true and the false. I pray for them in fact.I pray in a pure spherical universality. I am going dear friends to go at new York, I will put an ocean of flowers and plants in this town.It is the country of the freedom. I will go !
Soon furthermore.and REVOLUTION SPHERIZATION WITH SCIENCES AND UNIVERSAL CONSCIOUSNESS.
Spherically yours.
ps to the Institute of Advanced Studies....be rational and respect the real generalists please.Don't make films in your heads but simply respect me.Change of strategy.
Regards
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Steve Dufourny replied on Aug. 9, 2012 @ 10:07 GMT
or probably that they confound what is the good equations and the general equations.Or perhaps that they show simply an ocean of words for the confusions and their own knowledges showed in live.Or it is just for this monney also.Or this or that.
In all case, I know this team and why they make that. Simply the hate probably.
I pray for their souls. They need help in fact. Furthermore you imagine their credibility if I am recognized.I understand their strategy and their fear.Probably that they are going to discuss between a kind of team band for a kind of pseudo politeness.Probably also that they think that they understand the maths of de sitter and riemann or ....but do they understand the maths of Dufourny.I doubt.
spherically yours
Regards
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Steve Dufourny replied on Aug. 9, 2012 @ 13:51 GMT
A few number of persons understand really the uncompleteness of Godel.If now people thinks that they have understood just because they make politeness between them.So indeed there is a probelm.
And the rule of the Institute of Advanced Studies is to be rational and deterministic. This Institute cannot be corrupted. and cannot be irrational.
Furthermore, the responsability of an institute like this one cannot imply confusions.
The axiom of dimensionality is not accepted at my knowledge. So why they insist ??? For the sell of books or what ?
the incompleteness of Godel shows us how we can axiomatize our foundamentals. It is like the hidden variables in fact. We cannot confound the young evolution of our universal sphere, and so our unknowns.With bizare irrational superimposings where our universal laws loose their meaning. I don't understand why people interpret the incompleteness like that. It is sad in fact. We are just young at the universal scale.And so it is logic to have unknowns, but they are rational these hidden variables,not need of extradimensions. The axiom of dimensions is not a reality, only the 3D is rational and this time constant of evolution. The geometrical algebras are not there to imply confusions, but are there to improve our equations with determinism. The beauty of sciences is to discover the truths, not to imply confusions by pseudo parallelizations. The walls separating this infinite light without rotations above our physicality, and the light inside a sphere in evolution. The central spheres are the secret of codes of singularities. The informations can only be transmitted by this infinity inside the main central spheres of systems of uniqueness. Why so the people wants to invent false hidden varibales. It is the road towards our main codes, these central spheres which are important. The "infinite" light creates the "finite" light !!! all is connected by this light indeed , but the real interEst is to understand the physical dynamic in taking it like a project of optimization. Why hidden variables or bizare decoherences ???? The universe is a dterministic spacetime. Godel and Cantor are in a bar, do you think that they think that the glass of beer is an infinite system or a pure number entangled spheres.In the same time, they can add, derivate or integrate, or multiplicate these numbers.....so is it infinite, or is it relativistic in the meaning of this infinity and the infinities and the finite groups ??? all possesse a specific number of spheres, finite and precise !!!! the volumes of this entanglement in the pure serie of uniqueness so imply several interesting road considering my equations and the velocities of rotations and their sense of rot. differenciating the bosons and the fermions. IF THE NUMBER DOES NOT CHANGE FOR THE SERIES OF UNIQUENESS so we can see the quantization more the evolution by polarity between hv and m.
Regards
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Steve Dufourny replied on Aug. 17, 2012 @ 12:34 GMT
their heart is not even sincere and pure.
this world does not turn correctly just due to these persons of bad.In fact we see only with our heart, the essential is invisible for eyes....don't lie about my faith.you do not even imagine my universal faith. I love Jesus Christ ok.
A real bad band in fact you are .like what , the habit does not make the monk.
You can lie for several but not for the real universalists understanding the sciences and its determinism, pure and simple.
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Steve Dufourny replied on Aug. 17, 2012 @ 19:13 GMT
you do not imrpove and your mathematical language is weak !
The team is knew since the begining. ahahah until soon at New york or pay people to kill me.
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Vladimir F. Tamari wrote on Aug. 9, 2012 @ 01:53 GMT
Hello Dr. Goodband
You plainly seem to have taken the bull by the horns, but with my limited technical knowledge I could follow some (but not all) of the skilful action and wish you good luck in finishing off the Quantum Bull and do a great favor to physics.
In
my fqxi essay Fix Physics! and my earlier
Beautiful Universe Theory (BU). I have tried to trace the steps by which modern physics went 'wrong' with suggestions on how it may be revamped. One major cause is the false particle-wave duality concept: It is not individual electrons or photons that show up as dots in a double-slit image-field - just sensor atoms reaching saturation point. Eric Reiter independently reached (and experimentally proved) the same idea. His fqxi essay shows how the point photon concept is simply wrong. With the fall of the point photon the probability interpretation as a physical 'fact' and much puzzlement in QM falls by the side.
You speak of a "finite physical network that is potentially infinite in theory, this situation could only arise in the context of an infinite network expansion about some object." This is very much like the node lattice of my (BU) theory. Indeed the 5th dimension of Kaluza-Klein has been somewhere interpreted as nodes of such an ether lattice.
Despite the mostly qualitative nature of my work, I would be honoured if you can read and comment on it.
Best wishes,
Vladimir Tamari
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Thomas Howard Ray wrote on Aug. 9, 2012 @ 14:25 GMT
Michael, I am impressed with your work to the extent that I tried to order your book from Amazon U.K. through you directly (Amazon is out of stock) and the order was rejected with a message that it can't be sent to my U.S. address. What gives? -- are you only allowed to sell your own book in the U.K.? :-) Please send an ordering link to my Email, thomasray1209@comcast.net and I guarantee you a sale, if the shipping cost isn't prohibitive. Otherwise, any chance of Amazon U.S. making it available?
Meantime, on the question of scientific realism, I too have looked at Joy Christian's framework with that question in mind. Rather than applying the Godel incompleteness theorem to the broad set of scientific theories which incorporate physically real terms (which would naively include the theoretical components of Joy's framework, i.e., the prediction of physically real quantum correlations) -- I find that mathematical completeness, as Joy describes, which meets the EPR criterion (every element of the mathematical theory corresponds to every element of the physical measure) also satisfies Godel completeness. I am willing to engage on this issue.
I think it is important to understand that Joy's framework is noncontextual, and not merely an interpretation of observed quantum mechanical phenomena. His logical judgment on the state of quantum correlations is completely closed, exactly as the mathematically complete judgments of relativity in the classical domain. Christian's research, by taking a global (topological) approach to local realism, breaks down the distinction between local and global and prescribes an exact limit to the range of observables, just as relativity does ("all physics is local"), though in an extended universal domain unrestricted by classical mechanics.
As a result, I find that Joy Christian meets Karl Popper's criteria for metaphysical realism (*Realism and the Aim of Science,* Routledge 1983). In turn, I think that your own variety of realism is satisfied, and that Joy Christian's result lies outside the set of constructs that would be subject to Godel incompleteness.
All best,
Tom
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Author Michael James Goodband replied on Aug. 10, 2012 @ 13:01 GMT
Thanks Tom. I'm still having problems with Amazon not displaying the correct stock and shipping settings. Just in case it takes a while, I'm setting up the option of making Agent Physics available from my website http://www.mjgoodband.co.uk at the same shipping rates as Amazon. This may take a day or two (will update). In the meantime there's more about Agent Physics on...
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Thanks Tom. I'm still having problems with Amazon not displaying the correct stock and shipping settings. Just in case it takes a while, I'm setting up the option of making Agent Physics available from my website http://www.mjgoodband.co.uk at the same shipping rates as Amazon. This may take a day or two (will update). In the meantime there's more about Agent Physics on http://www.agentphysics.org
I think your comments pointing out that Christian's framework "breaks down the distinction between local and global ... in an extended universal domain unrestricted by classical mechanics" points at the core of the issue. In conceptual terms, I see Joy's analysis in terms of initial and final conditions about observations and what correlations there can be between them. However, one of the consequences of transcending classical mechanics is that there is inevitably no discussion of dynamics, and so there is no discussion of *how* these conditions are met. I note that terms like 'entanglement' are implicitly about dynamics.
The point about Gödel's incompleteness theorem is strictly in his original context, where the local-global structure issue appears to arise in terms of discrete and continuous valued arithmetic systems. The collection of statements expressed within some system of integer arithmetic could be viewed as a linked network of nodes spread out in a space, where the links are steps of logical deduction. In conceptual terms, Gödel proved that the discrete character of integer arithmetic is such that there can exist closed loops of nodes in this network which are stated in the same terms as the axioms of the mathematical system, but cannot be reached from the axioms. However, Gödel's proof is explicitly dependent upon the discrete character of numbers *and* number-theoretic functions over the integers. Switch from discrete integers to the continuous reals and Gödel's incompleteness proof no longer holds in this context, almost certainly because of the far richer structure of functions over the reals. This could be viewed in terms of the 'global' structure of functions over the reals being richer than the 'local' structure of functions over the integers, such that the 'global' case doesn't suffer the incompleteness of the 'local'. Conceptually this is because it can fill in the gaps between the discrete nodes of the network in the integer case. This switch from discrete terms counting the numbers of objects in classical physics to continuous real-number description of the same objects in a scientific theory in order to escape the 'local' restriction of Gödel's incompleteness is a far more generic point in science that applies beyond particle physics, as is discussed in http://www.mjgoodband.co.uk/papers/Godel-science-theory.pdf (http://vixra.org/abs/1208.0010).
In general conceptual terms, I see Joy's functional analysis showing that 'global' functional structure can account for observable correlations in a way that 'local' functional structure cannot. But this still leaves the question, where's the physics? By this we generally mean the dynamics, which means locally tracking the causation as we do in classical mechanics. I show that the above switch from discrete terms to continuous terms gives all the features of Quantum Theory. However, a consequence of this switch appears to be that the underlying 'global' functional structure appears as non-local identity in the dynamics of the quantum field terms (wave-function). The descriptive issues of QT appear to arise in resolving the underlying 'global' functional structure back to the 'local' terms of strictly countable discrete particles.
The philosophical point is that realism in terms of observational predictions is retained, but at the expense of the descriptive realism of the dynamics being compromised.
Best,
Michael
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T H Ray replied on Aug. 10, 2012 @ 15:15 GMT
Dang it -- I messed up cutting and pasting. I will repost correctly here, and hope I can get the last version deleted. Sorry.
Michael,
I am so grateful -- as I expect Joy is as well -- to be able to have meaningful dialogue on the real issues. For so long, and for Joy many years longer than I, we've been forced to respond to straw man arguments. Very debilitating and...
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Dang it -- I messed up cutting and pasting. I will repost correctly here, and hope I can get the last version deleted. Sorry.
Michael,
I am so grateful -- as I expect Joy is as well -- to be able to have meaningful dialogue on the real issues. For so long, and for Joy many years longer than I, we've been forced to respond to straw man arguments. Very debilitating and demoralizing.
One of those persistent straw men describes Joy's model as algebraic (though one has to be innocent of what "geometric algebra" really means, to think that way), when of course a topological framework can't be other than analytical. The detractor then proceeds to identify a nonexistent "algebraic error" and dismiss the whole argument.
Anyway:
I think it fruitful to approach the subject the way you're doing, because the issues do go deep into FOM as well as physics -- and actually, as you imply, have to do so -- in order to reconcile local discrete measures with globally continuous functions.
Key to the structure is orientability, that only a topological model can supply. I really only became aware of this about a year ago -- when I read a 30 year old unpublished paper by the eminent computer scientist
Leslie Lamport titled "Buridan's Principle." His analysis of the Stern-Gerlach apparatus convinced me that the principle ("A discrete decision based upon an input having a continuous range of values cannot be made within a bounded length of time") really does generalize, as a physical law, to all measurement functions continuous from an initial condition. I suggested to him that the paper really needed to be published, and fortunately, the medium I suggested -- Foundations of Physics -- accepted and published it in the April 2012 issue.
I've filled 3 notebooks with arguments and equations in the last year and half, and I'm itching to get it into publishable form -- back in 2 March I wrote " ... the continuous range of measurement results are recorded -- not on unit S^0 as Bell assumed by the functions A(a,l) = + 1 or - 1, but on S^1, a unit 2-sphere. As Joy Christian explains, 'After all, no one has ever observed a 'click' in an experiment other than about some experimental direction a. With this simple change in the function A now takes on values in a topological 2-sphere, not the real line, thereby correctly representing the EPR elements of reality. The values of the spin components are still + 1 or - 1, but they now reside on the surface of a unit ball.'" Orientability matters. It matters, though, over the whole range of parallelizable spheres, which are simply connected and therefore accommodate the flatness condition.
Like you, I have tended to translate Joy's research into my own familiar terms of complex analysis, information theory and number theory. I have tried not to do that, though without complete success. In any case, we bump up against your conclusion: "The philosophical point is that realism in terms of observational predictions is retained, but at the expense of the descriptive realism of the dynamics being compromised." And that is why, as I think you'll see is obvious, that I apply the criterion of Godel completeness rather than the incompleteness theorem. It meets Popper falsifiability, in the context of Tarski correspondence theory of truth, and it satisfies metaphysical realism. In other words, we recover the dynamics in a continuous function model of argument and value -- I characterize Joy's correlation result, E(a,b) = - a.b as the input argument to a continuous range of values, which generalize Buridan's Principle to the topological limit.
I hope you get a chance to visit my essay site, where some of these same issues are discussed in a different way.
All best,
Tom
(P.S. I trust that you got my email reply with my mailing address. Looking forward to reading your book!)
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T H Ray replied on Aug. 10, 2012 @ 15:21 GMT
Fixing the link (hopefully):
Leslie Lamport http://research.microsoft.com/enus/um/people/lamport/pubs/pu
bs.html#buridan
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Joy Christian replied on Aug. 10, 2012 @ 16:50 GMT
Hi Michael,
You have raised a key question: "...where's the physics? By this we generally mean the dynamics, which means locally tracking the causation as we do in classical mechanics."
You have correctly recognized that my framework is entirely kinematical as it stands. A fully local-realistic theory based on it would inevitably have to postulate dynamics, and this dynamics must match with that of quantum theory (if not quantum gravity). My latest mini-grant from FQXi is precisely for investigating this issue of dynamics. I have some preliminary ideas about this, but I am not yet ready to discuss them in public.
Best,
Joy
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Author Michael James Goodband wrote on Aug. 13, 2012 @ 14:07 GMT
Hi Joy and Tom,
I too am grateful to you for engaging in meaningful discussion. I was previously unaware of Joy's work (and Buridan's principle ) and your comments have advanced my thinking to the point where I am certain that the key issue really is a mathematics description problem in trying "to reconcile local discrete measures with globally continuous functions".
In the spirit...
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Hi Joy and Tom,
I too am grateful to you for engaging in meaningful discussion. I was previously unaware of Joy's work (and Buridan's principle ) and your comments have advanced my thinking to the point where I am certain that the key issue really is a mathematics description problem in trying "to reconcile local discrete measures with globally continuous functions".
In the spirit of the essay contest of questioning assumptions, I realised I have been making an assumption about Joy's work. This is partly because the initial point of comparison was the dependence on the 4 spheres S0, S1, S3, S7. In my case, these are physical spaces in a classical metric field theory where the Relativity meta-principle - make no preference - selects them all, and the unification principle gives only one possible unification which yields these spaces (
STUFT). The fact that the dimensionally reduced version of this KKT derives the Standard Model Lagrangian with the correct electroweak vacuum (and Weinberg angle) and spectrum of 12 fermionic particle-like objects in classical physics is a nice feature (and the coupling constants, including the Higgs scalar coupling which predicted the classical Higgs boson mass to be 123GeV). Then comes the *real issue*, what is Quantum Theory all about?
I think this is the real point of comparison of my work (primarily in Agent Physics but also as presented in
Science Theories) with Joy's, where the QT context for Bell's analysis has distracted me from Joy's functional analysis of hidden variable theories being more general than *just* QT. Bell's analysis started from the existence of QT and asked whether there exist a hidden variable theory that can account for the same correlations between observables as QT. However, a functional analysis whose only conditions are local causation and correlations between observables can surely be applied to any assumption of a hidden variable theory in science (ie. without the pre-condition that is replacing QT)?
The reason for considering this possibility is that my physics-based analysis of numerous physical systems identifies a recurring feature of a self-consistent (causally closed) dynamic state residing on the giant connected component of some physical network. Any physically-real theory of these systems can be proven to be incomplete because of the discrete character of the dynamics of the network - this specifically includes the classical physics of particles, as in my essay. It seems to only make sense for the possible undecidable proposition in the physically-real theory to describe a collective property of the dynamic state residing on the giant connected component. This can potentially give a description problem in physically-real terms, because the inputs to the network cause discrete changes to propagate through the giant network component, with its undecidable feature, to the outputs. Encountering a network state with undecidable properties would surely have some effect on the outputs, such as altering the correlations between the outputs observed?
Joy's functional analysis of correlations between observables in a non-relativistic context would seem to be wholly appropriate to this situation. The combination of my work and Joy's functional analysis leads me to the proposition: the presence of the undecidable property on the core network component causes correlations between the network outputs that cannot be accounted for in a discrete theory in physically-real terms. Assuming that the correlations can be accounted for if only we knew some extra missing terms constitutes an assumption of a hidden variable theory. The follow on from the above proposition is that the richer functional structure of continuous functions can account for the correlations in output, where such terms do not directly correspond to the inherently discrete physical components of the network system and so are non-physically-real terms (like the wave-function of QT).
Extending the functional analysis to this scenario could potentially provide a mathematical proof (or disproof) of my proposition that the presence of an undecidable feature on a discrete network system is the *cause* of the correlations that cannot be accounted for by a discrete hidden variable theory. I show that the required network conditions can occur in biology, psychology and economics ... with the prediction following on from this proposition that there will exist correlations between observables in these system which cannot be accounted for by a physically-real scientific theory. These disciplines implicitly make the assumption that there will exist a hidden variable theory that will account for all experimental observations. It seems to me that Joy's work provides the basis for the construction of experimental tests of these assumptions throughout science.
Best
Michael
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Anonymous wrote on Aug. 15, 2012 @ 16:56 GMT
Dear Michael:
The conclusion of your paper that QM is not a fundamental theory is vindicated in my paper – “
From Absurd to Elegant Universe”. My paper also provides evidence to what is fundamental universal reality and how to explain the inner workings of quantum mechanics (including wave-particle duality) and resolve its paradoxes.
I would greatly appreciate your comments on my paper.
Best of Luck & Regards
Avtar Singh
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Anonymous wrote on Aug. 15, 2012 @ 16:59 GMT
CORRECTION - Reposting the above under my name:
Dear Michael:
The conclusion of your paper that QM is not a fundamental theory is vindicated in my paper – “
From Absurd to Elegant Universe”. My paper also provides evidence to what is fundamental universal reality and how to explain the inner workings of quantum mechanics (including wave-particle duality) and resolve its paradoxes.
I would greatly appreciate your comments on my paper.
Best of Luck & Regards
Avtar Singh
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Avtar Singh replied on Aug. 15, 2012 @ 17:03 GMT
Sorry - my LOGIN did not work. Please post your comments on my paper under my posted paper “
From Absurd to Elegant Universe”.
Thanks
Avtar Singh
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Jonathan J. Dickau wrote on Aug. 23, 2012 @ 05:29 GMT
Hello Michael,
I greatly enjoyed reading your essay, and I find myself almost completely in agreement with your thesis. Well done! Edwin Eugene had made a recommendation a while back, but then when I read your comments on Vladimir's essay page, I knew I had to find time to read your essay immediately.
You have put some of the pieces together nicely. I like your STUFT theory rather well. And it further explains some of what I found interesting and intriguing in Joy Christian's work.
Like Tom Ray, I've got notebooks full of ideas after finding inspiration there. I like your response to Tom's comments, regarding global and local functional structure, though, and your comments to Joy above resonate with me also. I guess it is a matter of perspective or emphasis, in some measure, depending on what you are trying to show.
I have much to learn, but I expect I'll find some interesting insights in the comments on this page. I've had an interest in related topics for some time, and you will find mention thereof in my essay "
Cherished Assumptions and the Progress of Physics."
But for now, I must sleep.
all the best,
Jonathan
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Jonathan J. Dickau wrote on Aug. 23, 2012 @ 20:49 GMT
Hello again Michael,
I have given considerable thought to what is implied by living inside a 3-sphere, what is seen by folks who reside inside a set of 'compact' dimensions, and so on. We might not notice. Size is relative, not absolute, and interiority/exteriority may be too, if we entertain higher order dimensions where geometry may be non-commutative or even non-associative.
That was part of what I was getting at, in my essay, when I was talking about the universe being inside out of the way we perceive it. We think we are pointing to an edge, or a spot on the universe's periphery, and yet we point at the center.
However; when we think we are pointing directly at the center of the planet, we are only getting the Schwarzschild radius away. This I see as related to the interlocking keyring example used to depict Hopf fibrations of S3. The actual center of the Earth is behind the event horizon, induced by the parallelization of the fiber bundle, it would seem.
My guess is the reason we don't 'see' space as octonionic, but appear to be inside the quaternionic space of S3 relates to the decoupling of matter and energy - which sets a time and distance scale for the universe, as a whole. More later in another missive.
Regards,
Jonathan
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Steve Dufourny replied on Aug. 26, 2012 @ 21:37 GMT
and you insist furthermore with your friends, how can you make this ? just for this papper and your hate and your vanity. You think what my friend ? That your faith is more than mine or what ? let me laugh, never I have crushed even an insect. You are not a scientist , it is not possible, and your firends also are not scizentists, it is not possible. In fact , you are just a team of vanitious false scientists.
Your maths are so ironical, I ask me even where you have studied our mathjs you and your friends.Frankly, I really suggest that you buy better books of maths. If you made a correct mathemtical improvement ok, but no, you are weak in fact.I just see an ocean of stupidities.In fact your maths and your team do not arrive even at 5 per cent of my works.
Ironical. Irritating that I arrive at New York soon no? you must become murders or pay people or invent an other strategy, because there, we are going to laugh you know. You know it also in fact :) isn't it ? probably that your hormons are touched , you and your friends, logic for the weak scientists. Even in team and even with your tools and your dtrategy, I continue all days to teach you my theory of spherization.:) I am not arrogant, it is god who said me that.He said me also, pay attention Steve, my son, the human nature is sometimes very bad. I know Father ! I continue just in praying and in showing them what is a real universal heart.
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Author Michael James Goodband replied on Sep. 3, 2012 @ 16:48 GMT
Hi Jonathan
The way I visualise compact dimensions and why we don't notice them, is that we are spanning them in the same way that our shoulders span a narrow corridor. After a while moving backwards and forwards in such a corridor, you could stop regarding going left and right as constituting a dimension at all! For a closed universe, an analogy would be the experience of a single celled organism living *within* the water film of a soap bubble - it could only move in 2D within the film of the bubble and would have no experience of the 'extra' third dimension because the cell spanned it.
In a KK theory with compact dimensions, a particle spans these dimensions and experiences changes in the relative orientation of the compact dimensions at different points in space as particle forces. Moving in the direction of these compact dimensions effectively amounts to rotating on the spot - like a hamster going around its wheel and going nowhere - such rotations are the origin of gauge rotations in the dimensionally reduced theory. A consequence of compact dimensions in STUFT is that they provide the 'measuring rod' for all measurements, up to and including the measurement of their own scale. So even if the scale of these dimensions changed, their measured scale in terms of themselves would remain the same - apparently 'constant'.
Michael
Jonathan J. Dickau wrote on Aug. 23, 2012 @ 21:33 GMT
Michael,
I forgot to mention that is does appear that you have successfully sketched out how Quantum Mechanics could be an emergent theory, rather than fundamental. Since that is the question you ask in your title, I thought I should let you know that it looks like you have indeed proved feasibility for your topological solution, and made significant progress toward a robust formulation.
Regards,
Jonathan
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Author Michael James Goodband replied on Sep. 3, 2012 @ 16:52 GMT
Hi Jonathan
Thank you for that acknowledgement of my essay showing how QT can arise as an emergent theory, you are the first to do so.
It is perhaps not as clear as it could have been, but I had to compress it to fit the word count so that I could put in the follow-up consequence of QT not being fundamental. Which is that physics unification must then be sought in classical physics, and to unify with GR this would seem to imply extending GR with extra dimensions, and there is only one way that adds up in terms of particles as topological defects, the Higgs field and coupling constants - STUFT - which is uniquely defined in terms of the 4 special manifolds S0, S1, S3, S7 and the Relativity meta-principle of 'make no preference'. Without the constraint of QT *having* to be fundamental, STUFT is uniquely the only purely geometrical theory giving the correct charge spectrum of 12 (and only 12) topological monopoles as fermionic particles.
Another dramatic consequence of this emergent QT proof, is that a similar pattern can systematically occur elsewhere in science under certain conditions - I use these conditions to define the domain of Agent Physics. A general science perspective of the extension of this emergence proof throughout science in given
hereRegards
Michael
Thomas Howard Ray wrote on Aug. 27, 2012 @ 13:27 GMT
Hello Michael,
I am looking forward to settling down with your book (have been traveling and have not been in a position to do so yet). I can already see, however, that it deserves slow and careful reading. Skimming through gives me the impression that the material is quite suitable for at least a 1-semester course ... I hope that you or another instructor can make that happen somewhere, in a physics or philosophy of science curriculum.
It's especially important, I think, that you emphasize both in the book and in your essay that inductive judgments (such as found in the standard interpretations of QM) cannot be logically closed. We seem to have gotten so far away from the fundamental tenets of scientific rationalism and mathematical completeness -- even I, who am quite familiar with the results of Godel and the philosophies of Popper and Tarski, did not immediately recognize that Bell's choice of measurement domain (S^0) obviates completeness. I only grew to understand the significance by following Joy's argument (reinforced now, by yours). So I do appreciate the breadth of applications of your program across a wide spectrum of disciplines and subdisciplines in physics, the foundations of mathematics, and the foundations of the philosophy of science.
All best,
Tom
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Steve Dufourny replied on Aug. 27, 2012 @ 14:10 GMT
yes of course TH, of course of course and evidently also .
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Joy Christian replied on Aug. 29, 2012 @ 05:29 GMT
Tom,
Not only "Bell's choice of measurement domain (S^0) obviates completeness" as you put it, but his choice is both a physical and a mathematical non-starter. His measurement functions A(a, L) do not (and cannot) satisfy the completeness criterion of EPR, unless their co-domain is chosen to be a unit parallelized 3-sphere (S^3). For no other choice of the co-domain (in the standard EPR-Bohm case) can Bell's local-realistic prescription A(a, L) for the measurement functions can be EPR-complete. For example, even a round 3-sphere will not do, let alone any other non-compact choice (such as the real line R). Thus Bell's argument is simply a non-starter---a scandal of epic proportions.
Joy
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T H Ray replied on Aug. 29, 2012 @ 17:15 GMT
Joy,
I'm getting it. :-) New post in my forum on the arithmetic issue.
Tom
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Steve Dufourny replied on Aug. 31, 2012 @ 17:56 GMT
and still the same ironical strategy. oh they are strong, wawww impressing.
I see an ocean of hate, an ocean of confusions and an ocean of irrationalities.
If Mr Witten wants, we can discuss about realistic convergences.
Tom you are really lamentable in fact, you act like a puppet obliged to continue his strategy like a poor frustrated full of hate. It is logic that we do not see real works, if you and your friends you loose your time with the play and the strategies. in fact I have pity in a pure universal point of vue with humility of course.
A real christian respects his fellowman when he is sincre and entire.The rest is vain. The pseudos shall fall down naturally as is rational the natural sciences.
ps hello to edwin, James,Jcn,Jonathan, Georgina, Mickael, Ted,Florin, Christi,Don,Tom,George,Joe,Joy,zebitsad,Lawrence,.....good band indeed.
ironical is a weak word.
Spherically yours
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Rick Lockyer wrote on Sep. 3, 2012 @ 15:16 GMT
Hello Michael,
I liked your essay very much. You have informed insight into areas of physics that I feel are quite important.
Joy Christian mentioned my work in one of his responses to you. You can get a good overview of my ideas by reading my essay
The Algebra of Everything. Your work is steeped in General Relativity, but perhaps what might be called Octonion Relativity might better connect up with your Octonion component. You will find this in my essay.
I am very interested in your opinion, especially on the Hadamard structure that is prevalent within the structure of Octonion Algebra. If you could weigh in on my blog, I would be in your debt.
Regards,
Rick
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Alan Kadin wrote on Sep. 4, 2012 @ 12:16 GMT
Dr. Goodband:
Your question about whether quantum mechanics is fundamental is a good one. But implicit in your question is the assumption that QM should be interpreted as a universal theory of all matter. On the contrary, I would suggest QM is rather a mechanism for generating localized particle properties from primary continuous fields (electrons, photons, quarks), where these localized (but not point) particles then follow classical trajectories (as derived from the quantum equations). (Please see my essay "The Rise and Fall of Wave-Particle Duality", http://fqxi.org/community/forum/topic/1296.) Composites such as nucleons and atoms are localized objects WITHOUT wave properties of their own. Beams of neutrons or atoms do not require de Broglie waves for quantum diffraction from a crystal lattice, which instead reflects quantized momentum transfer between the beam particle and the crystal. Remarkably, this reinvisioned quantum picture is logically consistent and avoids quantum paradoxes. Even more remarkably, this interpretation seems to be virtually new in the history of quantum theory, although it could have been proposed right at the beginning. The FQXi contest would seem to be an ideal venue to explore such concepts, but this has drawn relatively little attention.
Thank you.
Alan M. Kadin, Ph.D.
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Author Michael James Goodband replied on Sep. 5, 2012 @ 18:48 GMT
Dr. Kadin
I apologize for not having yet commented on your essay, I am woefully behind!
I agree with you that seriously reconsidering quantum theory is drawing much less attention in this FQXi contest than it should be - it is as if it is the assumption that still cannot be questioned, even when all other assumptions are up for grabs! My essay makes a rather more serious challenge to the assumptions of quantum theory than is perhaps initially apparent, and proceeds to show that QT isn't fundamental as its mathematical form can be derived by a change in mathematical representation.
It is not just us essay contestants who are encountering problems challenging the assumption of quantum theory. Joy Christian's work shows that Bell's theorem doesn't prove that QT has no replacement - which effectively seems to me to amount to a proof that QT isn't fundamental - and has been getting serious stick, as opposed to being ignored. My essay outlines a totally independent proof of the same thing. In strict physics terms this opens the door to seriously questioning the status of QT, and hopefully this may happen before the end of the contest.
I think your closing lines nicely capture what's gone wrong with physics:
"Generations of physicists have been educated to ignore physical intuition about the paradoxes, while focusing on mathematics divorced from physical pictures. In response, the field of theoretical physics became more mathematically abstract, straying far from its origins explaining the behavior of real objects moving in real space."
Incidentally, the same is also true of general relativity, which has become something of a mathematical map detached from its physical territory - a trend which looks as though it is set to get a lot worse with notions of emergent dimensions.
Michael
Jonathan J. Dickau wrote on Sep. 4, 2012 @ 20:46 GMT
Hello Michael,
I am re-posting a comment I made elsewhere, with minor edits, as it pertains to your work.
I thought this might be a good place to raise the question of whether viewing particles and spaces as topological objects might account for the observations of Jenkin and Fischbach of varying decay rates for nuclei, depending on Sun-Earth distance. Apparently this has taken on a new dimension recently, as with more sensitive measurements it works as a kind of early warning system for solar storms.
This would argue heavily for the interpretation that the fabric of spacetime is of the nature of S3, topologically speaking. Or at least; I think that a topological description with a non-trivial twist in the fibration might easily account for such an effect as follows. When there is a mass ejection, this is a ripple in the topological fabric in the region of the Sun, in effect it is a rapid partial eversion of the Sun's mass. And this ripple propagates because of the topological connectedness.
Would you care to comment? Is this relevant here?
All the Best,
Jonathan
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Jonathan J. Dickau wrote on Sep. 5, 2012 @ 00:54 GMT
Regarding the Jenkins and Fischbach findings,
These slides from Recontres de Moriond tell the whole story.
Evidence of Solar Influences on Nuclear Decay RatesEnjoy,
Jonathan
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Author Michael James Goodband replied on Sep. 5, 2012 @ 18:06 GMT
Hi Jonathan,
You raise a very interesting point that I hadn't registered. I was just adopting the standard closed universe picture of GR and not registering it implied that S3 space-time must be a fibre-bundle, which as you suggest could result in unexpected effects. Further non-standard effects could arise in my model because the electroweak vacuum is of the form of a twist in the compactified dimensions in going all the way around the universe. So the sort of ripples you suggest might also involve changes in the electroweak vacuum, which could result in changes to the decay rates of particles. Such results could well be relevant, and perhaps provide a test for the topological structure of space-time. The problem I would have is that the particle masses and particle family mixing angles are not calculable in my model, which is a bit of problem for calculating changes to particle decay rates.
With particles being topological defects in my model, simple heuristic arguments say that neutrinos must have a non-zero mass, which is suggested in the link as being a possible factor. The topological defect particles take the form of compactified rotating black holes, which means particles would have rotational frame-dragging that should give non-standard spin interactions - but with a cross-section that would be too small to be of relevance for particle decay effects.
Another non-standard thought that occurred to me reading Joy Christian's book is that S3 can occur as a flat sphere with zero curvature - so could the universe be closed and flat at the same time?
I did enjoy, thanks!
Michael
Joy Christian replied on Sep. 5, 2012 @ 18:37 GMT
Hi Michael,
You asked: "...could the universe be closed and flat at the same time?"
Indeed it can. And I claim that it is. That is the message coming out of my work, as you seem to have gathered.
Without the universe being closed as well as flat, the strength and origins of the quantum correlations are impossible to understand in local-realistic terms.
Joy
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Author Michael James Goodband replied on Sep. 5, 2012 @ 19:31 GMT
Hi Joy,
I am currently reading your book, and it is the highlight of my year! - unless I am completely missunderstanding it ;-)
Your disproof of Bell's theorem seems to me to be effectively amount to a proof that QT is not fundamental, as your model demonstrates that a local classical physics theory *can* exist, would I be correct? If so, then my proof is a totally independent proof...
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Hi Joy,
I am currently reading your book, and it is the highlight of my year! - unless I am completely missunderstanding it ;-)
Your disproof of Bell's theorem seems to me to be effectively amount to a proof that QT is not fundamental, as your model demonstrates that a local classical physics theory *can* exist, would I be correct? If so, then my proof is a totally independent proof that QT is not fundamental. Now that I am coming to understand your work better I think that my work is related - I have come from the physics side, whereas you have come from the maths side.
It seems to me that the usage of the word 'local' is causing problems, because it can have several meanings. This is the point I was trying to make with my diagram in the attachment below. Your usage of the word 'local' seems to correspond to the physics intuition of a continuous path of subluminal causation, whereas there is also 'local' space-time separation in relativistic dynamics and the two won't be the same if the background metric changes. The illustration seems to provide the only way I can think of squaring physics intuition 'local' with apparent non-local space-time separations. Since your analysis is for R3, is it possible that such a relativistic change in metric signature is being captured in the global structure of the S3 function space?
Chapter 7 gives the general case as being a local function of the form
A(x,l): X*L -> Y sub Z
Where x is some orientation in the space X, and Z is constrained to be either S3 or S7. For the common case of spin orientation - which is an internal particle property - x is a 3-vector and X=R3. It seems to me that the same argument would apply to the gauge orientation x of the internal particle property space of gauge symmetries. As the isospin group space is S3 and electromagnetism is S1, the option of Z=S3 is too smal ... which *only* leaves S7. Is this correct?
I register that this S7 could also be flat as well. I don't yet know how this would square with my S10 unified field theory as I am currently on chapter 7.
Michael
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attachments:
2_Local_to_nonlocal.pdf
Joy Christian replied on Sep. 6, 2012 @ 06:43 GMT
Hi Michael,
Thank you for your kind words. I think we are on the same page as far as the understanding my central message is concerned, but we may have different views about some of the details.
In particular, you are correct to read my disproof as a proof that QT is not fundamental. The credit for this observation, however, must go first to Einstein, and then to Bell, before my work...
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Hi Michael,
Thank you for your kind words. I think we are on the same page as far as the understanding my central message is concerned, but we may have different views about some of the details.
In particular, you are correct to read my disproof as a proof that QT is not fundamental. The credit for this observation, however, must go first to Einstein, and then to Bell, before my work is even considered. Einstein argued most of his life that QT is not a fundamental theory, and Bell's work (which is based on the earlier work on hidden variables by von Neumann) clarified and quantified Einstein's position tremendously. My work is entirely in the tradition of Einstein, von Neumann, and Bell, but of course these giants do not consider going beyond the algebra of the real line, whereas both you and I consider the most general division algebra possible, namely the octonionic algebra, associated with S7. I too feel that our work is related, but I must admit that I haven't had time to digest some of your arguments (these days I am preoccupied in clarifying the relationship between SU(2) and SO(3) even further to understand the issue of "flatness" you alluded to above).
You have rightly raised the question about my usage of the word "local." I have used a very precise definition of "local" provided by Bell. This definition is theory-independent. In particular, it is independent of relativistic considerations. On the other hand, it may not remain valid if the space-time metric itself changes its signature during the course of dynamics, say, of an EPR pair. I am not sure whether a relativistic change in metric signature of the kind you have considered is captured in the global structure of the S3 function space. My feeling is that if such a change in signature is allowed then strong quantum correlations would be wiped out. That is not such a bad thing, however, for we do observe both quantum as well as classical correlations. In fact, more often than not we observe classical correlations rather than quantum correlations.
I think you are right to think that the same argument would apply to the gauge orientation x of the internal particle property space of gauge symmetries, with S7 substituted for S3. But the details here are beyond my field of expertise, so I am unable to be all that confident about this.
The octonionic S7 is indeed flat, and it is this discipline of "flatness" of S7 that is responsible for the strong quantum correlations. That is my claim in any case.
Thanks again for your kind words about my book. It is good to be appreciated.
Best,
Joy
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Steve Dufourny wrote on Sep. 5, 2012 @ 18:52 GMT
always a poor team still of strategists full of hate, still a poor band of frustrated, probably that your young life at school was difficult, probably that you makes a kind of revenge in making the bad. Jonathan , I have pity my friend and for your frustrated friends also. You are not foundamental, nor universal, nor relevant and still less an imrpover. Let me laugh in seeing your poor strategy and your hate increasing. I love USA and I am christian.
What is your poor probelm ? the vanity. I don't know me, buy a bibble and makes a redemption.I don't know, you are not relevant in fact even in your strategy.
Become a murder, it is better you know. And we shall see how shall be your humility in front of our god. You are a comic.Ok he said, ok.
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Yuri Danoyan wrote on Sep. 6, 2012 @ 13:47 GMT
Michael
"Concerns can also be raised about the gravitational “constant” G and the “constant” speed of light c, asking...
Your concerns is valid.See my essay
http://fqxi.org/community/forum/topic/1413
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WANG Xiong wrote on Sep. 8, 2012 @ 12:30 GMT
Dear Michael
Your paper is very interesting.See my essay
http://fqxi.org/community/forum/topic/1468
I believe QM is not As Fundamental As It Seems
If we want to reconcile quantum, we should give up one implicit assumption we tend to forget: the differentiability. What would be the benefits of these changes? It has many surprising consequences. We show that the weird uncertainty principle and non-commutativity become straightforward in the circumstances of non-differentiable functions. It's just the result of the divergence of usual definition of \emph{velocity}. All weirdness of quantum mechanics are due to we are trying to making sense of nonsense.
Thanks,
Xiong
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Jonathan J. Dickau wrote on Sep. 8, 2012 @ 17:49 GMT
Hello again Michael (and Joy),
It gives a whole new meaning to the term 'fabric of space' when you are talking in literal terms about fibers in the bundle from the Hopf fibration of S3, which constitute that fabric. I'm continuing here where my comments will be visible.
My understanding is that it's the parallelism within that fibration which produces both correlations and flatness. The fact that S3 and S7 are parallelizable is what guarantees - in effect - that this is what will happen when we examine how the fiber bundle is disposed in these spaces.
I too am reading Joy's book, but I have not gotten too far yet. Ergo; given some familiarity with the topic of debate, most of what I have read so far is familiar and easy to follow.
It would appear that both your work Michael, and Joy Christian's, point to a road by which Quantum Mechanics may be derived emergently. Curiously, it also ties in with some theoretical ideas I've been working on for a couple of decades, or at least it appears that it may.
More later,
Jonathan
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Joy Christian replied on Sep. 8, 2012 @ 18:38 GMT
Hi Jonathan,
I will let Michael respond to your comments in his own way, but let me just endorse two of your observations:
"My understanding is that it's the parallelism within that fibration which produces both correlations and flatness."
This is essentially correct as far as parallelism is concerned, but one need not consider fibrations of S3 or S7 at all to parallelize them. Since both of these spheres are simply-connected spaces, their parallelization amounts to vanishing of their Riemann curvature tensors. This ensures that torsions within them would be non-vanishing, because otherwise they would reduce to flat Euclidean spaces. Fibrations thus simply provide nice visualizations of these features. Full details on this can be found in Chapter 7 of my book. In addition, I am currently working on a new paper that may clarify the issue of parallelization further, at least in the case of the 3-sphere.
"It would appear that both your work Michael, and Joy Christian's, point to a road by which Quantum Mechanics may be derived emergently."
This is correct. In fact I have already derived ALL possible quantum correlations within my local-realistic framework, thus reproducing the kinematical part of quantum mechanics in toto. Moreover, my latest FQXi grant is for investigating how the dynamics of quantum theory would emerge from my framework. So far no progress has been made in this front, but, as they say: watch this space.
Joy
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Author Michael James Goodband replied on Sep. 10, 2012 @ 12:55 GMT
Hi Jonathan,
Taking the "fabric of space" as literally being a physical surface is the first assumption of my STUF-Theory, the second is that this physical surface realises *all* of the spheres S0, S1, S3, S7. This comes from the relevance of the normed division algebras to metric spaces, and the Relativity meta-principle of make no preference - so all of them. The map condition from S7...
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Hi Jonathan,
Taking the "fabric of space" as literally being a physical surface is the first assumption of my STUF-Theory, the second is that this physical surface realises *all* of the spheres S0, S1, S3, S7. This comes from the relevance of the normed division algebras to metric spaces, and the Relativity meta-principle of make no preference - so all of them. The map condition from S7 -> S3 could be added as a pre-condition, but I think that will come unstuck on the cyclicality S1 of the closed S3 universe. So the unification principle - S3 and S7 unified in S10 - perhaps doesn't really have the status of an assumption. I then apply GR to this assumed physical surface in the extended number of dimensions. Despite appearances, I make NO further assumptions beyond the unification being undone S10 -> S3 * S7 and the non-trivial map S7->S3.
The Kaluza-Klein style of theory results from a compactification-inflation see-saw powered by the transfer of radiation from S7 to S3. This gives the compactified dimensions of a KK style theory, but this is NOT an assumption. It follows from a *correction* to GR to make it into a physical theory of a physical 'fabric of space' - global conditions applying to a closed space require the cosmological term to vary with radius (see attachment). Not having such a dependence is a simplistic error that is neither mathematically nor physically correct. Like Joy's correction to Bell's assumed S0 space, it is a naïve mistake that is quite astonishing we have gone along with - revealing the power and dangers of group-think euphemistically labelled 'scientific consensus'.
With a quantum field theory background I haven't fully switched my thinking to all the repercussions of a physical 'fabric of space' and what it physically means for a closed universe to be the fibre-bundle S3. I hadn't registered that it meant there could exist non-standard connections between gravity and particle decays until your Sept 4 comment.
Michael
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attachments:
Balloon_world.pdf
The Spherical Jedi replied on Sep. 12, 2012 @ 12:34 GMT
weak reasoning ! it lacks a lot of generalities dear Badband in your reasoning and strategies.:)
In fact you repeat always the same :) SO AND SO3 AND SO7 AND AFTER YOU SHALL INSERT THE SO8 AND AFTER THE SO11 and after what , a book sent for the so12. Let me laugh.
I have pity in fact. You think what with your hate ? I forgive you all ahahah
KK theory for the compactification...
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weak reasoning ! it lacks a lot of generalities dear Badband in your reasoning and strategies.:)
In fact you repeat always the same :) SO AND SO3 AND SO7 AND AFTER YOU SHALL INSERT THE SO8 AND AFTER THE SO11 and after what , a book sent for the so12. Let me laugh.
I have pity in fact. You think what with your hate ? I forgive you all ahahah
KK theory for the compactification and what after ? Mr Witten but what do you do there ? is it the businessmen around you which implies this kind of reasoning? If yes, I am understanding why this world does not turn correlctly. It is simply not universal these kind of comportments.The Planet, this earth merits more. Why these kind of systems decrease the velocity of evolution? instead of imrpoving it. Is it that? the earth ? I am shocked in fact simply in seeing these comportments. In fact Mr Witten,Mr Tegamrk and Mr Aguire are universal I am persuaded like Penrosqe and Hawking,and Sussking also.So why it exists these business around which implies a real probelm. It is not that the aim of this universal sphere. The Christianity is the torch of the universal love. The suit does not make the monk ! A goodband is universal. A bad band does not respect the real universalists. Their strategies are like an error in fact. They insist due to their lack of competences in ciences, so their only one solution is the business. These kind of persons like to be in team, because alone they cannot make concrete things. Their tools are simply the hate, the vanity and the envy. In fact I pray for their poor souls and I forgive them with love. Hope they shall understand one day what is the spherization theory invented by Mr Steve Dufourny, a young horticultor, humble in seeing the sky and its spheres. In fact, the usa has a responsability for this sphere, the earth.The imperialism american can optimizing the earth with India ,China,europa. Why a global commission above the bricks and the otan, having a lot of universal wisdom and consiousness, does not appear on this sphere? What are these high spheres so? who governs so this earth if it is not the Usa. China has a lot to give to the world, the india also. The prosperity can be implanted on earth, so why? It is not logic all this. I beleive that the corrupted systems must be stopped quickly . We cannot accept the unconsciousness and the corruptions. If the high spheres of this earth does not take its responsabilities quickly, we shall add chaotical global probelms and we shall reach several possible chaotical exponential. The prosperity can be global for all. The USA must take its responsabilities for the well of all. The capitalism can be liberated with more monney. The stock of Au(gold) or Pt or the financial products or this or that must be architecturated with a real universality. China and Usa And India and Europa must work together. The Africa ,it, is very weak, and must be helped with universality also. The prosperity like a torch of evidence. It permits to decrease the hate.
The probelms of religions also can be optimized. The imperialism american has a pure universal responsability !!! It is essential for our future. I ask me if the high spheres are really universal. I say me that this monney sometimes implies a lot of problems. The system , global can be harmonized.Have you seen the increasing of humans.Have you seen the energetical probelm.Or the poverty, the sufferings everywhere.It is not acceptable for universalists and generalists. The sciences have the solutions. The competences, scientific, must be centralized for the well of all.Above the borders and frontiers and differences. We are all humans waiting for a better world. The prosperity is, like said a friend that I have knew when I was moderator of the group Africa on Xing, woman, Deborah Boyd, a catalyzer of peace. People are less nervous when they create,They are more in serenity with their minds. It is a simple evidence. The hour is serious dear scientists. The solutions exist. It is time to act concretally.
Usa has a responsability !!! This country must showing the example.
Regards
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Author Michael James Goodband wrote on Sep. 10, 2012 @ 13:03 GMT
FQXi'ers - On the connection of my work to Joy Christian's (in parts because it's long)
Joy expressed Bell's analysis about whether there could exist a 'complete' 'local' theory that could replace Quantum Theory, as Bell considering functions of the form
A(n,l): R3 * L -> S0 (see eqn 1.1)
R3 is a co-ordinate based denotation of the flat Euclidean space E3 in...
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FQXi'ers - On the connection of my work to Joy Christian's (in parts because it's long)
Joy expressed Bell's analysis about whether there could exist a 'complete' 'local' theory that could replace Quantum Theory, as Bell considering functions of the form
A(n,l): R3 * L -> S0 (
see eqn 1.1)
R3 is a co-ordinate based denotation of the flat Euclidean space E3 in which the 3-vector orientation n resides, the space L is a space of 'hidden' variables which gives 'complete' states and S0 is the function co-domain for the observable A. Joy identified that the function co-domain S0 is rather trivially wrong, it should be S2 sub S3 (
see eqn 2) as the possible orientations of the 3-vector n define a 2-sphere. Quantum correlations follow from the topology of the spaces.
My work effectively addresses what is meant by 'hidden' variable and 'complete' states in physics, neither of which were sufficiently well-defined by Bell. There are effectively 2 different underlying meanings for 'complete'
1) mathematical completeness - every theorem in a formal system can be derived
2) scientific completeness - every observation can be predicted
Bell fails to specify which he means. This shortcoming can be viewed as originating with the original EPR paper which gives the meaning of 'complete' as: "every element of the physical reality must have a counterpart in the physical theory". But this isn't physics! It fails to specify how you would verify that this was true - namely by experiment. This is why I use 'physically-real' to specify a term in a theory that *directly* corresponds to an observable feature in reality (I took this term from a QT textbook discussion of Bell's theorem). Any mathematical term which does not have this 1-to-1 correspondence is a 'non-physically-real' term, eg. the wave-function denotes strictly countable numbers of electrons by the real-numbers, and since 0.5 of an electron is never measured in an experiment, the wave-function is a non-physically-real term.
There are also 2 possible meanings for 'hidden' and Bell fails to specify which
1) hidden from the subset A, B of observables considered in a correlation experiment - in which case the hidden variable could be found in the future by a new experiment
2) hidden from all possible observables - in which case it is a non-physically-real term!
Option 2 is what is implicitly meant by Bell, but how such a conspiracy of Nature could arise is not considered. The missing element is dynamics, which is because the physical space of the EPR scenario isn't just Euclidean space E3, but a Euclidian sub-space of Minkowski space-time M4. There are an infinite number of ways of picking out E3 from M4, parameterised by the velocity v of the reference frame, i.e. E3(v) sub M4. Joy didn't make this correction either, but it doesn't change his correlation results because they depend upon integrating over the space of the 'hidden' variable to get expectation values. This may suggest that the parameterisation E3(v) could just be dismissed. However, this would effectively amount to setting v=0 for all the reference frames of the scenario, but without any relative motion there is no dynamics and so nothing happens - thus setting v=0 is unphysical!
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Author Michael James Goodband replied on Sep. 10, 2012 @ 13:09 GMT
In the archetypal EPR scenario, the interaction point is stationary and the two objects move in opposite directions:
A(n, l): (E3(v>0) sub M4) * L -> S2 sub S3
B(n, l): (E3(-v) sub M4) * L -> S2 sub S3
The condition E3(v>0) sub M4 adds the minimum dynamics condition to Joy's analysis - and adds Relativity - where constraints on the expectation value integral (eqn...
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In the archetypal EPR scenario, the interaction point is stationary and the two objects move in opposite directions:
A(n, l): (E3(v>0) sub M4) * L -> S2 sub S3
B(n, l): (E3(-v) sub M4) * L -> S2 sub S3
The condition E3(v>0) sub M4 adds the minimum dynamics condition to Joy's analysis - and adds Relativity - where constraints on the expectation value integral (eqn 3.2 in Joy's book) or normalisation of the 'hidden' variable should make it possible to turn Bell's 'locality' condition of factorisation (
eqn 4) into the space-time separation condition v<c (v parameterises E3 and c is in M4). My work predicts that this should be the case, because I identify a scenario with a suitable conspiracy of Nature that gives a hidden domain L.
Any observable (A, B) is ultimately based upon some particle reaction which will take some minimum time t_min to occur, so if the local causation of the domain L occurs on times scales t<t_min then it will be hidden from all possible observation. This will be the case for a particle with a physical scale of the Planck length and internal dynamics that occur on a time-scale set by the Planck time - which is the case in my model where particles are Planck holes with radius of the Planck length. Furthermore, as every observation takes so long that very many cycles of the local dynamics on the time-scale of the hidden domain L occur within the measurement time-scale, the calculation of all observables *must* take an average over the domain L (such as
eqns 5 and 6).
However, for the hidden domain being that of a black hole particle on the Planck scale, the rotation causes a maximal ergo-region where the metric signature of Minkowski space-time M4 is reversed, ie. (-,+,+,+) -> (+,+,+,+). This means that there will be one more +1 or -1 issue in Joy's analysis, where the prediction of my work is that averaging over this metric reversal in the hidden domain L is the *source* of the illusion of non-locality in QT. I would expect that extending Joy's work by applying it to the correct physical space E3(v) sub M4 would explicitly show this - and in so doing snooker Joy's critics (even if they all don't register it). Being brutally accurate about the applicability of Bell's analysis to the spaces of physics would score him as 0 for 3.
Joy's flatness condition on the topological spaces S3 and S7 is actually in agreement with my results - despite appearances given by previous discussion. The issue is that the flatness condition doesn't technically apply to empty space, as that would mean there were no particles in the EPR scenario - so nothing happened! EPR requires 2 particles to dynamically interact, and so the flatness condition applies to the space in the vicinity of the 2 particles - this is *not* the same thing as empty space. The particles of my work are topological defects in the structure of space, which necessarily will give a torsion in the space around them - torsions in space is how the particle forces arise in a Kaluza-Klein style theory. In my work, I show that the formalism of QT is an *approximation* that is required to get a scientifically complete theory because the physically-real classical physics theory is mathematically incomplete, and that the approximation *only* holds in the limit of point-like particles and flat space-time. This approximation limit effectively integrates over the region of space of the ergo-region and gravitational curvature, and this gives the origin of the hidden domain L.
My flatness condition is a local condition - as in only applies in the local vicinity of particles - and not a global condition on all of space ie. the universe isn't required to be flat. Joy's flatness condition is also such a local condition that doesn't necessarily imply that the whole universe is flat - if it did that would imply teleparallel gravity. But as a local condition, it just implies that the particle forces are associated with torsions in space - which is the case in my work - and gravity is left being due to curvature of space. This distinction would naturally explain the difference between the forces of gravity (curvature) and particles (torsion).
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Thomas Howard Ray replied on Sep. 10, 2012 @ 14:22 GMT
Hi Michael,
You're talking my language now (or rather, the language of Nature) ...
" ... the hidden domain being that of a black hole particle on the Planck scale, the rotation causes a maximal ergo-region where the metric signature of Minkowski space-time M4 is reversed, ie. (-,+,+,+) -> (+,+,+,+). This means that there will be one more +1 or -1 issue in Joy's analysis, where the...
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Hi Michael,
You're talking my language now (or rather, the language of Nature) ...
" ... the hidden domain being that of a black hole particle on the Planck scale, the rotation causes a maximal ergo-region where the metric signature of Minkowski space-time M4 is reversed, ie. (-,+,+,+) -> (+,+,+,+). This means that there will be one more +1 or -1 issue in Joy's analysis, where the prediction of my work is that averaging over this metric reversal in the hidden domain L is the *source* of the illusion of non-locality in QT."
That's exactly what I mean by the source of all information from the point at infinity. I think this is well supported by Lamport's result (Buridan's principle) for all continuous measurement functions. No quantum entanglement, just the illusion, as Joy allows -- with orientability playing the key role. The point at infinity in Minkowski space is everywhere close to the observer, while the physical measurement is nondegenerate near the singularity.
"I would expect that extending Joy's work by applying it to the correct physical space E3(v) sub M4 would explicitly show this - and in so doing snooker Joy's critics (even if they all don't register it)."
I don't know. I think we're back into this question of measure space vs. physical space. My sentiment is still toward S^7 as a complete physical space, just as Joy has it. No compactification, octonionic degrees of freedom.
" ... the universe isn't required to be flat. Joy's flatness condition is also such a local condition that doesn't necessarily imply that the whole universe is flat - if it did that would imply teleparallel gravity."
Actually, I think that is what he means to imply. Flatness and curvature have to be relative for a fully relativistic theory consistent with your definitions of completeness (which are nice). As in ordinary geometry the straight line is a special case for the curve, topology renders the continuum in curved space.
All best,
Tom
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Author Michael James Goodband replied on Sep. 10, 2012 @ 16:19 GMT
Hi Tom,
The question of measure space vs. physical space is *precisely* the point to address, especially in the context of the distinction between local - as in the local vicinity of particles - and global structure. Both Joy's and my results regarding QT are local (vicinity) results about the description of measurements, i.e. conditions on measurement space which imply conditions on...
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Hi Tom,
The question of measure space vs. physical space is *precisely* the point to address, especially in the context of the distinction between local - as in the local vicinity of particles - and global structure. Both Joy's and my results regarding QT are local (vicinity) results about the description of measurements, i.e. conditions on measurement space which imply conditions on physical space, namely that it must be locally (vinicity) flat.
Extending this result to the global structure of space and teleparallel gravity does seem to be Joy's intent (is stated in his book as such). My point is that this is not technically a *necessary* implication. Joy's results are fully compatible with a locally flat spatial structure and gravity being due to the curvature of space. It must be noted that the flatness condition coming from the condition of scientific completeness of the measurement space is restricted to the local vicinity of the particle interaction. Extending the result beyond this domain is technically an invalid induction.
I was concentrating on Joy's work and missed your discussion where you mentioned compactification and Kaluza-Klein theories. Mine is only a KK-style theory as it explicitly does *not* assume a fixed size compactified dimension as in standard KK - which you quite rightly in my opinion object to as that was the problem I had with KK. I refer you my reply to Jonathan about the cosmological 'constant' being a naive error that is not correct in GR! My extended GR includes the correction for a *physical* GR theory and consequently contains a compactification-inflation see-saw - I *derive* both inflation and dimensional compactification as consequences of assuming that the 'fabric of space' is a real physical surface.
A further consequence of the compactified S7 is that all scales are measured relative to them, and measuring the scale of S7 relative to itself gives the constant of 1. So the constant scale of the compactified dimensions is a total illusion, NOT an artificial assumption. This gives a non-trivial example of the sort of point Jonathan makes about measuring rods in his essay.
Michael
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Yuri Danoyan replied on Sep. 11, 2012 @ 02:07 GMT
My be contradiction "global vs local" is wrong assumption?
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Thomas Howard Ray replied on Sep. 11, 2012 @ 18:05 GMT
Hi Michael,
I look at it this way: Bell's theorem proves explicitly that quantum configuration space cannot be mapped onto physical space without a nonlocal model. To believers, this amounts to saying that there is no analytical explanation of locally real quantum correlations. One cannot logically extrapolate to that conclusion, however:
Quantum configuration space requires us to assume a bounded set of perfect information (such is the source of quantum mysticism inherent in a probabilistic measure). The orientable topology, as Joy has it, requires only that Nature have a choice of output in every measurement function continuous from the initial condition. This necessarily eliminates support for nonlocal realism from all proofs based on the law of the excluded middle, which of course is all the nonconstructive proofs of Bell's theorem.
Bell's theorem is then reduced to an existence proof for the inequality between local measure results and simultaneous results of nonlocal experiments not performed. Trivial -- because relativity already denies simultaneity of events.
Best,
Tom
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Jonathan J. Dickau wrote on Sep. 11, 2012 @ 15:15 GMT
Greetings folks,
I must say that reading the comments above brings the feeling of coming home, or finding myself unexpectedly in a familiar place. Reading your essay, Michael, brings with it a sense of being told things I already knew or believed, with the sense that an expert is telling you why it's finally OK to believe those things. The correct application of Gödel's theorem as opening up possibilities and choices, rather than closing things down, is most welcome.
But a lot of what I read in your STUFT paper and the material discussed in Joy Christian's book put me in a geometrical playground of unlimited proportions, and let me have my favorite toys in the sandbox with me. I learn a lot through visualization. I take Alain Connes' recommendation to budding mathematicians seriously, by taking time to recline and reflect periodically when absorbing new concepts, and I find it serves me greatly.
The thing is; it keeps me on track, because it is harder to visualize things - including abstract formulations in higher Math - that lead to impossibilities. This is why I find the work you and Joy are doing so exciting, because it jibes well with what my visualizations tell me, and it appears to lead to physically realistic possibilities. Of course, that doesn't mean that it IS what is real, but it could be.
Regards,
Jonathan
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Joy Christian replied on Sep. 11, 2012 @ 16:11 GMT
Hi Jonathan,
What you are saying is music to my ears. And I suspect it is music to Michael's ears too.
However, while you, Rick, Michael, Tom, Fred, and others are trying to take these ideas further, I am engaged in addressing your very prudent caution: "...that doesn't mean that it IS what is real..."
I want to make sure that it IS real before proceeding further. And in physics we do that by testing our hypotheses experimentally. Despite opposition, scepticism, detraction, and even scorn and derision, I am completely convinced by my theoretical analysis. What I am not sure about, however, is whether Nature prefers to side with me and Michael or with the quantum mystics. Only she can answer this question correctly, and I intend to get her answer.
Joy
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Thomas Howard Ray replied on Sep. 11, 2012 @ 17:16 GMT
My faith in rationalism agrees with Joy -- scientific results cannot be objective without a clear correspondence between the abstract description and the physical measurement.
If this framework isn't true, then I have to agree with Einstein: "I would feel sorry for the dear Lord ..." There is no rule that says the world has to be rational; if it isn't, though, we've been doing science all wrong for 300 years. I can't imagine the alternative.
Tom
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Author Michael James Goodband replied on Sep. 11, 2012 @ 17:44 GMT
Hi Joy,
Does my description of the connection of my work to yours seem correct to you?
On the topic of experimental tests, would I be correct in thinking that the correlation inequalities for observables arising through gravitational interactions, i.e. astronomical observations, could provide a test for teleparallel gravity? As your work implies that this would be required for gravity to be quantied, is there a test here for whether gravity is quantised or not?
Obviously I don't think it is - as QT is not fundamental and so Nature is under no obligation to comply with the prior beliefs of physicists and have quantised gravity - but an experimental test would nice.
Michael
Joy Christian replied on Sep. 11, 2012 @ 19:21 GMT
Hi Michael,
I think your criticism of either Bell or EPR about their ideas of completeness and hidden variables is not justified. EPR, for example, were very cautious in stating that their condition of completeness is only a necessary condition (for their intended purposes), not a sufficient condition. Your understanding of what Bell meant by "hidden variables" is also incorrect. What Bell...
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Hi Michael,
I think your criticism of either Bell or EPR about their ideas of completeness and hidden variables is not justified. EPR, for example, were very cautious in stating that their condition of completeness is only a necessary condition (for their intended purposes), not a sufficient condition. Your understanding of what Bell meant by "hidden variables" is also incorrect. What Bell had in mind was what you write as option 1, not what you write as option 2. The issue of dynamics is also irrelevant for the analysis of both EPR and Bell. Given their premises, the argument of EPR is logically impeccable. Given the premises of Bell---which are based on the premises of EPR and the views of Einstein---his theorem too is both logically and mathematically impeccable. It does contain a massive blunder, however, in the very first equation of his famous paper, as I bring out in my work. Whether to call this a mathematical error or merely a wrong assumption is a matter of taste.
Having said this, we are of course not required to adhere to either EPR's logic or Bell's mathematics beyond what is demanded by physics. So, in that respect, in the spirit of exploration and investigation, I fully endorse your efforts. In particular, the issue of dynamics should indeed be considered as you are considering, and you have some very insightful remarks in this regard. I myself have very different ideas about how to investigate the issue of dynamics, since my primary concern is basic quantum mechanics, not relativistic or gravitational physics.
I also like your thoughts about the flatness condition and whether or not it should be extended to the universe as a whole. I largely agree with what you have written about this. But again I would not discount any options at this stage because neither of us have anything near a full theory of physics (in fact mine is not even a theory---I prefer to call it a mere "framework").
As for the experimental test of my framework I do not have anything as exotic as teleparallel gravity or quantum gravity in mind. At the moment I am simply trying to test whether the topology of our physical space respects SU(2) symmetry in the macroscopic domain as I claim, or SO(3) symmetry. This may seem disappointing, but my entire framework depends on this distinction. If this test is successful, then I have some further ideas about how to test the S7 hypothesis.
Finally, since I agree with the view that QT is not a fundamental theory, the question of quantizing gravity does not even arise. QT and GR are simply two epiphenomenal sides of a yet to be discovered perfect, one-sided coin.
Best,
Joy
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Anonymous replied on Sep. 12, 2012 @ 11:26 GMT
Hi Joy,
Thanks for your feedback, it is much appreciated.
My premise was implicitly moving beyond Bell - something that I didn't think was possible until I read your work! I did initially think that Bell's intended meaning of "hidden variables" was option 1, and this is the meaning I used in my essay. But it struck me that Bell's framework would also extend to option 2 as well, and...
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Hi Joy,
Thanks for your feedback, it is much appreciated.
My premise was implicitly moving beyond Bell - something that I didn't think was possible until I read your work! I did initially think that Bell's intended meaning of "hidden variables" was option 1, and this is the meaning I used in my essay. But it struck me that Bell's framework would also extend to option 2 as well, and that the spatial topological defects of my model actually give a realisation of option 2. These 2 meanings could lead to confusion in the usage of the term "hidden variables" - I see that I have inadvertently included both options.
The potential ambiguity of the EPR usage of "complete" is not apparent in the EPR context because their usage is sufficient. But the relevance of Godel's incompleteness to physics requires the more careful distinction I give, otherwise the point that mathematical incompleteness of theories describing countable numbers of objects under certain physical conditions can be by-passed to give scientific completeness is missed, as are the consequences of the required change in mathematical representation (theories with some of the weird features of QT).
The term "local" is another multi-meaning word that could lead to potential confusion, especially in the context of EPR and spatial topology:
1) local vicinity - local structure as opposed to global structure
2) local causation as captued by the fatorisation condition
3) local time-like separations
E.g. my metric reversal example confuses usages 2 and 3, and suggests the following "recipe" for the illusion of non-locality:
1) Metric reveral in the hidden domain
2) Average over paths of strictly local causation in the hidden domain
3) Interpret the results as if there was no metric reversal in the hidden domain
=> apparent non-locality
I understand your focus on the sort of tests you're considering; I was just wondering out loud how far tests within your framework could go.
All the best,
Michael
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Yuri Danoyan wrote on Sep. 13, 2012 @ 01:38 GMT
If the Planck length not valid in 2D, because no, gravitation no G?
See essay 1413
See Wilczek articles
http://ctpweb.lns.mit.edu/physics_today/phystoday/Ab
s_limits388.pdf
http://ctpweb.lns.mit.edu/physics_today/physt
oday/Abs_limits393.pdf
http://ctpweb.lns.mit.edu/physics_toda
y/phystoday/Abs_limits400.pdf
Is trinity sacred?
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Yuri Danoyan wrote on Sep. 13, 2012 @ 02:53 GMT
Sorry for broken links
http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_l
imits388.pdf
http://ctpweb.lns.mit.edu/physics_today/phystoda
y/Abs_limits393.pdf
http://ctpweb.lns.mit.edu/physics_today/p
hystoday/Abs_limits400.pdf
Is trinity sacred?
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Joy Christian wrote on Sep. 17, 2012 @ 11:59 GMT
Hi Michael,
Let me introduce you to
Jens Koeplinger's essay, in case you haven't seen it already. It is amusing and entertaining. His main work however is much more substantive. Parts of it is based on Rick Lockyer's approach to octonions. I thought you might benefit from it since it also takes the division algebras seriously.
Joy
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Author Michael James Goodband replied on Sep. 17, 2012 @ 19:45 GMT
Hi Joy,
Thanks for the pointer. I can see where you, Rick Lockyer, Jens Koeplinger and others are hoping to go with the octonions.
In contrast, I have gone to the very end of the line with Einstein: to his vision of physics unification in a purely geometric theory. I *conclude* S0, S1, S3, S7, I don't assume them, and arrive at the conditions of your framework. If you read my
S10 Unified Field Theory paper you will see that it *is* a full theory based on 11D GR. I have checked your book carefully for any condition which specifies your favoured choice and rules out my realisation of Einstein's vision, and I cannot find one.
Just as you said the credit had to go to Einstein, my STUF-Theory is the form of physics unification that Einstein envisaged it to be - purely geometric GR in which QT is *not* fundamental. The things to pin down were the number of dimensions, the separation of space dimensions from extra dimensions, and the way QT arises: the dimensions of the spheres add to 11D; a cosmological 'constant' for a closed space just isn't physics; and the origin of QT is with a mathematical representation change because Nature is *described* by Maths, Maths is *not* Nature. The distinction is actually the crux of it, which is why I made it the topic of my essay.
Michael
Thomas Howard Ray replied on Sep. 18, 2012 @ 17:31 GMT
Michael & Joy,
"I have gone to the very end of the line with Einstein: to his vision of physics unification in a purely geometric theory."
That's the way I think, too. Einstein did say that if algebra (quantum numbers) were going to contribute to the basis of a complete theory, the algebraic methods would have to be improved. With all the emphasis on octonion algebra, though, I still see the fundamental framework of physics as analytical, which I much better understand and which I htink most closely resembles experience. I think I have made the point before that if Hestenes were not able to explicitly translate his method to Minkowski space, I don't think it would hold my interest.
It's still the property of orientability, however, by which the mathematical structure informs the physics, so we need that discrete part to make the whole thing work, don't we?
Tom
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Joy Christian replied on Sep. 18, 2012 @ 18:18 GMT
Hi Michael and Tom,
If Albert was alive today and knew all the physics we know (which is orders of magnitude more than he could have hoped), then would he have accepted Michael's claim? That is the question I want to answer for myself. But to do that I will have to put in at least as much time and effort into Michael's theory as he has into my framework. I will try to read at least some of his papers---with serious intention to agree with him---and then we will see. For now I remain sceptical.
Best,
Joy
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Jens Koeplinger replied on Sep. 18, 2012 @ 21:49 GMT
Hello Joy, Michael.
Joy - thanks so much for your note! It's good to hope that we're working on pieces of a puzzle that will ultimately fit together - as opposed to random scrap on the junkyard ... :)
Michael - your work on finding symmetries of the Standard Model from the parallelizable spheres reminds me of Geoffrey Dixon's. Are you familiar with his work? He's been advocating such a model over the past decades. You find points and references from his site: http://7stones.com/ with free material e.g. from http://7stones.com/Homepage/AlgebraSite/algebra0.html , "U(1)xSU(2)xSU(3): Original Derivation". If I remember correctly, Dixon proposes a 9+1 dimensional background geometry of nature (but I better stop here before writing something wrong). A newer approach to using such spheres comes from a somewhat different, algebraic angle: Cohl Furey's "Unified Theory of Ideals" ( http://arxiv.org/abs/1002.1497 ; recently accepted into PrD as I just found out!).
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Thomas Howard Ray replied on Sep. 19, 2012 @ 00:14 GMT
What keeps me from being a Platonist in the vein of Penrose, Godel and Rick Lockyer -- though I have the highest respect and admiration for all of them -- is exactly the dichotomy that Michael describes, between the language of nature and the facts of nature.
Joy, that's what compels me to accept Bell's theorem as a mathematical truth, while acknowledging that your topological framework is far superior for describing quantum correlations in a mathematically complete and physically falsifiable schema.
Mathematics always depends -- exactly as natural language depends -- on rules and assumptions. Take the Banach-Tarski paradox -- mathematicians know that the name is historical; it isn't actually a paradox though it is a highly counterintuitive construction. Dropping an assumption changes the game, however -- can one prove B-T without the axiom of choice? (I hope to someday, in fact.) Point is, that dropping assumptions -- paring a proposition to its bare essentials -- is the very definition of mathematical beauty. It's what attracted me to the Joy Christian framework like a moth to flame -- the idea that globally continuous measurement functions share identity with locally real results isn't something that one just wakes up believing in. It means suspending belief, in favor of a deductive argument and rational correspondence between the mathematical theory and physical result. Proving quantum correlations without assuming nonlocality is absolutely equivalent to proving the B-T construction without AC.
Don't speak to me of "disproof" -- speak to me of correspondence between language and experience.
Best to all,
Tom
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Joy Christian replied on Sep. 19, 2012 @ 05:07 GMT
Hi Tom,
Here is a statement of Bell's theorem by Abner Shimony (the S in the Bell-CHSH):
"No physical theory which is realistic as well as local [in the senses specified by EPR and Bell] can reproduce all of the statistical predictions of quantum mechanics."
And here is a
Disproof of Bell's theorem.
Bell's so-called theorem was NOT a mathematical theorem. Its defenders would very much like to promote it as an ironclad mathematical theorem. But that is just selling tactic, not scientific truth.
Joy
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Anonymous replied on Sep. 19, 2012 @ 11:17 GMT
Joy, no mathematical theorem is a scientific truth. It's a mathematical truth; that's what "theorem" actually means. Science and mathematics are not identical, even though we speak informally of the "mathematical sciences."
From the beginning and to this day, I have maintained that there is not a mathematician in the world who will agree with you that a theorem can be disproved. If that...
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Joy, no mathematical theorem is a scientific truth. It's a mathematical truth; that's what "theorem" actually means. Science and mathematics are not identical, even though we speak informally of the "mathematical sciences."
From the beginning and to this day, I have maintained that there is not a mathematician in the world who will agree with you that a theorem can be disproved. If that were the case, we wouldn't need mathematics to describe the natural world -- because we couldn't distinguish between events and numbers. That is, in fact, the very weakness of Bell's theorem that you spotted -- whether you are consciously aware of it or not -- and corrected.
Bell's theorem is perfectly sound as a theorem of arithmetic; on the interval {0,oo} there exist integers such that a bijection dependent on orientation of copies of N on the plane compels an inequality of the bijective sets. Easy to prove.
Problem is, the plane is not orientable. The existence theorem in arithmetic applied to Bell's experiment has the observer orienting the events by fiat, and ordering the numbers by the rules of arithmetic, and hence we get an observer created reality.
You are absolutely right, and I am your strongest defender -- a topology solution answers the challenge to have an objective, non-anthropocentric physics with a natural orientability that obviates nonlocality and preserves the observer's free will. I'm no voice in the wilderness, either -- I agree without qualification with what Boris Tsirelson told you on his Wikipedia talk page: "Evidently, your idea of Nature is substantially different from that of EPR, Bell and many others. Basically, Bell theorem says that Nature cannot be what is was assumed to be. Quantum theory proposes one new kind of Nature. You propose another new kind of Nature. So what? It will be exciting if your proposal will ultimately work better that quantum theory. But even that will not disprove Bell theorem. If the old kind of Nature is dead anyway, then Bell theorem is alive. So, here is your choice. Either you waive your author rights on the S^3/S^7 physics and kill Bell theorem, or you keep your author rights on the S^3/S^7 physics and withdraw your claim against Bell theorem. Wow! Your decision will tell us, whether you really hope that your S^3/S^7 physics will replace the quantum theory, or not. Surely you do not want to miss Nobel price and instead win a battle on Wikipedia! Boris Tsirelson (talk) 10:02, 4 June 2012 (UTC)
Trust, Joy that your physics *does* work better than quantum theory, and leave the theorem proving to the mathematicians. For surely, a purported disproof is identical to a proof which disproves itself. You'll never be able to escape that logical strait jacket. Don't let them put you in it!
As always, all my best,
Tom
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T H Ray replied on Sep. 19, 2012 @ 11:18 GMT
Must have been logged out. The above is mine.
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Joy Christian replied on Sep. 19, 2012 @ 12:23 GMT
Tom,
You missed my point, as did Boris Tsirelson. Bell's so-called theorem was never a mathematical theorem. The word "theorem" in this context is simply a sells tactic, and you have fallen for it.
I have not disproved any mathematical theorem. That has never been my claim. This was a claim imposed on me by Philippe Grangier. Please read my reply to Grangier.
What I have disproved is the following statement of a so-called theorem:
"No physical theory which is realistic as well as local [in the senses specified by EPR and Bell] can reproduce all of the statistical predictions of quantum mechanics."
I categorically and strongly object to the mischaracterization of my framework by Boris Tsirelson (which you have quoted). Please read my reply to Boris on his page. In particular, I strongly object to his statement that "[my] idea of Nature is substantially different from that of EPR, Bell and many others." This statement is preposterous.
I stand by my use of the word "disproof." Neither Abner Shimony, nor any other well known foundationalists like Lucien Hardy, has ever objected to my use of the word "disproof" in this context. Only mathematicians have a problem with the word, and for all the wrong reasons. What has been disproved was never a theorem to begin with.
The issue is purely linguistic as far as I am concerned. It is not worth debating about.
All best,
Joy
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Thomas Howard Ray replied on Sep. 19, 2012 @ 13:01 GMT
On the idea that I may as well be hung for a sheep as for a lamb, let me add that Abner Shimony's statement ...
"No physical theory which is realistic as well as local [in the senses specified by EPR and Bell] can reproduce all of the statistical predictions of quantum mechanics."
... is also true.
The problem is, there's no way to prove it false. That is, if there is no physical domain that is both local and real, Shimony's tautology says that the probabilistic nature of quantum mechanics (nonlocal and real) is physical.
Just as Einstein held, though, if quantum mechanics were a complete physical theory it would necessarily describe the whole of reality in discrete quantum numbers. No statistical theory can do this.
What a classical, deterministic theory can do, however, is to specify the physical domain as a bounded continuum. That the bound of 4-dimension spacetime (Minkowski space) includes the 3-manifold as a local plane of measurement space -- a complete theory need only extend the bound to show that global distant events are also manifest on that local plane as a function of measurement continuous from an initial condition. Joy's topological framework meets that standard -- statistical inference on a bounded domain of globally continuous measurement functions means something quite different than that on an unbounded space of probability measurement.
Tom
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Thomas Howard Ray replied on Sep. 19, 2012 @ 13:31 GMT
Hi Joy,
Our replies crossed. I posted mine before I read yours.
We agree on everything except whether the issue of disproof is worth debating. You're absolutely right that only mathematicians are concerned about it; not as a debate, but as a principle of mathematical logic.
I've always said I agree with Grangier and Tsirelson on this relatively narrow yet important point.
Thing is, there may be methods of formal language that will preempt conventional mathematics in the future -- Lev Goldfarb's ETS formalism, Gregory Chaitin's experimental mathematics, and Steven Wolfram's prgram are possible examples -- yet any of these systems have to remain internally self-consistent, or else there's no need to even have a formal language to describe natural phenomena.
Yes of course I read and comprehended your reply to Boris "... A possibility is that we will find exactly where the boundary lies. More plausible to me is that we will find that there is no boundary. ... It is this possibility, of a homogeneous account of the world, which is for me the chief motivation of the study of the so-called 'hidden variable' possibility.'" I even agree with your reply. That doesn't change my mind that Boris is correct that the mathematics of Bell's theorem is true -- it's an easy sell, if that's the way you think of it. There's plenty of trivial mathematics in the canon.
All best,
Tom
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Thomas Howard Ray replied on Sep. 19, 2012 @ 13:51 GMT
I wanted to deal with this separately:
"I strongly object to (Boris Tsirelson's) statement that '[my] idea of Nature is substantially different from that of EPR, Bell and many others.' This statement is preposterous."
Preposterous to you, Joy, because you know intimately the topology by which you support your conclusions. Put yourself in the position of those who are not living in that framework. My own first reaction to your claim that Bell based his theorem on the wrong topology was, "So what? He wasn't doing topology." And that's true. Neither EPR, nor Bell, were aware of any topological implications of a complete local realistic theory -- and most still aren't.
Being right and being believed aren't always congruent. We can only strive to stand on the side of truth, even against belief.
Tom
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Joy Christian replied on Sep. 19, 2012 @ 14:29 GMT
Tom,
Boris should have known better. He is a very competent mathematician (unlike some we have encountered in the recent past). His mischaracterisation of my work stems, not from his lack of understanding of any mathematical concept such as topology, but from his total disregard for the original arguments by EPR and Bell. Here is what he says about Bell's own paper: "And frankly I never read carefully the original Bell's argument... Why? Just because I do not care much about the history of physics etc..."
After making such a startling confession, how can he go on to claim that "[my] idea of Nature is substantially different from that of EPR, Bell and many others"? What does he know about Bell's idea of Nature, let alone that of EPR? He has not even read Bell's original paper, let alone read that of EPR and the later crucial elaborations on their paper by Bell, Clauser, Shimony, and others which I have closely followed in my analysis. So, I am afraid, I am not impressed by Boris's wrongful assertions about my work.
Best,
Joy
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Author Michael James Goodband replied on Sep. 19, 2012 @ 14:49 GMT
Hi Joy and Tom,
I agree that the issue of "disproof" is a linguistic one, but I would argue that it is an important one as the underlying issue is the choice between maths or physics. The use of the word "theorem" in the Bell context is a choice of maths meaning that is "simply a sells tactic" in the physics context, and until I read Joy's work I too fell for it.
I would question continuing to group EPR and Bell together as if they were dealing with the same physics context, as Joy's work shows that Bell's context is not the correct physics context for EPR - Joy's starting point is a statement of observational physics, for which one feels rather silly for not having noticed before. The real point in physics is that Bell's "theorem" is not the barrier to QT not being fundamental that the usage of the word "theorem" implies. Usage of "theorem" has been a very effective sales tactic that has effectively prevented searches for alternative explanations for QT for decades. In the physics context of what "Bell's theorem" has been claimed to mean, "disproof" seems appropriate to me.
I think that we probably agree that "no mathematical theorem is a scientific truth", the problem is that a great many physicists believe that Maths=Nature, which entails the belief that "a mathematical theorem is a scientific truth". It seems to me that some of the opposition that Joy is encountering is due this belief (the character of some of the responses seem to indicate that it is not a rational belief).
Michael
Joy Christian replied on Sep. 19, 2012 @ 15:40 GMT
Yes Michael, I tend to agree with what you have summarized.
We know, at least since Wigner, that interplay between maths and physics is a subtle one, and one has to be careful not to get carried away by maths as if it were physics. But maths is a siren too tempting for some, including myself.
Joy
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Author Michael James Goodband replied on Sep. 19, 2012 @ 15:53 GMT
Hi Jens and Tom,
There is a definite connection with Geoffrey Dixon and Cohl Furey - the difference is the discrete part of countable particles (by * I mean otimes):
Dixon considers the algebra: T=C*Q*O
Furey considers the algebra: R*C*H*O
I consider a physical manifold: S0*S1*S3*S7
The difference is between the space of an algebra and considering the physical...
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Hi Jens and Tom,
There is a definite connection with Geoffrey Dixon and Cohl Furey - the difference is the discrete part of countable particles (by * I mean otimes):
Dixon considers the algebra: T=C*Q*O
Furey considers the algebra: R*C*H*O
I consider a physical manifold: S0*S1*S3*S7
The difference is between the space of an algebra and considering the physical manifold for a cyclical (S1), closed universe (S3) with compactified particle dimensions (S7) in 11D GR without *any* additional fields. The previous issue with such pure geometric theories such as Kalzua-Klein theories has been: no particles, the discrete part - S0 for particle/anti-particle - has been missing. The existence of a non-trivial map (electroweak vacuum) from the S7 to the S3 is *critical* here, because it breaks the sphere S7 into S3 fibre and S4 base-space which further separates into S3 and S1. This transition from S7 to a space locally of the form (S3*(S3*S1)) gives the condition for topological monopoles/anti-monopoles and the required S0 to give the full picture with discrete particles - the correct spectrum of 12 fermionic topological defects. The same algebraic structure which gives the correct eigenvalues in the algebraic case of Dixon and Furey gives the same eigenvalues for the topological defects - despite a colour difference.
It is on this point of deriving the discrete part S0 of particles/anti-particles that my physical manifold framework differs with the others, and the pure octonion view. In those views the discrete part of particles has to be explicitly added *on top of* the algebraic view. Adding a continuous real number valued field, i.e. R, to the algebra of C*H*O (i.e. Furey) then has to add a means of getting the discrete part S0 from R for particles/anti-particles. This is natural for QT being fundamental - but it isn't! (see Joy's book or mine, or the papers).
The comparison of my results with those of Dixon and Furey reveals the critical difference and what may turn out to be the deciding factor:
1) If QT were fundamental then R*C*H*O would be the right (algebraic) choice and the colour group SU(3), but matter fields, electroweak vacuum and QT would have to be added by hand
2) If QT is not fundamental then the continuous physical manifold S1*S3*S7 with a twist in it (electroweak vacuum) gives discrete particles S0 and QT is *derived* as a change in mathematical representation, but the colour group would be locally SO(3) (not globally SO(3) because the colour space is S3 fibre of S7) by identifying physical spaces with group spaces. This identification gives the correct coupling constants for SU(2) and U(1) (and Weinberg angle) as geometric scale factors between the physical sub-spaces of the broken S7 and the unit spheres of the group spaces.
QT is proven *not* to be fundamental by 2 different routes (mine and Joy's). How to get QT and the discrete S0 of particle/anti-particle is the critical element - which is why it is the topic of my essay. What is the fundamental assumption standing in the way of physics? Answer: assuming QT is fundamental.
Michael
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Anonymous replied on Sep. 19, 2012 @ 16:25 GMT
Hi Michael & Joy,
Good discussion.
Allow me to reference the title of Michael's essay. I think we all agree that the answer is "no." I think we can all agree that the continuum cannot be deduced from the assumption of discrete elements in a multiply connected space.
If I capitulate to agreement that Bell's theorem should never have been called a theorem, however, I am...
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Hi Michael & Joy,
Good discussion.
Allow me to reference the title of Michael's essay. I think we all agree that the answer is "no." I think we can all agree that the continuum cannot be deduced from the assumption of discrete elements in a multiply connected space.
If I capitulate to agreement that Bell's theorem should never have been called a theorem, however, I am compelled to say that the arithmetic arguments of Gill, Moldoveanu, Aaronson, et al are wrong. Except they aren't. According to all mathematical logic as we know and accept it, Bell's theorem and the inequality argument derived from it, is a logically closed judgment of how numbers behave -- as simple an an Excel program, as Gill describes it. As simple as a 2-player game with four outcomes and no equilibrium point, as Aaronson describes it. Anything we program as a continuous iteration of discrete values in a nonorientable measure space is going to give us those results, because the space is not simply connected. The outcome probabilities are true.
Michael, I am not convinced that most physicists think maths = nature. I think that they just don't care about the role of mathematical language in physics, and really why should they in any operational sense? One can roll the dice, input data to an Excel program, or feed random bits to Alice and Bob, and see what happens.
To convince someone that E(a,b) = - a.b requires the same level of physical demonstration as E = mc^2 because we cannot see a full 4pi rotation in a simply connected space that Joy's result implies, any more than we can see the atomic binding energy that supports Einstein's result, until after experimental data are compiled. So it is at least as clear to me -- as I think it is to Boris Tsirelson -- that there *is* a profound difference between conventional interpretations of quantum theory via Bell's theorem -- and Joy's framework, which is not another QM interpretation but an entirely different framework for predicting quantum correlations.
I don't want to be put in the position of debating the meaning of "theorem" with mathematicians, because I know I am going to lose if I allow a theorem to be the subject of disproof. When I talk to a mathematician, I want only to be clear that we are working in the same domain and range. Sure I agree with you both that Bell's theorem does not apply to the physical domain -- I said so in my essay. Only after we establish domain and range, can we speak of proof. So one can say that Bell's theorem is not proved in this domain of continuous measurement functions, not that it is disproved in some domain of probability measure.
All best,
Tom
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T H Ray replied on Sep. 19, 2012 @ 16:26 GMT
Don't understand why I keep losing my log in. The above is mone.
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T H Ray replied on Sep. 19, 2012 @ 16:34 GMT
" What is the fundamental assumption standing in the way of physics? Answer: assuming QT is fundamental."
Nailhead, meet hammer.
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Joy Christian replied on Sep. 19, 2012 @ 16:55 GMT
Tom,
"...Bell's theorem is not proved in [the] domain of continuous measurement functions, not that it is disproved in some domain of probability measure."
Fair enough.
What interests me and Michael, though, is that Bell's theorem is disproved in the *physical* domain. Who cares if it is proved in some mathematical domain that is irrelevant to physics?
Joy
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Thomas Howard Ray replied on Sep. 19, 2012 @ 17:01 GMT
"What interests me and Michael, though, is that Bell's theorem is disproved in the *physical* domain. Who cares if it is proved in some mathematical domain that is irrelevant to physics?"
We don't know what mathematical domain (if any) is irrelevant to physics. We do know, however, that the physical domain can be defined as the complete space of continuous measurement functions. Your framework captures it. Bell's doesn't.
Tom
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Joy Christian replied on Sep. 19, 2012 @ 17:18 GMT
"We don't know what mathematical domain (if any) is irrelevant to physics."
True.
But we *do* know---and precisely so---what physical and mathematical domains are relevant in the context of the EPR-Bohm experiment, which is the context of the Bell's so-called theorem. Bell and his followers were mistaken to think that his theorem is applicable in these domains. It is not, as I have shown.
Joy
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Author Michael James Goodband replied on Sep. 19, 2012 @ 17:28 GMT
Hi Tom,
I said many - not most - physicists seem to believe Maths=Nature; some can be found in this essay contest. Being lax about the role of mathematical language in physics can lead to explicit or implicit assertions of the form Maths=Nature slipping into physics unchallenged by those who don’t share this belief; the claim that Bell's theorem applies to EPR seems to be one of them. The...
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Hi Tom,
I said many - not most - physicists seem to believe Maths=Nature; some can be found in this essay contest. Being lax about the role of mathematical language in physics can lead to explicit or implicit assertions of the form Maths=Nature slipping into physics unchallenged by those who don’t share this belief; the claim that Bell's theorem applies to EPR seems to be one of them. The standard interpretation of QT doesn't depend on Bell; only the false "proof" of don't bother looking past QT depends on Bell and this gives the physics sense for Joy's "disproof". Joy's initial correction about the analysis of EPR (1 to 2):
1) A(n,l): R3*L -> S0
2) A(n,l): R3*L -> S2 sub S3
is basically just a piece of observational physics that is framework independent. An alternative description for Bell's Theorem would be that it is irrelevant to physics, but this fails to take into account the impact that the "proof" has had on physics. The phrasing of a "disproof" that the maths doesn't apply to EPR conflicts with maths usage and is consequently contentious, but on the other hand it parallels the inappropriate use of "proof" in the first place - which is really the point of Joy's work.
Joy's framework does have a non-trivial topological condition that differs from the flat empty space normally taken to be the background for QT. It is a condition I am happy with because the EPR scenario doesn't involve flat empty space, but the space around two particles and Joy's correlation results reproduce QT for this space not being the same as empty space far away from particles. In my case, particles are topological defects in spatial structure and so the space about 2 particles is non-trivial. For the conditions of EPR, space would be flat because the spatial curvature is within the hidden domain, but charges in dimensionally reduced theories give torsion in space - the same basic topological conditions on space as required for the correlation.
Einstein's hoped for elimination of probabilities from predicted measurement results doesn't really work out with a hidden domain because it is ... well ... hidden. So all measurement results involve an average over the hidden domain - such as Joy's correlation results. The difference is that this is just a normal classical physics average and not a "weird" quantum physics one - whether this would have quite hit the spot for Einstein is debatable.
Michael
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Thomas Howard Ray replied on Sep. 19, 2012 @ 17:35 GMT
"But we *do* know---and precisely so---what physical and mathematical domains are relevant in the context of the EPR-Bohm experiment, which is the context of the Bell's so-called theorem. Bell and his followers were mistaken to think that his theorem is applicable in these domains. It is not, as I have shown."
Conceded. :-)
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Joy Christian replied on Sep. 19, 2012 @ 17:49 GMT
"Conceded. :-)"
You are a true scientist, Tom.
Only a true scientist would have the courage to concede.
Joy
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Author Michael James Goodband replied on Sep. 19, 2012 @ 17:52 GMT
Hi Joy,
The comment by Jens with the references to Geoffrey Dixon and Cohl Furey, and my reply above, really crystallizes the point I made in my essay and that I was trying to make earlier to you about the colour group. Furey's algebraic space R*C*H*O reproduces the spins (H) and charge eigenvalues (O) for the particle symmetry group SU(3)*SU(2)*U(1) as would apply to a continuous field (R) with a cyclical (C) component, i.e. a wave (I mention this pattern in my book - it's in the Bodleian). This is what I would expect for QT being fundamental, but it isn't.
The equivalent physical manifold realisation S0*S1*S3*S7 arises in 11D GR with no added fields - Einstein's vision with the number of dimensions specified :) - and QFT is derived through dimensional compactification and a representational change. BUT the colour space is the S3 fibre of S7, which means that it cannot be SU(3) but locally SO(3). These 2 features seem to be linked: continuous QT matter fields and SU(3); or discrete particles and SO(3). Take out QT as being fundamental and the space-based approach seems destined to dispute the colour group - that would seem to include your framework.
Michael
Thomas Howard Ray replied on Sep. 19, 2012 @ 17:52 GMT
Hi Michael,
" ... all measurement results involve an average over the hidden domain - such as Joy's correlation results. The difference is that this is just a normal classical physics average and not a 'weird' quantum physics one - whether this would have quite hit the spot for Einstein is debatable."
Good point. You're preaching to the choir as to whether Joy has it right (it's a great 'sermon,' however, and I appreciate your beautifully compact way of explaining things).
The above is something I looked at very early on when assessing Joy's research -- whether or not we would have to apply some Bayesian-type reasoning to connect the dots of statistical inference, in which case I would have a hard time accepting the completeness of the result. I was relieved to find -- not. Personally, I think Einstein would have agreed in principle at least, that correspondence between the mathematical prediction and the experimental data keeps things kosher, in the context of rational science.
Tom
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Joy Christian replied on Sep. 19, 2012 @ 18:47 GMT
Michael,
Thanks for your comments. It is good to know that your book is in the Bodleian. I did have a look at it at amazon.co.uk, but 45 pounds is bit steep when my detractors are trying to cut off all my financial resources. In any case, I intend to take a serious look at your papers as soon as I get a chance. Your comments here will certainly help me to understand your point of view quicker.
Joy
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Thomas Howard Ray replied on Sep. 21, 2012 @ 10:37 GMT
Joy,
Thank you for the vote of confidence. There isn't any higher compliment that I could have wished for. You know that I feel the same toward you, Michael and all the other members who practice the standards of objective knowledge.
I hope you all can visit my site where I posted an attachment that I think lays to rest the misguided arguments over arithmetic and probability that Gill particularly has been flogging for the last year or so. It's a direct comparison of the incomplete probabilistic measure model to a complete continuous measurement function. Because the comparison is head-to-head in 2 dimensions, it preempts any objection of extra dimension mathematical trickery, and explains why LH and RH independence doesn't break any algebraic rules (I linked Joy's one-page paper, which I still don't understand why anyone has such a hard time comprehending).
Anyway, I would be interested if one can spot any errors in this argument.
All best,
Tom
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Anton W.M. Biermans wrote on Sep. 18, 2012 @ 03:12 GMT
Dear Michael,
''The experimental observation of electrons passing through slits generating the wave characteristic of an interference pattern challenges this divide, although this is only really clear when the electron beam intensity is reduced to the point of a single electron passing through the slits at a time.''
If we were to assume that we live in a universe which creates...
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Dear Michael,
''The experimental observation of electrons passing through slits generating the wave characteristic of an interference pattern challenges this divide, although this is only really clear when the electron beam intensity is reduced to the point of a single electron passing through the slits at a time.''
If we were to assume that we live in a universe which creates itself out of nothing, without any outside interference so particles have to create themselves, each other, then it seems logical to assume that particles and particle properties must be as much the product as the source of their interactions. If so, if particles in such universe only exist to each other if, as far and as long as they interact, exchange energy, with all particles within their interaction horizon, then the electron, on nearing the slits, would 'see' its world split into two slightly different worlds, worlds which from both sides of both slits interfere with its path.
As to its wave character, the Uncertainty Principle (UP) is interpreted to say that virtual particles can appear by borrowing the energy to exist from the vacuum, for a time inversely proportional to their energy. This suggests that real particles can be thought of as virtual particles which by alternately borrowing and lending each other the energy to exist, force each other to reappear again and again after every disappearance, at about the same place. As in this view particles express and at the same time preserve each other's mass by continuously exchanging energy (the sign of which then alternates), the origin of mass is obvious, as is the equality of inertial and gravitational mass.
The hidden variables Einstein wanted to exist to avoid indeterminism can be identified as the energy exchange by means of which particles express and preserve each other's properties. However, the unpredictability Einstein wished to eradicate remains if particles indeed are as much the effect as the cause of their interactions. It is because their exchange is unobservable as long as the particles are at equilibrium, because it serves to preserve the status quo, that we have been able to remain ignorant of it: because we've always assumed that particles only are cause of forces. Only when their equilibrium is disturbed so the frequencies they exchange energy at changes and net energy is emitted or absorbed, the effects of this exchange become observable. In the study I propose a mass definition based on the UP: the less indefinite the position of a particle (or mass center of an object) is, the greater its mass is, a definition which might make it possible to derive the equations of relativity from the UP. For other interesting features of a self-creating universe, see my essay or the more extended study at www.quantumgravity.nl (which also contains some remarks on (CTRL+F) 'Gödel).
Regards, Anton
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Author Michael James Goodband replied on Sep. 19, 2012 @ 18:38 GMT
Dear Anton,
The notion of a self-creating particle that you allude to could be one way of viewing the problematic dynamics that I identify in my essay for a "bare" particle being a topological defect in space. In my pure GR theory, such topological defects have the appearance of Planck scale black holes bearing charges, but their spinning creates an ergo-region that can contain virtual radiation. Despite virtual matter appearing in QT, it is actually a relativistic concept m^2
Hoang cao Hai wrote on Sep. 22, 2012 @ 20:31 GMT
Dear Michael James Goodband
Of course the physics indispensable the quantum theory,because it is the basic values that constitute all.
Maybe I understand your problem,let try temporarily excluded all equations and formulas of mathematical in your essay(they are still unknown and there is not enough data)and see a very simple idea of mine:
The ABSOLUTE THEORY of me and an explanation of the nature of the Mass :
Be identified due to the change by the purely feel and rely on
the determination by our measurement equipment.
Must be the impact to get this changes,and the absolutely is only
one the mainly reason,that of course is the impact of a type of
the force.
So: the absolutely nature or the definition of mass would be:
Expression due the impact of force on to the material.
What do you think about this idea?
Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?
The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?
Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?
Kind Regards ! Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY
August 23, 2012 - 11:51 GMT on this essay contest.
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Jonathan J. Dickau wrote on Sep. 25, 2012 @ 02:59 GMT
Hi Folks,
I appreciate the kind remarks by Joy in response to my comments above. I also greatly appreciate the comparison by Michael of his work with that of Dixon and Furey. I was just reading from Dixon's recent work earlier today, so it was nice to see the differences spelled out.
Sorry for not commenting sooner. I'm catching up here after a hiatus to take care of unexpected responsibilities. But I'm happy to see such interesting exchanges in the comments above.
As regards the people who confuse Math and Physics; I think that Hestenes has the right idea - that the need for congruent Geometry determines what mathematical possibilities are physically realistic. It's easy enough to use symbolic Math to create expressions that don't make sense geometrically, but I think good geometry is what nature requires.
This is why Michael's approach is different from Dixon's or Furey's, though some might confuse them. This same confusion explains why some people fail to grasp Joy's central point. Michael and Joy both make Geometry fundamental, and use the Maths to represent the geometry. Those who do the reverse or believe the algebra is more fundamental see things differently.
Regards,
Jonathan
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Author Michael James Goodband replied on Sep. 25, 2012 @ 12:08 GMT
Hi Jonathan,
On comparison with Dixon and Furey, they are attempting to match up the symmetry groups SU(3), SU(2), U(1) with the algebras O, H, C, which they do but fail to find the 3 families of particles. I contend that this is because the colour group isn't really SU(3) but Spin(3). I followed field theory practise of focusing on the local structure and gave SO(3), which in retrospect...
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Hi Jonathan,
On comparison with Dixon and Furey, they are attempting to match up the symmetry groups SU(3), SU(2), U(1) with the algebras O, H, C, which they do but fail to find the 3 families of particles. I contend that this is because the colour group isn't really SU(3) but Spin(3). I followed field theory practise of focusing on the local structure and gave SO(3), which in retrospect wasn't helpful because simple representation arguments rule out SO(3) as the colour group BUT they do not apply to its double cover Spin(3) [the group space of SO(3) is S3 with opposite points identified, which won't give the colour and anti-colour in a meson, but the group space of Spin(3) is the full S3, and so includes the required opposite points]. With colour group Spin(3), the group spaces are S3, S3, S1 and fit into S7. In conceptual terms, remove the unbroken U(1) of electromagnetism from S7 to give S6 and map to a spatial sphere S2 - the homotopy group is PI6(S2) = Z12 = Z3*Z4 and so gives a 3 by 4 table of topological monopoles. The non-associativity of the octonions is conceptually the reason why there are 3 families of 4 particles each: trying to match a colour group of SU(3) with the octonions won't give the correct spectrum of 12 particles in this way. Geometry triumphs over Algebra?
I have also found the point of view for comparison with Joy's work: view the hidden domain as being of finite size with an enclosing S2 surface. The map of the rotation group space S3 to this S2 has 2 orientations for homotopy group PI3(S2)=Z2 [note this is stamped on by the fibre bundle mapping with homotopy group PI3(S2)=Z but the Z2 one fits a general SN pattern and is still there]. The map of a compactified S7 space associated with particle symmetries to this S2 also has 2 orientations, as homotopy group is PI7(S2)=Z2. When the hidden domain surface S2 only encloses empty space, the symmetry operations of rotation (S3) or particle symmetries (S7) are free to act everywhere to rotate +1 orientation into -1 orientation as they are reachable through S3 or S7. BUT when the hidden domain encloses holes in space (as in STUFT) or singularities where the symmetry operators don't apply, this is not possible and the hidden domain S2 surface will have an orientation.
As
STUFT is about a physical space with a metric, Joy's Clifford algebra approach where the hidden variable IS the orientation, effectively constitutes the correct framework for analysing singlet states of topological monopoles in STUFT. Specifically, the topological orientation feature that seems to have raised objections IS precisely the feature generated by the topological monopoles of STUFT. The hidden feature is whether the particles are AB or BA, but AB = -BA as both the quaternions and octonions are non-commutative and this is effectively manifest on the S2 surface of the hidden domain as an orientation - the hidden variable.
I am in the process of preparing a short article outlining the topological features of STUFT and this comparison with Joy's work - it is taking longer than expected.
Michael
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Joy Christian replied on Sep. 25, 2012 @ 12:50 GMT
Hello Everyone:
Michael,
I am both delighted and curious about what you say in the last two paragraphs above. I eagerly look forward to your new article.
Tom,
I looked at your latest attachment but couldn't really understand it---may be because I am too distracted at the moment by life in general. I must meet a couple of deadlines and there is also some progress being made on the experimental front. But I want to thank you for your continuing efforts to explain things your way. We have to accept, however, that some people will never get the point.
Jonathan,
You wrote: "Michael and Joy both make Geometry fundamental, and use the Maths to represent the geometry. Those who do the reverse or believe the algebra is more fundamental see things differently."
I couldn't agree more. This, however, does not undermine the importance of algebra in our works.
Best,
Joy
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Author Michael James Goodband replied on Sep. 25, 2012 @ 15:33 GMT
Hi Joy,
I have yet to accomplish the final critical step in the comparison as I am currently distracted by what looks as though it will prove to be a fruitless essay contest, despite the essay presenting the correct false assumption that is preventing progress towards physics unification (also outlined in the essay).
A hidden domain containing either holes or singularities and being...
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Hi Joy,
I have yet to accomplish the final critical step in the comparison as I am currently distracted by what looks as though it will prove to be a fruitless essay contest, despite the essay presenting the correct false assumption that is preventing progress towards physics unification (also outlined in the essay).
A hidden domain containing either holes or singularities and being bounded by S2, to which the S3 spin space or S7 particle symmetry space is mapped is the basis for comparison as it is the basis of the topological monopoles. The global mapping of S7 to the spatial S3 breaks the particle symmetry space S7 into its subspaces S3, S3, S1, but also breaks the isospin symmetry with the second S3 space - so that can be crossed out. This leaves intact the particle physics symmetries of spin (S3), colour (also S3 for colour group Spin(3)) and electromagnetism (S1) which are the subspaces of S7. Interpreting your results in this context would mean that for any number of correlated particles within the S2 of a hidden domain, these 3 spaces fit together into S7. For the simple topological monopole/anti-monopole (S0) case with charges arising from S7 and spin (S3), this doesn't look likely ...
BUT this doesn't take into account the entire point of my essay: the discrete monopole theory is mathematically incomplete, and for them being particles (S0) the wave property (S1) is the undecidable feature and gives wave-particle duality - the Hopf fibre bundle S1. Particles would then simultaneously be in representations of: S0 - particle; S1 - wave; S3 - spin; S7 - charge, which in itself gives a significant uniqueness condition (as stated in the book). The combining of spaces S3 (spin), S3 (colour), S1 (electromagnetism) in S7 for any number of correlated wave-particles (fibre bundle S1) within a S2 hidden domain then has this extra significant factor.
The non-associativity of the octonions would seem significant in resolving this general embedding issue, which appears to be the crux of establishing equivalence, but is currently the open problem ...
Michael
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Joy Christian replied on Sep. 25, 2012 @ 16:16 GMT
Hi Michael,
Thanks for the update. There is no rush about this. Please take your time. It is important to get the comparison right, if it is indeed possible.
One thing you may want to keep in mind is the way I handle the non-associativity of S7 in my framework. I simply sidestep it. Since Clifford algebra is associative, what I do is trade the non-associativity of S7 in for variable torsion (i.e., different torsion tensor at each point of S7). This is a nifty trick I learned from some string theory and super-symmetry folks. Full details can be found in Section 7.4.5 of my book.
Joy
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Rick Lockyer replied on Sep. 25, 2012 @ 16:23 GMT
Hi Michael,
I must say I find your ideas and discussion very thought provoking. I thank you for this. While this may not help you through your angst about this "fruitless essay contest", let me say I feel your pain.
On your statement AB = -BA for Quaternions and Octonions, this is strictly speaking true for only non-equal non-scalar basis elements, which I would suggest have insufficient standing for the points you are trying to make.
The nice thing about each of these algebras is that both the commutator A*B – B*A and the associator A*(B*C) – (A*B)*C do not include the full set of product terms. This means portions of algebraic expressions may be commutative and some may be non-commutative (but expressly anti-commutative) and some portions may be associative and others may be non-associative (but expressly anti-associative). If you accept Octonion Algebra and its subalgebras are fundamental, there is no conflict with any physical need for commutation or associativity, or non-commutation and non-associativity. The important thing to keep in mind is this all is relevant for algebraic expressions that include multiplication, not delineated topology or geometry, nor a narrow view of the algebraic rules by themselves. There is the space of algebraic results after application of these specific and instructive algebraic rules. What about the topology of this space or its geometric implications?
This need to delineate, to separate physics from math, algebra from geometry, etc.; what is the point, the benefit in doing this, the validity of doing this? I see none. Jonathan?
Rick
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Thomas Howard Ray replied on Sep. 25, 2012 @ 17:28 GMT
Hi y'all,
Michael, I wouldn't call it fruitless -- there's life after the essay contest, and you've already breathed plenty of potential into it already. I have a strong feeling that this enterprise will succeed, and history is being made here.
I'm at a disadvantage in connecting the mathematics to particle physics; frankly, my eyes glaze over at the subject. As an analyst, my head wraps naturally around field concepts, as in Joy's comment, " ... what I do is trade the non-associativity of S7 in for variable torsion (i.e., different torsion tensor at each point of S7). This is a nifty trick I learned from some string theory and super-symmetry folks." Yes, indeed, that physical reality manifests as field excitations of continuous variability easily translates to continuous discrete measurement functions -- Joy, I hope you see that as key to understanding the attachment I posted. All it requires is orientability and global continuity -- both of which are supplied by any simply connected topology. In my language, continuous curves are traded for discrete points (infinite quantization obviates collapse of the wave function).
All my best to Jonathan and Rick, too ...
Tom
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Author Michael James Goodband replied on Sep. 25, 2012 @ 17:50 GMT
Rick,
The statement AB = -BA was made in the context of a singlet state of 2 particles (for which it is true in both H and O), and not for general A and B. The A and B were a reference to the observers Alice and Bob when they measured the spins or particle charge vectors - a mixture of terminology, sorry for the confusion.
The topological mapping and geometry arguments outlined above give the limit of what can be reached in such conceptual terms. The issue of whether the wave(S1)-particle(S0) fibre-bundle for the particles inside the S2 hidden domain provides the necessary element that can combine the unbroken symmetry spaces spin S3, colour S3 and electromagnetic S1 into S7 requires algebraic proof. Having reached what feels like a delineation between geometry and algebra, apparently there is one.
The spin space S3 has a spatial origin, whereas colour space S3 and electromagnetism S1 have an origin in the particle symmetry space S7 in STUFT - so the spaces are in a physical sense "alien" to each other. It seems to be the very features you describe which make it even conceivable for these "alien" spaces (spin and the particle symmetry spaces) to cohabit the same S7 and so meet the general correlation condition of Joy's work.
Tom
The particle physics is inside the hidden domain, but for those particles being topological monopoles, that topology is projected onto the S2 surface enclosing the hidden domain. Sort of doing particle physics, but without the particles. Although the process seems to also require turning the wave(S1)-particle(S0) duality similarly into a topological condition projected onto the S2 domain surface. Any ideas?
Michael
Joy Christian replied on Sep. 25, 2012 @ 22:13 GMT
Rick,
I have a question for you.
As is well known, in 1956 Milnor made the sensational discovery of smooth manifolds that were homeomorphic to the 7-sphere but not diffeomorphic to it (cf. the attached paper).
My question to you then is: How does the discovery of exotic spheres fit-in with your rather algebraic perspective? Do you think that Milnor, or someone else, could have discovered the exotic spheres by purely algebraic means?
If "yes", then can you please sketch a possible line of reasoning which could lead us to such a discovery?
If "no", then doesn't that count against your insistence on a predominantly algebraic methodology in physics?
Please don't take my question the wrong way. I am just trying to understand how far you think your algebraic perspective can lead us. Can it lead us all the way?
Thanks,
Joy
attachments:
Exotic.pdf
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Jonathan J. Dickau replied on Sep. 26, 2012 @ 02:59 GMT
Hello Folks,
Paul Kainen made a comment in a paper (attached) on Octonion Physics that answers Rick's question to me, addresses Joy's challenge to Rick above, and relates to Michael's description of the open problem above that. Kainen wrote:
"Of course, multiplication in the octaval arithmetic fails to be either commutative or associative, but that could be a blessing in disguise. If multiplication depends on the order of the elements being multiplied together and even on how they are grouped, then at one fell swoop, geometry enters the calculation in an organic way. The Principle of Indeterminacy could then arise in a natural fashion from relativistic considerations, making quantum theory a consequence of an underlying 8-dimensional hidden-variable process, very much in the flavor of the theories of de Broglie and Bohm. Uncertainty of measurement would be a corollary of our inability to absolutely order events or to absolutely control the way in which they are grouped."
When Michael said above "The non-associativity of the octonions would seem significant in resolving this general embedding issue, which appears to be the crux of establishing equivalence, but is currently the open problem ..." I think this is partly addressed by this quote. It speaks to the unity of algebra with geometry. But it also nicely illustrates how the fact that the Octonions "don't let you drive" can be advantageous.
Regards,
Jonathan
attachments:
1_octophys.pdf
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Jonathan J. Dickau replied on Sep. 26, 2012 @ 03:28 GMT
Hello Michael and Friends,
My comment above has a wonderful quote from Paul Kainen, about how the non-associativity of the Octonions could be a blessing or solution rather than a problem. I'd like to elaborate here. I think Rick's insistence that the Octonions 'don't let you drive' is partly based on the fact that they are drivers themselves, or tend to drive process-like evolution - and guide it in a specific direction. I've been giving the idea quite a lot of thought and study lately, and I'm currently writing a paper relating to this matter. Briefly; it appears that not only are they heavy on dynamism, but the octonions drive processes through evolutionary stages.
Just a thought to stir the pot.
Regards,
Jonathan
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Thomas Howard Ray replied on Sep. 26, 2012 @ 09:33 GMT
Hi Michael,
You wrote: "The particle physics is inside the hidden domain, but for those particles being topological monopoles, that topology is projected onto the S2 surface enclosing the hidden domain. Sort of doing particle physics, but without the particles. Although the process seems to also require turning the wave(S1)-particle(S0) duality similarly into a topological condition projected onto the S2 domain surface. Any ideas?"
You bet! That's exactly what I implied in my
2006 paper by the continuous projection between S^1 and S^3 that I referred to yesterday in my forum. I don't think in terms of particles at all; they exist only as the result of measurement functions, not as "things."
Best,
Tom
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Thomas Howard Ray replied on Sep. 26, 2012 @ 10:53 GMT
Michael,
Attached, a particle experiment where particles aren't really particles, but measurement results of a continuous wave function.
Tom
attachments:
1_fermionic_condensate_test.pdf
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Author Michael James Goodband replied on Sep. 26, 2012 @ 11:24 GMT
Hi Jonathan and all
The octonions have a strange dichotomy between coherent whole and composite space. For example, my theory starts with the coherent whole of S7, but its mapping to a cosmological S3 breaks S7 into its components, where picking out the unbroken S1 of electromagnetism and mapping S6 to spatial S2 yields 3 families of 4 monopoles - surely because of the ability to pick out associative subsets from the non-associative whole. The trick Joy uses in Section 7.4.5 effectively selects a view of the octonions as a coherent whole by transferring the non-associativity to torsion of S7. In contrast, the issue I have is with the composite view: whether the differential manifolds of the particle symmetry spaces (S3, S3, S1) spaces can form S7. At best they could only give the topological S7 and *not* the differential manifold S7, which is what is required for Joy's parallelisation condition.
However, that condition applies to the codomain of a function A(n,l) that determines the expectation value of an observable. The factorisability condition (AB)(n,l)=A(n,l)B(n,l) expressing locality, and the notion of completeness give the condition of closure under multiplication for the observable functions. So for component spaces S3, S3, S1 - whatever their origin - this demands that from the perspective of observable functions these spaces *must* form the topological space S7, and then the parallelisation condition of Joy demands that it *must* be the differential manifold S7. This is effectively a top-down condition, whereas proceeding from the bottom-up the question is: how is Joy's requirement of the *observable functions* met?
Michael
Thomas Howard Ray replied on Sep. 26, 2012 @ 11:40 GMT
Michael,
Beautiful!
" ... whereas proceeding from the bottom-up the question is: how is Joy's requirement of the *observable functions* met?"
It doesn't have to be! The framework is fully relativistic (no preferred reference frame) and the geometry is coordinate-free. Top down and bottom up are both manifestly local.
Tom
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Author Michael James Goodband replied on Sep. 26, 2012 @ 11:52 GMT
Hi Tom
Thanks for your kind words earlier.
On the subject of dealing with particles, without the particles, I have a question: does my condition that the hidden domain of Joy's analysis be enclosed by a S2 surface give a form of the holographic principle?
For the hidden domain containing topological monopoles, the S2 surface - with a radius small enough to render it hidden -...
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Hi Tom
Thanks for your kind words earlier.
On the subject of dealing with particles, without the particles, I have a question: does my condition that the hidden domain of Joy's analysis be enclosed by a S2 surface give a form of the holographic principle?
For the hidden domain containing topological monopoles, the S2 surface - with a radius small enough to render it hidden - can be labelled with the spin and particle charges within; for a singlet state this labelling includes a non-trivial spin and particle symmetry orientation, but as hidden variables. The S2 surface can be labelled with all the values of its contents for the case where those contents are topological monopoles and so the properties of the hidden contents of the domain are in effect projected onto the S2 surface.
Joy's Clifford algebra formulation proceeds on the basis of the hidden variable being an orientation - although not explicitly of such an S2, it is compatible with this interpretation. With this view, Joy's framework connects experimental correlation results with the topological properties of the S2 surface. In which case, experimental results viewed through the perspective of Joy's framework would determine the properties of the S2 surface, and so apply constraints upon the possible theory describing the contents of the hidden domain. Given the uniqueness conditions I find for my theory, I have an obvious suspicion about the answer.
I would note that the purely geometric view only gives topological monopoles/anti-monopoles (space S0), but no wave property. The replacement of S0 by the S1 fibre-bundle of wave(S1)-particle(S0) duality for the particle content of the hidden domain marks the transition which is normally associated with the appearance of QT. So the theory of the hidden domain would have to explain the origin of this replacement. In my work this comes from a replacement of the integers with the reals, which has underlying it issues about the "geometry" of (infinitely recursive) functions over the counting numbers compared to the reals. As you know, this is a separate issue from the S7 space of the observable functions, but surely it impacts the nature of the functions themselves?
Michael
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Rick Lockyer replied on Sep. 26, 2012 @ 16:43 GMT
Joy’s question to me in this thread probably would have been better suited for my essay blog, but since it was posted here I will try to answer it here. I have only done a small amount of thinking about algebra : topology -> homeomorphic topology : algebra in terms of algebra algebra if this is what you are getting at, and had previously read about exotic spheres. On the question of whether...
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Joy’s question to me in this thread probably would have been better suited for my essay blog, but since it was posted here I will try to answer it here. I have only done a small amount of thinking about algebra : topology -> homeomorphic topology : algebra in terms of algebra algebra if this is what you are getting at, and had previously read about exotic spheres. On the question of whether or not one could demonstrate the diffeomorphism issue with exotic spheres in a purely algebraic fashion, I have neither answer nor informed opinion or guess. On the question of how it fits in to my “rather algebraic perspective”, I can’t say it does.
Understand that I do not think all of physical reality is on the unit 7-sphere. Within my perspective I fully expect the p coefficients for the native Octonion position algebraic element p_i e_i to freely range from +oo to – oo. This is not to say I think your representation as well as Michael’s can’t be so restricted, because I actually agree they may. But this does not require me to be similarly restricted, nor does it preclude my approach from having some topological agreement at some level of abstract representation.
I am not looking to morph coffee cups into donuts. My Ensemble Derivative indicates the proper transformation characteristics for an Octonion analytic form within a single topological space. The 1/J scaling emphasizes the requirement for the Jacobian of any suitable transformation to be non-zero hence reversible hence a diffeomorphism. It works, as demonstrated by demanding the Lorentz transformation for EM.
Octonion Algebra demands the form of the Ensemble Derivative and the Law of Algebraic Invariance as stated. The need to have algebraic invariance within covariant differential equations on potential functions describing observables produces equations of algebraic constraint. It dictates the form for the mathematical expression of all stresses, strains that must integrate to zero to describe stable stuff, be it electrons, protons, neutrons, atoms, photons, etc. I have provided the explicit form for all of this, and nothing is inserted “by hand”. Is there enough there to “lead us all the way” as you ask? I think there is enough to produce a family of solutions for the potential functions that would give us a clear picture of just what reality is. Achieving these solutions I think will be a non-trivial task. I loathe solving differential equations, and really wish people with better skills would jump in.
One question to all: if you do not plan on "doing the math" in both homeomorphic topologies, does it matter if they are not diffeomorphic? I wonder if this precludes some meaningful connection.
Does this answer things satisfactorily?
Rick
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Thomas Howard Ray replied on Sep. 26, 2012 @ 17:35 GMT
Hello Michael,
" ... does my condition that the hidden domain of Joy's analysis be enclosed by a S2 surface give a form of the holographic principle?"
My opinion? -- Yes. And I base it on first principles alone: simple connectivity, orientability, geometric projection. As I note in my essay, the strength of quantum correlations orients complementary quantum properties on a line...
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Hello Michael,
" ... does my condition that the hidden domain of Joy's analysis be enclosed by a S2 surface give a form of the holographic principle?"
My opinion? -- Yes. And I base it on first principles alone: simple connectivity, orientability, geometric projection. As I note in my essay, the strength of quantum correlations orients complementary quantum properties on a line from the horizon, to a middle value. Because the middle value sweeps the entire horizon, holographic projection is assured.
Making this mathematically rigorous will, I am confident, depend heavily on the non-trivial topological properties of S^3 (as Joy has frequently emphasized). Of the four spacetime dimensions,because S^2 is the middle value of the parallelizable S^0, S^1, S^3, S^7. we should expect a continuous projection on the S^2 manifold between S^1 and S^3.
"I would note that the purely geometric view only gives topological monopoles/anti-monopoles (space S0), but no wave property."
Yep. That's why probabilistic functions on the interval {- OO, + OO} cannot provide a space of complete measurement functions.
"The replacement of S0 by the S1 fibre-bundle of wave(S1)-particle(S0) duality for the particle content of the hidden domain marks the transition which is normally associated with the appearance of QT. So the theory of the hidden domain would have to explain the origin of this replacement."
And would have to include a continuous wave function, rather than a probability function.
"In my work this comes from a replacement of the integers with the reals, which has underlying it issues about the "geometry" of (infinitely recursive) functions over the counting numbers compared to the reals."
Right on, brother. It's what motivated my NECSI ICCS 2006 paper, getting a well ordered counting function without Zorn's lemma (axiom of choice). Eliminates a host of evils.
"As you know, this is a separate issue from the S7 space of the observable functions, but surely it impacts the nature of the functions themselves?"
You bet it does. It makes orientability work in every simply connected space of S^n. Seeing the limit of S^n physical space in Joy's research (corroborated by Hestenes's spacetime algebra and Rick's octonion space) was a major piece of the puzzle for me. Then getting the S^3 X S^7 ---> S^10 mapping from your research explains discrete particle events without having to assume discrete particles. I like!
All best,
Tom
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Joy Christian replied on Sep. 26, 2012 @ 21:14 GMT
Hi Rick,
Thank you for your detailed reply. I appreciate that.
You kind of addressed my question. Let me summarize what I have gathered from your answer.
You wrote: "On the question of whether or not one could demonstrate the diffeomorphism issue with exotic spheres in a purely algebraic fashion, I have neither answer nor informed opinion or guess. On the question of how it fits into my "rather algebraic perspective", I can't say it does."
Well, for what it's worth, my guess is that one cannot address the diffeomorphism versus homeomorphism issue of exotic spheres in a purely algebraic fashion. Therefore I am not surprised that it does not fit into your algebraic perspective.
Having said that, I do appreciate the power and versatility of your approach---your results speak for themselves! But I think it leaves out important, global aspects of the 7-sphere, such as Milnor's startling discovery. And that is what I was deriving at. The issue, for me, is not about homeomorphism versus diffeomorphism. The issue is about local versus global. And your approach is at best silent on that issue.
Joy
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Joy Christian replied on Sep. 27, 2012 @ 08:40 GMT
Typo: In the last para I meant "driving at" not "deriving at."
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Author Michael James Goodband replied on Sep. 27, 2012 @ 10:24 GMT
Hi all,
Local-global differences are at the heart of this algebra-geometry issue: algebra can see the local, but it requires geometry to see the global. I stumbled across a quote by David Hestenes and Garret Sobczyk which seems to capture it:
"Geometry without algebra is dumb! - Algebra without geometry is blind!"
Edwin's point in the thread below is about the struggle with...
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Hi all,
Local-global differences are at the heart of this algebra-geometry issue: algebra can see the local, but it requires geometry to see the global. I stumbled across a quote by David Hestenes and Garret Sobczyk which seems to capture it:
"Geometry without algebra is dumb! - Algebra without geometry is blind!"
Edwin's point in the thread below is about the struggle with the local-global difference, where conceiving S3 as locally being S2*S1 but globally a sphere and not a torus is doable, but S7 is just that more difficult.
Equivalence of my work with Joy's framework would be strictly local as formulated, because it is GR with curvature. But as all the relevant experiments would similarly be local, this is not really an issue. I have a critical global condition of the electroweak vacuum being a map from S7 to S3 in the product space S3*S7, which is globally a torus - a hole has to physically inserted into the "unified" S10 to get the global change from a sphere to this torus. It is this mapping S7 to S3 which picks out a S3 from the S4 base-space of S7 (the coordinate parameterisation given in my essay notes indicates that this S3 is not just the S4 equator). The identification of the S7 subspaces defined by the electroweak vacuum map with group spaces gives the form of the *local* theory in the "broken" S3*S7 phase - note physical spaces in the global theory become group spaces in the local theory. As Lie group spaces are parallelisable, it is this identification (common to Kaluza-Klein-style dimensional compactification theories) which gives the parallelised spheres (spin S3, colour S3, electromagnetism S1) in the *local* form of the theory. The possibility of a flat S3 cosmology with teleparallel gravity, suggests that the product space S3*S7 being a flat torus with a global electroweak map from S7 to S3 may also be possible. This would require the map to be a precondition, something which unifying S3*S7 into S10 by a topological transition removes - hence its appeal to me. There are also GR issues which are resolved by the same S10 unification.
Michael
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Rick Lockyer replied on Sep. 27, 2012 @ 16:41 GMT
Michael,
“Geometry without algebra is dumb” is on the money. The second half: “Algebra without geometry is blind” certainly works for algebra applied to physical reality but not for algebra in total. Your conclusion “algebra can see the local but it requires geometry to see the global” is somewhat counter-factual if you admit geometry generally (more than the “dumb”) requires algebraic expressions for its representation, since the two cannot then be cleanly bifurcated.
I think we could come up with a similar quote using mathematics and physics instead of algebra and geometry. And just what is this algebra – geometry controversy anyway? I hope you are not including me in it based on my detailed analysis of Octonion Algebra and attempts to use it to define a better mathematical basis for Physics. Joy’s response here that my approach does not address “the global” suffers from too narrow a view on just what this means and just what I am trying to accomplish.
Mathematics per se, physics, topology in many forms, algebra, geometry, and group theory etc. are all interlocking components of physical reality. I see no justification for pitting one against another. Anyone needing to be dismissive of any should re-evaluate their position, for it should be interpreted as a well lit billboard sized warning sign stating “Dead End Ahead”.
Rick
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Thomas Howard Ray replied on Sep. 27, 2012 @ 18:29 GMT
Joy, shut up and derive. :-)
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Joy Christian replied on Sep. 27, 2012 @ 18:54 GMT
Michael,
Here is a better quote, from Michael Atiyah:
"Algebra is the offer made by the devil to the mathematician. The devil says: I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvelous machine."
Sorry, Rick. I couldn't resist (I know; I am being frivolous).
Tom, I can both drive and derive at the same time!
Joy
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Rick Lockyer replied on Sep. 27, 2012 @ 19:01 GMT
Joy,
With the response I am getting in this essay contest, I am sure many yelled out “Blasphemer. Stone him, stone him” as soon as they got to the word “Octonion” in the abstract, no need to read further. I am happy Michael is doing as well as he is, but he should be doing better.
Rick
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Thomas Howard Ray replied on Sep. 27, 2012 @ 19:11 GMT
I had not heard that quote of Atiyah, and I absolutely love it! It fits to a "t" Wheeler's information-theoretic view, imbedded in our classical world experience of continuous functions.
Tom
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Joy Christian replied on Sep. 27, 2012 @ 19:25 GMT
Attached is a talk given by Sir Michael at Princeton a year or so ago.
It seems appropriate to attach it here, for he too is one of us---namely, an octonion.
attachments:
AtiyahTalk.pdf
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Author Michael James Goodband replied on Sep. 28, 2012 @ 12:29 GMT
Joy,
That's a wonderful quote! I have to admit that I was a reluctant octonion, but not accepting one's own conclusions would just be bad form.
Coming from a QFT view, my natural way to accommodate QT not being fundamental is to just accept it as an approximate descriptive form with illusions, and not try to interpret them literally. Your experience seems to indicate an attachment by some to the illusions being literal. Since to me it is just about description, I accept that there may be another way. Proponents of geometric algebra have to my mind clearly demonstrated that in some sense it is the natural way to describe space, as the descriptive form is free from the illusions - such as in your work.
Tom,
Before you get too excited about the idea of dealing with particles without having particles, a hidden domain enclosed by a small radius S2 looks somewhat like a particle itself, or a type of multi-particle containing any number of correlated particles. It is also only a non-relativistic view that doesn't include particle reactions that change particle numbers ... yet?
What the octonion view of such a 2D surface (homeomorphic to S2) does give you, is an easy explanation of colour confinement. With coloured particles being topological monopoles with unbroken symmetry group (Spin(3)*U(1))/Z_3 the same topological unwinding arguments as for topological defects in field theory can be applied, with conclusions:
1) a monopole/anti-monopole pair are connected by a colour string
2) the Z_3 means that the colour field of 3 coloured monopoles with no net colour charge can be unwound outside of the S2 domain
Energy minimisation then implies the S2 is shrunk to the smallest size possible, giving colour confinement in classical physics - because the monopoles come from S7. This adds to the suspicion that the conclusion is going to be, in the words of Clinton: it's the octonions, stupid ;-)
Michael
Joy Christian replied on Sep. 28, 2012 @ 13:07 GMT
Michael,
I too have been a reluctant octonion. "Extra dimensions" were anathema to me until my own investigations in the origins of quantum correlations persuaded me otherwise. There is no way to reproduce all of the observed quantum correlations local-realistically without embracing the octonionic 7-sphere fully. All other attempts to understand quantum theory will eventually hit a brick wall. In this context my attitude towards the octonion algebra is very much the same as Rick's.
On the other hand, you are right to think that the proponents of geometric algebra have got it right. The credit for their insight, however, must go to Hermann Grassmann first before anyone else (cf. the attached slides).
Joy
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Rick Lockyer replied on Sep. 28, 2012 @ 18:28 GMT
Joy,
Sounds like you want to have your cake and eat it too: non-associative Octonion Algebra and associative Geometric Algebra.
Rick
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Joy Christian replied on Sep. 28, 2012 @ 18:50 GMT
Absolutely, Rick. That is exactly what I want, and can have it too.
I use Clifford algebra for octonions following Lounesto (cf. the first attached paper), with an additional trick I learned from string theory and super-symmetry folks. I trade the non-associativity of S7 in for variable torsion (i.e., different torsion tensor at each point of S7). Full details can be found in Section IV.E of the second paper attached. This is very convenient and well suited for my work.
attachments:
Lounesto.pdf,
6_1101.1958v1.pdf
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Author Michael James Goodband replied on Sep. 29, 2012 @ 14:10 GMT
Hi Joy,
Can any physical significance be attached to the torsion variation of the trick you describe?
I ask because in conceptual terms the correlation of observables is due to the torsion of the parallelised spheres, so variable torsion would conceptually be associated with some variation in observable correlations. I have yet to get to grips with how the trick works its way through to observable correlations. Since it is just a trick, any such variation would be equivalent to the effect of the non-associativity of the octonions.
Michael
Joy Christian replied on Sep. 29, 2012 @ 16:09 GMT
Hi Michael,
Yes, the variability of torsion within S7 is a measure of the non-associativity of the octonionic observables (which, in statistical terms, are the standard scores corresponding to the raw scores +1 or -1). So, indeed, variable torsion is associated with the variations in the observable correlations, and these variations are indeed due to the non-associativity of the octonions.
Now suppose the variation in the torsion happens to be zero in some special case. Then we would still observe quantum correlations as long as this torsion is non-zero, but they would not be due the non-associativity of the octonions. For example we could observe quantum correlations even when all of the observables are confined to a single fiber of S7---namely to some S3---despite the fact that the torsion within any S3 is always constant, because the quaternions that make up S3 are associative. To put it differently, when we have variations in the torsion we have variations in the observed correlations that are in addition to those arising from the non-commutativity of the quaternions.
Perhaps these additional variations can be understood as purely gravitational effects (as opposed to, say, strong or electro-weak effects) within your 11D GR?
Joy
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Author Michael James Goodband replied on Sep. 29, 2012 @ 17:27 GMT
Hi Joy,
If the S7 in question was the particle symmetry space, then such additional variations would almost certainly be inter-family correlations - e.g. between electron, muon and tau - which are outside the domain of strong and electro-weak interactions. The Z_3 of the monopole homotopy group PI_6(S^2) = Z_3*Z_4 gives 3 particle families, which is due to: the fibre-bundle structure of S7; the non-associativity of the octonions; and is presumably related to the triality discussed in the Lounesto paper.
In correlations between particles with spin (S3) and electromagnetic charge (S1), could the condition of the 3 particle families being entering into the analysis to require S7 and consequently these additional variations? This would appear to square with the origin of particles in my 11D GR. Unfortunately, my theory has the handicap on this issue of apparently saying that the CKM and PMNS inter-family transition matrices are not calculable (a further consequence of incompleteness).
Michael
Joy Christian replied on Sep. 29, 2012 @ 21:24 GMT
Michael,
There is another issue which may be worth keeping in mind here. In the context of Milnor's discovery of the exotic spheres I noted above, it is worth keeping in mind that there are in fact 28 distinct classes of differential structures possible on S7, compared to just one unique differential structure on S3. If we are to view S7 as a differentiable manifold with variable torsion, then this fact may be important. It is also worth keeping in mind that S10 admits 6 distinct differential structures, and S11 of your 11D GR admits 992 distinct differential structures. I would think that each choice of a differential structure on S11 would give rise to different physics, at least in principle.
Joy
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Author Michael James Goodband replied on Sep. 30, 2012 @ 12:37 GMT
Joy,
Your point about there being 6 distinct differential structures on S10 is an excellent one. My 11D GR starts with a physicality assumption that an initial S10 manifold is the "fabric of space" - there is no S11, the full scenario is cyclical in time.
Actually there are 6 different types of physics in my model. The electroweak map of S7 to S3 has 2 possibilities (PI7(S3)=Z2) which can be given chirality labels {L, R} - electroweak interactions say we are in the L version. This leaves 3 possibilities per {L, R}, which would seem to correspond to the physics of the 3 particle families, where gravity, strong and electroweak interactions are equivalent for each family, yet must be different in some sense otherwise there wouldn't be 3 families.
I note that this chiral-family correspondence on 6 is only possible for unification of spatial S3 and compactified S7 into S10.
Michael
Note: My full model is cyclical in time because closed universes must expand and contract in GR, so time occurs as S1 and the universe has existed forever. The S10 expands and contracts in this "unified" phase, then goes through a topological transition S10 -> S3*S7 to a "broken" phase. A radiation driven compactification-inflation see-saw inflates the S3 universe and it carries on expanding to a maximum size, and then contracts; at the same time the S7 compactifies and reflates, so is not of a constant size as is artificially assumed in Kaluza-Klein. For me, this resolves the conceptual problems I had with extra dimensions - the size of S7 defines the scale of *all* physical measurements (the Planck scale), including measuring the scale of S7 relative to itself to give a constant scale in a physical (relativistic) theory. My physicality assumption is critical for this dynamics, and my other results, but does constrain the possible interpretations for features of the theory.
Joy Christian replied on Sep. 30, 2012 @ 16:23 GMT
Michael,
Very good!
Let me make a note of few things and ask a few questions:
(1) You mention that there are 6 different types of physics in your model. Perhaps these are indeed connected to the 6 possible differential structures on S10 as you seem to think. It would be nice, however, to bring out this connection more explicitly. I don't know the details of the 6 differential structures admitted by S10. I only know the number. It would be interesting to explore how closely these structures are connected to the 6 types of physics in your model.
(2) Another open question is what you have already been puzzling about. In my analysis S3 and S7 appear as spaces of all possible measurement results. Because measurement results are simply events in spacetime (a click of a detector is an event in spacetime), I tend to think of S3---and more generally of S7---as the actual physical space where these events are occurring. In your analysis, on the other hand, S3 and S7 are symmetry spaces. The connection between these two facts is still an open question.
(3) One of the things I would like to understand is the status of the equivalence principle within your model. Does it remain an exact principle in S10? How do you account for the strong equivalence principle? If it does not hold as an exact principle, then how does it hold as an approximation? Any thoughts on this matter would be useful for me to understand your overall picture.
(4) Have you followed Roger Penrose's recent work on cyclical universe? I myself have not followed it, but I know he is very excited about it. It would be interesting to see how his work squares with the cyclical conception of time and eternally existing universe of your model.
Joy
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Thomas Howard Ray replied on Sep. 30, 2012 @ 17:40 GMT
Hi Michael,
You wrote: "Before you get too excited about the idea of dealing with particles without having particles, a hidden domain enclosed by a small radius S2 looks somewhat like a particle itself ..."
Well, it isn't particles per se that I'm interested in, but rather complete structural information that is tractable to analysis (continuous measurement functions). That's what motivates me to topology in the first place. The same questions that Joy asks above are inextricably bound to that view, because all except (3) involve simple network connectivity. (3) adds relativity.
Tom
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Author Michael James Goodband replied on Sep. 30, 2012 @ 19:29 GMT
Joy,
Interesting questions, only question 4 can I completely answer: short answer, it doesn't sqaure.
1) I don't know the details of the 6 differential structures on S10 either, or if they can be connected to the chiral-family physics distinction in the way I suggest. The topological transition would have to divide them in half, but the 3 remaining options would be required at the...
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Joy,
Interesting questions, only question 4 can I completely answer: short answer, it doesn't sqaure.
1) I don't know the details of the 6 differential structures on S10 either, or if they can be connected to the chiral-family physics distinction in the way I suggest. The topological transition would have to divide them in half, but the 3 remaining options would be required at the same time for the 3 families. I don't yet know if this is possible or even makes sense.
As S3/S7 are conceptually within the space of quaternions/octonions - giving a 12D space - I think I would first have to find the relation of my manifold - with its transition S10->S3*S7 - to this background - and find the time dimension in 12D - before I could consider the differential structure.
2) There is also a local-global confusion. Globally S3*S7 is a physical manifold where the spheres are curved - demanded by them being unified in S10 which isn't parallelisable. The KK identification for the construction of a local dimensionally reduced theory involves identifying the compactified space with a group space - this gives a flat S7 in the local theory, in which the rotation group space gives the other flat S3. Your analysis then requires the measurement spaces to be (flat) S3 and S7. This gives 3 types of spaces - physical, symmetry, measurement - to square with each other. If the physical curved space of my model is dropped, then the S10 "explanation" of the S7 to S3 map is lost, and so is the condition of 6 differential structures.
3) My model is simply constructed as an 11D extension of GR, with an initial radiation density of metric waves as extra-dimensional extension of gravitational waves. This requires the addition of an energy-density term with gravitational coupling, and using the same term necessarily involves the same assumptions. However, the definition of some physical quantities depends upon the number of dimensions, which changes with dimensional compactification (e.g. entropy). In 4D GR mass has a definition via the lst Casimir invariant of the Poincare group. In 11D the relation between the equivalent invariant mass and energy will be different from the 4D case, which raises questions about the relation between inertial mass and gravitational mass. The mass invariant in whatever number of dimensions will be the inertial mass, whereas the source of gravitational curvature in N-D GR is defined by the stress-energy tensor as being energy. The equivalence principle in 4D has a hidden assumption about the relation between mass and energy in 4D, but with dimensional changes the relation between mass and energy changes.
As the particle charges come from the topology of the space - including spin being a topological "charge" - they are independent of this mass issue. The incompleteness of the calculation of the reduced mass of the Planck scale particle black hole, makes mass the major unresolved issue of the model - the masses of the fermionic particles have to be added by hand from experiment, through a renormalisation process. In contrast, the W and Z boson masses are derived in terms of closed geometric formulae involving the electroweak scale - a Higgs boson mass of ½ electroweak scale is derived in the dimensionally reduced Lagrangian.
4) I hadn't followed Penrose's work of Conformal Cyclic Cosmology (CCC), but the first thing I note from is most recent arxiv paper is that the word "cyclic" is somewhat misleading - it is more iterative or recursive. My model won't square with CCC because mine is genuinely cyclic (it bounces).
Michael
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Joy Christian replied on Oct. 1, 2012 @ 07:11 GMT
Michael,
Although S10 is not parallelizable, as a product of two parallelizable spheres the space S3 x S7 *is* parallelizable. However, it cannot be used as a co-domain of the Bell-type measurement functions A(a, L), because S3 x S7 is not closed under multiplication, and hence the corresponding set of A(a, L) cannot produce a locally-causal theory.
The difference between S10 and S3 x S7 is a single mathematical point. Locally S10 would "look" just like S3 x S7. However, S10 cannot be charted by a single set of orthonormal bases (there will always be one point unaccounted for), whereas---as a parallelizable doughnut---S3 x S7 can be charted by a single, singularity-free coordinate system made out of quaternions and octonions.
As for the 3 types of spaces---physical, symmetry, and measurement---I tend to identify at least the first and the third, because any measurement result is a codification of an event in spacetime, and any event in spacetime can be reduced to a yes/no question with a +1 or -1 answer. It is in the identification of the symmetry or configuration space such as SU(2) with the physical space such as S3 that my analysis takes a radical and unusual step compared to the usual separation of the physical space and the state or configuration space. So the difficulty in matching your model with my analysis may be genuine only as far as the first and the second spaces are concerned.
Since we are simply exploring things here, I would not be too pessimistic about your observation that "f the physical curved space of [your] model is dropped, then the S10 "explanation" of the S7 to S3 map is lost, and so is the condition of 6 differential structures." The difference between the curved S10 and the flat S3 x S7 is simply due to a different choice of a Riemannian metric. Topologically this amounts to a single mathematical point.
Joy
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Thomas Howard Ray replied on Oct. 1, 2012 @ 10:43 GMT
"The difference between S10 and S3 x S7 is a single mathematical point. Locally S10 would 'look' just like S3 x S7."
Right on, Joy. That's the basis of a result I came up with a few years before I was introduced to your framework: The 10 dimension limit (actually either 11 - 1, or 9 + 1, accounting for the horizon point at infinity) is identical to the 4 dimension horizon. Today, I prefer the elegance and completeness of your description, which obviates compactified dimensions.
Tom
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Author Michael James Goodband replied on Oct. 1, 2012 @ 11:43 GMT
Hi Tom
Your vision of physics is different from the perspective I had coming from QFT, but I am coming round to it - especially as my theoretical framework provides endorsement for it. The calculation of reduced mass discussed in my essay naturally defines a S2 surface around the topological monopole/black hole particle where space is flat and there is no virtual-radiation field. I face...
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Hi Tom
Your vision of physics is different from the perspective I had coming from QFT, but I am coming round to it - especially as my theoretical framework provides endorsement for it. The calculation of reduced mass discussed in my essay naturally defines a S2 surface around the topological monopole/black hole particle where space is flat and there is no virtual-radiation field. I face down the mathematical incompleteness in my scientific theory with the apparently novel question: so what?
As the incompleteness is explicitly over the natural numbers it is avoided by switching to a real-number valued field - including the undecidable wave property - for particle numbers. The radius of the S2 around the problematic region is then approximated as a point, so that the field can be taken to apply everywhere - this gives the form of QFT as an approximation.
However, the topological space approach is an alternative, and arguably more direct approach, especially since the charge and spin properties of the monopoles are due to spatial structure which applies everywhere, and not just inside the S2 domain. In this approach, the S2 domain effectively becomes the domain of a hidden theory, i.e. my full theory. This could be perceived as being a problem as it hides the derivations of the theory, whereas for my theory it is actually a virtue as it hides the non-derivation of the wave property. Mathematical incompleteness in my theory specifically means that there exists a statement within the domain of the theory - a particle has a wave-property - that cannot be derived within the theory. The S2 surface marks the domain of the theory - the wave-property is within that domain - but hides the derivations of the theory - which fail to include the wave-property anyway. The net result is the mathematical incompleteness is bypassed, and a scientific theory outside of the S2 hidden domain can be scientifically complete.
To achieve that full result, the topological space approach has to be made relativistic and include particle reactions.
Michael
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Author Michael James Goodband replied on Oct. 1, 2012 @ 12:35 GMT
Joy,
I was focusing on the count of differential structures you gave for S7 (14) and S10 (6), which seems to imply that in differential terms S10 doesn't locally look like S3*S7, unless the product space somehow eliminates 8 of the 14 possibilities on S7 alone. I don't know the subject well enough, but I see I am going to have to! Besides, my current approach has reached a natural end point for me, except for a QFT check of whether the colour group Spin(3) is compatible with experiment - but I lack the resources to do this.
I noticed that the doughnut S3*S7 was parallelisable, but it should be noted that to get monopoles as particles the equivalence of the 7 dimensions of S7 *must* be broken - a simple twist in the doughnut breaks the equivalence in just the right way to get the correct spectrum of 12 fermionic particles. In my theory, this global twist *is* the electroweak vacuum, i.e. it is what the Higgs field is describing in a local, and consequently rather misleading, way.
As for closure under multiplication, measurement functions of the form A(a, b, L) could be closed on S3*S7 for independent a and b. So a theory that is locally-causal separately over S3 and S7 could be possible, but then the required twist in the torus mixes it up. I've been pondering whether this can explain things in particle symmetry terms or not: in effect the S3 isospin subspace (picked out by the twist and has its symmetry broken) of S7 would be swapped for the S3 spin space (rotation group of the S3 physical space of the torus) to give a S7 configuration space that is closed under multiplication for measurement functions. In following KK practise, I also identify symmetry space with physical space, but this doesn't have the same meaning as your identification of configuration space with physical space. Resolving the different meanings would look like a step in the right direction - note the switch from symmetry to configuration space above.
Michael
Joy Christian replied on Oct. 2, 2012 @ 04:44 GMT
Michael,
O.K., I think I know how to deal with the apparent conceptual incompatibility between our respective approaches, at least in principle.
The central issue is how to understand the role of three different spaces---physical, symmetry, and measurement---in our respective approaches. In my approach the space of measurement results is seen as constraining the physical space, and...
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Michael,
O.K., I think I know how to deal with the apparent conceptual incompatibility between our respective approaches, at least in principle.
The central issue is how to understand the role of three different spaces---physical, symmetry, and measurement---in our respective approaches. In my approach the space of measurement results is seen as constraining the physical space, and hence these two spaces are identified. Thus, I see the measurement events, codified by +1 or -1 results, as occurring within a parallelized 7-sphere. In other words, I identify the physical space with the space of measurement events.
The real issue, then, is how we view the symmetry space in this picture. It is better viewed in my approach as a configuration space. For example, SU(2), or equivalently S3, is a space of all possible spinorial (or quaternionic) rotations in R3. Similar, S7, which I represent by a set of octonionic spinors, is a configuration space of all possible octonionic rotations in R7.
The question then is: How does this square with the 11D GR you have postulated? Well, here is my suggestion. This suggestion will be technically difficult to implement, but would be conceptually most satisfactory. So far you have been working with the usual tensorial language of GR, albeit extended to 11D (more precisely to S0*S1*S3*S7). However, the language of GR better suited for my framework is the language of spinors introduced by Penrose in 1960's (cf. the attached paper). In this language it no longer appears unusual to think of the quaternionic S3 as the physical space. In fact, as Penrose puts it, spinors are simpler and more deeply rooted then tensors. In principle, then, a similar spinorial approach can be adapted to your S3*S7 manifold, with the spinors now being the octonionic spinors in general (as in my section 7.4.5).
I am by no means suggesting that this can be done within a week. Nor am I suggesting that it can be done with the mathematical rigor that, say, Penrose would approve of (octonions are analytically not as well behaved as quaternions). But such a treatment would certainly remove the apparent conceptual incompatibility between our respective approaches, at least to my satisfaction.
Joy
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Author Michael James Goodband replied on Oct. 2, 2012 @ 12:27 GMT
Joy,
I think you're right, and it occurs to me that the necessity of switching from vector to spinor language (there was no attached paper, what was it?) is itself saying something.
Vector language seems to capture the basic nature of a physical space, whereas even simple orientation examples seem to show spinor language better captures the nature of configurations of physical...
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Joy,
I think you're right, and it occurs to me that the necessity of switching from vector to spinor language (there was no attached paper, what was it?) is itself saying something.
Vector language seems to capture the basic nature of a physical space, whereas even simple orientation examples seem to show spinor language better captures the nature of configurations of physical systems in the background physical space. This suggests that vector and spinor language are not talking about exactly the same things:
1) vector language describes the physical space
2) spinor language describes the physical configurations possible in that space
As the spinor language can describe physical configurations that are aligned with the vectors of the vector language description, this can give a false impression that spinor language is describing the physical space itself. The assertion that (1) is the same as (2) implicit in some spinor framework presentations may well provoke resistance as it conflicts with physical intuition - this was the case for me.
With this distinction, our respective usage of the term "physical space" is different: my usage is (1), whereas yours is (2). This may also explain some of the resistance to, as you say, physicists registering the obvious. Meaning (2) when readers think (1) may also add to the hang-up on non-locality, because the correlations in your analysis are found after an integral that looks like it is over the global space S7. For the space being (1) this would give the impression of non-locality. The parallelised spheres can then make it even more confusing, because for them local structure is the same as global structure, up to orientation - the hidden variable. In contrast, correlations being determined by the global structure (equivalent to local for parallelised spheres) of configuration space (2) in a strictly locally-causal theory is entirely sensible. That structure of configuration space (2) is obviously determined by the structure of physical space (1), and experimental results on (2) imply (1) - i.e. experimental metaphysics.
In these terms, your analysis implies that "quantum entanglement" is nothing more than "orientation entanglement" in the orientations of physical configurations (2) in the physical background space (1). This is not mysterious, and is seen in mechanics - such as your gimball lock example.
With this distinction between (1) and (2), the correct way to compare frameworks is as your say: to find the configuration space (2) for the physical toroidal manifold (1) S3*S7 with a *twist* in it. In symmetry terms, the twist breaks the isospin symmetry (the S3 subspace of the S4 base-space of S7 that twists in going around the outer S3 of the torus), suggesting that the configuration space for the twisted physical space would only be 7-dimensional and could be described by octonionic spinors.
Michael
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Joy Christian replied on Oct. 2, 2012 @ 14:21 GMT
Sorry, Michael. The attachment did not go through. There is an upper limit on the size of the document we can attach here. If the size is too big, it won't attach.
The paper I wanted to attach was this one: R. Penrose, ANNALS OF PHYSICS: Vol 10 (1960) pp 171 to 201.
A more complete treatment can be found in his famous two-volume book with Rindler: Spinors and Space-Time (CUP, I think).
I am still reflecting on the rest of your comments.
Joy
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Fred Diether replied on Oct. 3, 2012 @ 06:38 GMT
Hi Joy,
Can you email me the paper by Penrose? I will see if I can compress it more to upload here plus I am interested in studying it. This is a very interesting thread. I am studying Michael's "Derivation of a chiral SO(3)..." paper now. It is pretty fantastic! Very good work, Michael. I will have some more comments / questions as soon as I get over this bad cold I have.
Best,
Fred
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Author Michael James Goodband replied on Oct. 3, 2012 @ 11:00 GMT
Thanks Fred,
You will see from the dynamics described by the terms of the virtual-radiation expansion - equivalent to vacuum polarisation - of section 6 in my
paper (outlined in section 5 of my essay) that the implication is there should exist some form of bag model such as yours. The S2 surface enclosing the region of this dynamics gives an outer boundary for a hidden domain which could potentially match up with Joy's correlation analysis on the outside, whereas the inner region should be describable as some sort of bag model that includes both particle and wave properties. Conceptually the radius of this S2 would have to be the Compton wavelength L=2h/mc because to get a wave interference pattern the extended bag-object/hidden-domain-object would need to extend over multiple slits.
Unfortunately, it is in the calculation of the object's mass that I find the theoretical framework to be subject to mathematical incompleteness, but contrary to popular opinion this is no reason to throw ones hands in the air and just give up - there are ways around it using observations and changing the form of the theory. QFT in one way, Joy's geometric framework looks like it is another, and there could be more.
I will outline the features implied by my model in comparison to your bag model (and the work of Geunter Poelz) under
your essay. I look forward to discussion when you have recovered.
Michael
Fred Diether replied on Oct. 3, 2012 @ 16:56 GMT
Hi Michael,
Thanks for reading my essay. I guess my "bag" model is like an inverse bag model compared to a hadron bag model.
OK, I was able to compress the Penrose paper a bit more so let's see if it will upload.
Best,
Fred
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Fred Diether replied on Oct. 3, 2012 @ 17:11 GMT
OK, guess that didn't compress enough to work. Here it is as a link,
SpinorGR-Penrose.pdfBest,
Fred
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Joy Christian replied on Oct. 3, 2012 @ 20:50 GMT
Hi Michael,
I have some further thoughts about the issues we have been discussing. I now think that there are actually three different approaches one could take to iron out the apparent incompatibility of our models.
(1) I have already discussed the first option; namely, to go with an extension of Penrose's spinorial reformulation of GR. I think this is the best approach one can...
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Hi Michael,
I have some further thoughts about the issues we have been discussing. I now think that there are actually three different approaches one could take to iron out the apparent incompatibility of our models.
(1) I have already discussed the first option; namely, to go with an extension of Penrose's spinorial reformulation of GR. I think this is the best approach one can take, but I am not sure whether to go all the way to his twistor theory, which is the next stage from his spinorial reformulation of GR. I don't think we need to go that far.
(2) The second possibility is to consider teleparallel gravity. At first sight this seems to be a better option, considering my parallelized spheres. Because then the distant parallelism within them would be naturally dictated by the theory itself. But there are disadvantages in taking this option. To begin with, you are not using teleparallel gravity in your work but a straightforward extension of GR to 11D. Teleparallel gravity, on the other hand, is an entirely different ball game. In particular, there would be no equivalence principle in such a theory, either exact or approximate. So I don't think this is an attractive option.
(3) Finally one can follow Hestenes's spacetime algebra, which would be a convenient language from the perspective of my framework, because it is a natural extension of the geometric algebra I have been using. But there is something very unattractive about spacetime algebra. At some stage Hestenes is forced to introduce what he calls spacetime split to separate time from space, and this allows him to transform GR into a gauge theory. But this can be done only at a price of loosing general covariance, which again is not very attractive from my perspective. Such a split would introduce a preference in the theory. But the whole point of my work (as well as your work) is to NOT having to put any preference by hand.
So I am back to option (1). If I had infinite time, energy, and financial resources, then I would explore all three options to see where they lead us. But in the face of the realities of the real world I would go for the best possible option, and that seems to me to be option (1).
Any thoughts?
Joy
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Edwin Eugene Klingman replied on Oct. 3, 2012 @ 21:41 GMT
Hi Joy,
With respect to your 3rd point, have you looked at Daryl Janzen's essay? It may be relevant.
Edwin Eugene Klingman
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Joy Christian replied on Oct. 3, 2012 @ 21:55 GMT
Hi Edwin,
No, I haven't. I will have a look.
Thanks,
Joy
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Author Michael James Goodband replied on Oct. 3, 2012 @ 23:06 GMT
Hi Joy,
I've been aware of (2) being the option most readily implied by your work since I read your book. Although a pure geometric model could conceptually comprise of parallelised spheres - with the non-trivial map between them - it does seem to require a dramatic change that would lose key GR features. It is not just at the 11D level, the dimensionally reduced theory requires 4D GR to be recovered as I use this to obtain Planck's constant from the angular momentum bound for a real-valued event horizon radius in the Kerr metric. This then enters into the geometric expressions for the coupling constants. In addition, the radiation driven compactification-inflation see-saw is linked to a physical GR theory, without which I would be back to the assumption of Kaluza-Klein theory (no-one would want that). So teleparallel gravity looks as though it would be a GR disaster for me.
Our discussion of the spheres in both our frameworks has noticeably not mentioned the time dimension. Your framework is currently not relativistic; in adding time to make it relativistic won't you encounter the same spacetime split issue of (3) in reverse? Or do you have an alternative in mind, or a trick? I'm also wary of gauge theory gravity (GTG) because I have a critical global feature in the non-trivial map between closed curved spaces S7 and S3 which GTG doesn't seem equipped to easily handle. It looks formulated for local gravity, not the global cosmology of a closed twisted universe in 11D.
And then there was (1); although I'm not sure about how to proceed for a globally twisted space S3*S7.
Michael
PS: thanks for the Penrose paper
Thomas Howard Ray replied on Oct. 6, 2012 @ 11:37 GMT
Hi Michael,
You write, "Your framework is currently not relativistic; in adding time to make it relativistic won't you encounter the same spacetime split issue of (3) in reverse?"
I would be interested in how you make this conclusion. I understand Joy's framework to be fully relativistic. While I realize he makes no reference to time, the spacetime algebra (Hestenes) obviates the need for such a reference, in that Hestenes' 8-dimension model is translatable to Minkowski space.
It seems to me that a coordinate-free geometry is exactly equivalent to the general relativity principle of no privileged frame. What am I misunderstanding?
All best,
Tom
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Joy Christian replied on Oct. 6, 2012 @ 12:24 GMT
Hi Tom,
Michael is correct to say that my framework is currently not relativistic. He is also correct to observe that in adding time to it to make it relativistic I will have to introduce the same space-time split that Hestenes has to introduce in his space-time algebra. That is why I am not so keen on his space-time algebra.
Having said that, you are also correct, at least to some extent, to say what you have been saying. My framework is *not incompatible* with special relativity, or with any other theory of local causality for that matter (such as general relativity). This is because it is based on Bell's local-realistic framework, which assumes very little prior theoretical structure. As I have stated on these pages many times before, it only requires the factorizability condition
AB(a, b, L) = A(a, L) x B(b, L)
on the actual joint results such as AB = +1 or -1. However, to turn my framework into a fully relativistic, dynamical *theory* of physics, one must correctly adapt it to some algebra, such as space-time algebra. But since I am not too keen on spacetime algebra, I am looking into other better options for this task, such as Penrose's spinorial reformulation of GR (extended to 11D).
I have to say, however, that more I look into the problem I am realizing that the apparent incompatibility between my framework and that of Michael is much more serious. It will take much more serious work to sort out.
In short, simply to say that "a coordinate-free geometry is exactly equivalent to the general relativity principle of no privileged frame" is not enough. That is just the first step. To construct a full theory based on this idea is a non-trivial task. A similar task took Einstein more than a decade to accomplish. And I am no Einstein.
Joy
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Thomas Howard Ray replied on Oct. 6, 2012 @ 13:12 GMT
"In short, simply to say that 'a coordinate-free geometry is exactly equivalent to the general relativity principle of no privileged frame' is not enough."
I think it is enough, Joy. Hestenes' space-time split does not obviate the continuum of quantum and classical domains, when Minkowski space (classical continuum) and complex Hilbert space (quantum) dynamics are reconciled in a topological model using geometric algebra.
As I keep emphasizing, general relativity suffers no loss of generality in conversion from an interpretation that is finite in time and unbounded in space, to a model finite in space (quantum dynamics) and unbounded in time (classically continuous).
Tom
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Author Michael James Goodband replied on Oct. 6, 2012 @ 21:26 GMT
Hi Joy,
On the compatibility issue, bear in mind that my framework enables me to derive electroweak theory exactly - isospin, hypercharge and Higgs couplings (~1% of standard model values), the complete electroweak spectrum of fermionic particles, the bosons masses (W, Z and Higgs to 1% of experiment), the Weinberg angle within experimental range, the correct eigenvalues for the electroweak...
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Hi Joy,
On the compatibility issue, bear in mind that my framework enables me to derive electroweak theory exactly - isospin, hypercharge and Higgs couplings (~1% of standard model values), the complete electroweak spectrum of fermionic particles, the bosons masses (W, Z and Higgs to 1% of experiment), the Weinberg angle within experimental range, the correct eigenvalues for the electroweak vacuum and the quadratic and quartic terms of the Higgs potential. I initially focused on the particle symmetry groups in our discussion because for the electrons and photons of the correlation experiments the colour portion is irrelevant, and the remainder is exactly as per the standard model. So incompatibility at this level would entail incompatibility of your framework with the electroweak portion of the standard model. But 2 experimental facts derived in valid mathematical frameworks (yours and electroweak theory) cannot be incompatible for a consistent reality (safe to assume that it is). As you say, Bell's local-realistic framework is so minimal that genuine incompatibility with the relativistic framework of (electroweak) field theory looks unlikely.
I raised the particle families because they are the unaccounted for cracks in the standard model, and seem to naturally fit with non-commutative subsets of a non-associative whole - as in the octonions. So even ignoring my framework and just considering the compatibility of your framework with the standard model arrives at pretty much the same place.
I think the experimental meta-physics aspect of your correction to Bell's analysis is brilliant, and now that I know it can be done, I am wondering about whether the same concept can be applied to my main incompleteness result in its general context. However, the downside of such a meta-physical constraints on measurements is that it seems to leave open an ambiguity in physical interpretation: from meta-physical constraint back to physics. Does the S7 constraint apply to the space of physical configurations or to the physical space itself, and in what way? If the S7 includes the physical dimensions of space, then not only is it incompatible with my framework but it will be incompatible with the standard model as there are insufficient degrees of freedom - the underlying reason why extra-dimensional considerations always ultimately arrive at 11 as the minimum. On the other hand, if the S7 doesn't include spatial dimensions then why does it work just for spin? So either way, direct interpretation of S7 as physical space has problems. That suggests the S7 constraint applies to physical configurations - irrespective of compatibility considerations with my framework.
I would argue that spinor based formulations are about the space of possible physical configurations in the physical space, and that considering the physical interpretation of the tensorial and spinorial GR formulations reveals this. In the tensorial formulation, the core consideration of covariant transport around a closed loop is for the geometric test element of a directed line, i.e. a vector, whereas in the spinorial formulation it is the test element of a spinor - the group eigenstate of a point. This is the zero radius limit of the case I consider of a hole in the space, where the S2 surface of the hole must be in a representation of the Poincare group and so have spin. When a space has curvature, or torsion, such a spinor will either process or have its angle of declination change in going around a closed loop. Such changes in the orientation of a spinor test element reveal the same curvature of the underlying physical space as using the geometric test element of a vector. This implies that the spinorial formulation is the correct way to go - again, irrespective of compatibility considerations with my framework.
I have given the differential structure issue some more thought and think Ben Dribus had a point about
Torsten Asselmeyer-Maluga's work on exotic differential structures on 4-manifolds, as a smooth GR manifold of the form M4*X with compactified space X would give an "emergent" 4-manifold MX4 with a non-smooth differential structure - I added a post just on this issue for the FQXi record.
Michael
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Fred Diether replied on Oct. 6, 2012 @ 22:14 GMT
Hi Joy,
For me, time in your framework is simply equivalent to the radius of the parallelized 3 or 7 sphere topology and is normalized to 1. Of course in the EPR-Bohm scenario, you have the experimental results happen exactly at the same time. I think it would be interesting to see what happens in your framework if the results for A and B were taken at different radii (time). Well, there actually should be some kind of generalization of that possible also. Perhaps using Penrose's spinor method as you mention above.
Of course you know my position that the "void" is filled with "less than virtual" Dirac spinors so a spinor approach does seem appropriate modelled with the spheres of the normed division algebras as Michael has done. The fact that you beat Bell with that topology indicates to me that this is the right approach.
Best,
Fred
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Member Hector Zenil wrote on Sep. 25, 2012 @ 05:01 GMT
Dear Michael,
Interesting ideas. I remain however skeptic of extended applications of Goedel's incompleteness to physics (or other natural sciences for that matter). I think there is a lot of risk involved in making such an adventurous connection, specially because models of physics are not necessarily the way nature works, they are only mathematical models, but more important because Goedel's requires consistency of axiomatic systems to apply which is not always clear how to interpret in physics specially if a physics theory is not fully axiomatic or axiomatizable.
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Author Michael James Goodband replied on Sep. 25, 2012 @ 11:13 GMT
Dear Hector,
The difference between mathematical models and the way nature really works, is precisely the point I'm making. Maths models of certain forms have mathematical restrictions that nature doesn't - maths can be incomplete but reality isn't - and we our free to fix our models by changing their maths form.
The Gödel connection is not as adventurous as it may at first appear,...
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Dear Hector,
The difference between mathematical models and the way nature really works, is precisely the point I'm making. Maths models of certain forms have mathematical restrictions that nature doesn't - maths can be incomplete but reality isn't - and we our free to fix our models by changing their maths form.
The Gödel connection is not as adventurous as it may at first appear, but does depend on a *very* careful meta-science analysis (
review paper) of what it means to construct a scientific theory such that it accurately models the physical world. This is related to Einstein's point that he makes in the EPR scenario, but involves being *far* more careful about the specification of the 1-to-1 correspondence between features of reality and a mathematical theory - this is captured in my usage of physically-real term.
Precisely because of the points you make, the domain of applicability of Gödel's original incompleteness proof to science theories is restricted to causal dynamic systems that implement arithmetic changes over countable numbers of objects of different types. As long as the different object types are physically identifiable as being different types, then they can be classified into different sets in a mathematical theory, where the cardinality of the sets gives the countable number of objects present in the physical world (an accurate 1-to-1 correspondence). Note that ZF set theory is not the appropriate set theory for science theories as in reality objects occur as different types, and ZF doesn't support urelements or types.
The modelling of causal changes in object type A->B necessarily gives a form of logical implication in a 1-to-1 model of reality, and by carefully tracking the mathematical modelling of causal changes to the numbers of objects in reality, the conditions for when Gödel's theorem applies *within* a science theory itself (the critical meta-science bit is to parallel Gödel's meta-mathematics exactly) can be itemised. These conditions for the original form of Gödel's proof are very restrictive but can exist for real physical systems - I show that this condition can be used to divide physics into Object Physics (where it doesn't apply) and Agent Physics (where it does).
The axiomisation required to apply Godel's incompleteness to a scientific theory is limited to the core features required to denote different object types in sets, such that arithmetic over the numbers of elements in the sets is supported - this just comes from the axiomisation of set theory and arithmetic. Application of the proof to real scientific theories with further mathematical features - that are not necessarily axiomised - is then explicitly dependent upon the corollary to Godel's theorem: as long as the additional axioms don't change the integer arithmetic captured in the core set of axioms about object numbers, then Godel's incompleteness theorem will still apply. Meta-science analysis of a physical system can identify whether the arithmetic axioms would be changed by the extra mathematical features of a scientific theory without necessarily having to axiomise the theory, as all is required is to constrain what they *must not* be like for the proof to still apply, ie. they must not effect the integer arithmetic over object numbers.
Consistency in a physically-real scientific theory with a 1-to-1 correspondence with the numbers of objects of different types is then, as you say, the key issue. For a 1-to-1 denotation of object A in reality, the logical truth value of A (true) in the maths means that object A exists in reality, and conversely not-A (false) means that object A does not exist in reality. In this context of a 1-to-1 physically-real scientific theory of arithmetic changes in object numbers, an inconsistency in the theory would necessarily imply that a statement of the form, A and not-A, could be derived. This statement has the meaning that object A *both* exists and doesn't exist at the same time.
Now our observation of reality has been very time limited so far, and so an object existing and not-existing at the same time might arise, but it hasn't been observed so far. As this sort of inconsistency would imply that real magic was physically possible, the induction from our time limited observations of reality to a general statement of truth about reality seems safe - all science implicitly makes this assumption, otherwise the pursuit of science would be somewhat pointless. In a 1-to-1 physically-real scientific theory this gives the required form of consistency for Godel's incompleteness theorem to apply and for the theory to be *known* to be incomplete over arithmetic changes in object numbers.
In the 11D pure geometric theory considered for physics unification (
STUFT), particles arise as topological objects that either exist or not, are of 12 different types (corresponding to the fundamental particles), and are countable. So when the full set of conditions for arithmetic changes in object number required by Godel occur, the theory is provably mathematically incomplete. But by changing the maths terms used in the theory, and including the observation of an undecidable wave property for particles, this restriction can be bypassed to give a scientifically complete theory. The notable feature is that this change - integer valued terms to real valued terms - gives a (meta-science) *derivation* of quantum field theory. As applications of Godel's incompleteness theorem go, it is hard to imagine a more significant and dramatic example.
Regards,
Michael
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Steve Dufourny Jedi replied on Sep. 25, 2012 @ 12:37 GMT
Your maths are false dear bad band.
In fact You have made your times dear strings theorists.In fact it is logic that you doubt.Just for the investments of course.and funds.
Jonathan, Lisi, you are not able to ponder correct universal extrapolations, so don't insist with your paralleizations, it is just weak and not general.
Ironical is a weak word.
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Steve Dufourny Jedi replied on Sep. 25, 2012 @ 16:05 GMT
or perhaps that Mr Aguirre and Mr Tegmark prefer the parallel universes for the mathematical universe hypothesis. Or perhaps that they do not know what you try to do. It is better indeed to put the false names.
MIT and Santa Cruz wake up.what is this circus? it is simply a sad story .You cannot accept that dear directors of FQXi.
Regards
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Steve Dufourny Jedi replied on Sep. 25, 2012 @ 16:24 GMT
and this person who does not exist furthermore.Just for the strategy of discriminations.Mr Tegamrk and Mr Aguire, Take your responsability or tomorrow I go at the television. and I show all the things recorded in live.
These persons must be pusished for their acts simply.
Don't play with my kindness. Or really your are going to fall down of very high mountain. Me I have nothing to loose dudes ok. I take an airplane and hop I show all this story at the television, it is not a problem because when I will speak they shall see how I am. you want really playing, ok dudes.I stop to smoke , I take a plane and me I am going to create a real Institute.
You are obliged to kill me now.
bad people you are.
be the force with me.ahahah band of darth vador.
Good band they say ahahahah yes of course.critic my faith band of comics, critic and try.NO PROBLEM.
Regards
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Jonathan J. Dickau wrote on Sep. 26, 2012 @ 04:02 GMT
Hello Michael and everyone,
One cosmological theory I've been examining involves a change in metric of space (a metric reversal?) associated with decoupling, or what is now called recombination. What I envision is that the 'fabric of space' turns inside out at that juncture, such that the expanding fireball that was contained is now excluded from the space that had contained it, or 'painted' on its surface - to become the CMB.
Of course; the microwave background appears to be all around us, but just as I suggest in my essay - we are in a space that is inside out. That is; we inhabit a closed space with the topology of S3 - which appears to be an extended space although it is compact with respect to the bulk. In one paper published with Ray Munroe, we speculated that this mechanism might provide a cutoff - to keep higher-dimensional spaces hidden at lower energies.
So I am asking here; does a metric reversal associated with decoupling - and thus separated from us by a vast distance - satisfy the requirements to establish equivalence by placing the hidden domain in the right place? Is beyond the horizon close enough to 'at infinity' to keep it hidden? Would someone situated in the pre-decoupling space see our local universe as part of their space, or perhaps as a ball (a 3-sphere of course) shrinking away?
All the Best,
Jonathan
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Edwin Eugene Klingman wrote on Sep. 26, 2012 @ 19:23 GMT
Hi Michael and everyone,
In another blog I said to Joy, "You remark that "one can view a 7-sphere as a 4-sphere of 3-spheres" and elsewhere "...a 7-sphere can be thought of as a six sphere worth of circles." Then I asked, "Can this 6-sphere then be divided into two 3-spheres...?"
Joy replied: "You ask: "Can this 6-sphere ... be divided into two 3-spheres worth of circles?" The answer is no, because 6-sphere worth of circles is not the same as two 3-spheres worth of circles. It makes no sense to replace the 6-sphere base with two 3-spheres base. No such fibration of the 7-sphere exists.
But in this current blog Michael says:
"...the group spaces are S3, S3, S1 and fit into S7. [where...] The spin space S3 has a spatial origin, whereas colour space S3 and electromagnetism S1 have an origin in the particle symmetry space S7... [but] the issue I have is with the composite view: whether the differential manifolds of the particle symmetry spaces (S3, S3, S1) spaces can form S7. At best they could only give the topological S7 and *not* the differential manifold S7, which is ...required for Joy's parallelisation condition. [...] So for component spaces S3, S3, S1 - whatever their origin - this demands that from the perspective of observable functions these spaces *must* form the topological space S7, and then the parallelisation condition of Joy demands that it *must* be the differential manifold S7"
Now my interpretation of the two spheres (S3, S3) was not the same as Michael's, but I fail to see what the physical interpretation ["whatever their origin"] has to do with it. Why did it "make no sense to replace the 6-sphere base with two 3-spheres base" in the other blog, but now seems to make sense that "(S3, S3, S1) spaces can form S7" in this blog. I'm sure I'm missing something, but what is it?
Edwin Eugene Klingman
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Joy Christian replied on Sep. 26, 2012 @ 20:02 GMT
Hi Edwin,
Michael is simply exploring whether there are any connections between our respective approaches. He is simply thinking out loud to get input from us.
But the answer to your question is simple. Michael is talking about the *total* or *bundle* space S7, which can be decomposed as S3 x S3 x S1 locally (i.e., at some point of S7).
You, on the other hand, were asking me about dividing the *base* space into S3 x S3. But for that to be possible there must exist a fibration of S7 of the form
S1 --> S7 --> S3 x S3.
But no such fibration of S7 can exist because S3 x S3 has a hole in it (i.e., it is not simply-connected). What *does* exist is a fibration of the form
S1 --> S7 --> S6.
Joy
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Edwin Eugene Klingman replied on Sep. 26, 2012 @ 20:31 GMT
Hi Joy,
You say, "Michael is talking about the *total* or *bundle* space S7, which can be decomposed as S3 x S3 x S1 locally (i.e., at some point of S7). You, on the other hand, were asking me about dividing the *base* space into S3 x S3. But for that to be possible there must exist a fibration of S7 of the form S1 --> S7 --> S3 x S3."
Actually, I was not asking about dividing the *base* space into S3 x S3. What I was trying to ask was whether S7 could be viewed as two S3's connected somehow by an S1. This seems to me equivalent to Michael's (S3, S3, S1) spaces forming S7.
There seems to be a lot of misunderstanding all the way around. There are many well-informed and bright people on this blog, but I don't think we're all playing on the same field. Nevertheless it's quite interesting to see this tennis ball being slammed between different courts.
Edwin Eugene Klingman
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Joy Christian replied on Sep. 26, 2012 @ 21:54 GMT
Hi Edwin,
You wrote: "What I was trying to ask was whether S7 could be viewed as two S3's connected somehow by an S1."
Yes, but only locally (in a local neighborhood). It is not possible to decompose S7 globally in that manner.
Joy
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Author Michael James Goodband replied on Sep. 27, 2012 @ 15:37 GMT
Hi Edwin,
There is room for confusion here, especially because there are a number of different spaces and a missing bit. The 3 spheres of my particle symmetry spaces - colour S3, isospin S3, hypercharge S1 - form S7 because that is where they came from in the first place. The electroweak vacuum (a map from S7 to the closed universe S3) breaks the isospin symmetry (S3), leaving intact...
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Hi Edwin,
There is room for confusion here, especially because there are a number of different spaces and a missing bit. The 3 spheres of my particle symmetry spaces - colour S3, isospin S3, hypercharge S1 - form S7 because that is where they came from in the first place. The electroweak vacuum (a map from S7 to the closed universe S3) breaks the isospin symmetry (S3), leaving intact symmetries: spin S3, colour S3, electromagnetism S1, which *do not* form S7 despite appearing to be the subspaces of S7.
The simple comparison of these spaces with Joy's S7 condition isn't valid as it isn’t comparing like with like. Joy's correlation condition applies to the codomain of functions giving observables, not to particle symmetry spaces. It comes from the EPR-Bell definitions of locality and completeness, and Joy's parallelisation - the conclusion is that the codomain can only be S3 or S7. This condition is independent of what the particle symmetries actually are, but should apply to any number of any correlated particles anyway.
For colourless particles like electrons and photons my S3 colour space is irrelevant and can be ignored. This gives the symmetry spaces S3, S1 for the particles considered in Joy's correlation analysis, where the S7 condition applies for 3 particles - but the S3, S1 don't form S7 either. Yet Joy obtains the correct correlation result, and these *are* the symmetry spaces - the missing bit is how to square these 2 facts with each other (note that this applies to Joy's framework irrespective of anything of mine). My contention is that whatever the mechanism, it will also work for the case when the colour space S3 is included - as it is still an S3 like the spin space - but not if the colour space isn't S3.
For the particles in question being topological monopoles arising from a broken S7 particle symmetry space, there is a connection through maps of S3 and S7 to a S2: topological monopoles in my case; the surface enclosing a finite hidden domain in Joy's. With the same collection of spheres, the same underlying geometric algebra and consequently a related specification of uniqueness, it doesn't just seem like co-incidence to me.
Michael
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Vladimir F. Tamari wrote on Sep. 29, 2012 @ 11:29 GMT
Hello. This is group message to you and the writers of some 80 contest essays that I have already read, rated and probably commented on.
This year I feel proud that the following old and new online friends have accepted my suggestion that they submit their ideas to this contest. Please feel free to read, comment on and rate these essays (including mine) if you have not already done so, thanks:
Why We Still Don't Have Quantum Nucleodynamics by Norman D. Cook a summary of his Springer book on the subject.
A Challenge to Quantized Absorption by Experiment and Theory by Eric Stanley Reiter Very important experiments based on Planck's loading theory, proving that Einstein's idea that the photon is a particle is wrong.
An Artist's Modest Proposal by Kenneth Snelson The world-famous inventor of Tensegrity applies his ideas of structure to de Broglie's atom.
Notes on Relativity by Edward Hoerdt Questioning how the Michelson-Morely experiment is analyzed in the context of Special Relativity
Vladimir Tamari's essay Fix Physics! Is Physics like a badly-designed building? A humorous illustrate take. Plus: Seven foundational questions suggest a new beginning.
Thank you and good luck.
Vladimir
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Steve Dufourny Jedi wrote on Sep. 30, 2012 @ 16:56 GMT
It is what your probelm Mr Spindel and Mr Milnor, you are not skilling to understand my works, so ....., you lacks of credibility and funds , it is that?. You want the nobel in fact. Let me laugh.Your sciences are limited and not general, so why you insist with your strategy.
You know what ? You can all keeping your monney dear band of limited scientists. I am laughing in seeing the pseudo sciences, really. even with my bad english , I give you courses all the times. And the milnor prizes
It is what the probelm dear bad band. You need funds and an international credibility or what ?. Put the balls in the spheres dudes. You can all keeping your money.Milner and Milnor, forget me and also you know what? .like that you can still focus on strategies. ok . Now put the balls where I think in the spheres and publish for the nobel band of comics. I dislike the corruptions.Me I have made my works, I am a real searcher me.
Just for you and for the evolution of physics, I will continue to share my works.Me I improve band of comics, you no. The abel prize, nothing to do.The milnor mentoring, nothing to do.The Milner prize, still less to do. Mr Spindel , still less to do.and what ? all is said band of pseudos startegists lacking of generalism. Make all what you want, all is said, between us you know the truth .Ironical no? Exotic spheres ahahahah and what after? multiverses also.and after the balls inserted in the spheres. let me laugh, I have pity spiritually speaking.
Regards
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Edwin Eugene Klingman wrote on Sep. 30, 2012 @ 23:19 GMT
Hi all,
Obviously there are unresolved local--global issues as pointed out above. But there is yet another issue that I am confused about. In general, I believe physicists tend to bifurcate into two main branches: Those who believe physical reality exists in its own right and that mathematical maps are the best tool to represent this territory, and the other branch seems to believe that reality is to be attached to the maps and that territory somehow falls out of such as exemplified by Lisi's E8, in which the effort is made to fit all relevant 'pieces' into the slots in the map and to postulate "yet undiscovered" pieces to fill unused slots.
Quotes from above seem to fall on one side or the other. At 17:27 Michael says that a group
"gives 3 particle families, which is due to: the fiber-bundle structure of S7..."
I don't conceive of particle families as "due to" mathematical concepts. I believe mathematical concepts derive from physical reality: No physical reality - no mathematical concepts.
At 16:23 Joy seems to fall on the physical reality side:
"I tend to think of S3 -- and more generally S7 -- as the actual physical space where these events are occurring. In your analysis,on the other hand, S3 and S7 are symmetry spaces."
To which Michael responds:
"This gives 3 types of spaces -- physical, symmetry, measurement."
Any clarifying comments?
Edwin Eugene Klingman
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Author Michael James Goodband replied on Oct. 1, 2012 @ 10:16 GMT
Hi Edwin,
I am most definitely on the physical territory side of the line, not the mathematical map side. My model is explicitly based upon a physicality assumption that the GR manifold is a real physical "fabric of reality" surface - not just a map - and the GR development is explicitly dependent upon this (see my Balloon World attachment for a 2D version that discusses this physicality of...
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Hi Edwin,
I am most definitely on the physical territory side of the line, not the mathematical map side. My model is explicitly based upon a physicality assumption that the GR manifold is a real physical "fabric of reality" surface - not just a map - and the GR development is explicitly dependent upon this (see my Balloon World attachment for a 2D version that discusses this physicality of GR for a real world example). The physical "fabric of reality" has a structure which will constrain what is physically possible - such as the possible particles as topological defects in the spatial structure - and the mathematical map captures those constraints. It is in this constraint context that I use "due to": the 3 particle families are physically due to the structure of space, which when it involves the space S7, will be subject to physical constraints related to the fibre-bundle structure of an S7 manifold.
What I really what is to elucidate the full relational sequence:
physical => symmetry => measurement
I follow the practise of Kaluza-Klein theories of identifying the mathematical symmetry space with the compactified physical space, i.e. symmetry = physical in terms of underlying structure. This confuses the distinction and can give a false impression of "mapism" - the belief that the mathematical map is reality.
The set of related physical measurements defines a mathematical measurement space whose relational structure is due to the reality of the physical territory. Joy's analysis proceeds on the basis of the EPR-Bell notions of what it would mean for all measurable features of the physical space to be locally determined, i.e. physical => measurement.
Joy finds constraints on the measurement space which ultimately must imply constraints on the physical space. Joy has proceeded on the assumption that this is direct, i.e. measurement => physical, which it could be. However, it could also be indirect, i.e. measurement => symmetry => physical, which might more readily relate to my model, and more generally to particle physics terminology. It has to be one or the other, it can't be neither without abandoning the concept of physics: we can measure the physical territory of reality. However, with the structure of the physical territory determining the symmetry space, this distinction between the two options might not be meaningful. This is an open question on which comparison perhaps depends.
Does this clarify, or just make it worse?
Michael
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attachments:
2_Balloon_world.pdf
Eckard Blumschein replied on Oct. 1, 2012 @ 11:43 GMT
Dear Michael Goodband,
Only mapists believe that the future can be measured. So they arrive at symmetries that my Fig. 3 in 1364 reveals as artifacts. I am really not a mapist.
Eckard
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Author Michael James Goodband replied on Oct. 1, 2012 @ 13:21 GMT
Dear Eckard
Note that the sequence (on pg 4 of your essay) R, C, H, O ends on O, there is no more. My pure geometric theory is of the form of a unified GR which yields the closed spaces S0, S1, S3, S7 in these algebraic spaces - it is this which makes it unique and consequently of interest. The fact that it yields the correct electroweak vacuum, bosons and 12 fermionic particles of the Standard Model - and no more - only adds to the interest. The particles are explicitly topological monopoles with the non-zero radius of the Planck length - no point particles or singularities anywhere here. One of the points of my essay is that QFT is an approximation that *requires* point particles for the approximation to work. As you imply in your essay (pg 7, 8), a physical theory with points is likely to be problematic somewhere. Ditto infinity - hence the appeal of closed finite spaces.
The future can be predicted - subject to limits. I am not a Parmenides who believes in block-time where the future is somehow fixed, only to be mapped by the fatalistic. The underlying issue here is still the nature of time, which the 2008 FQXi essay contest apparently did not resolve ;-) Did this set the precedent for FQXi essay contests in addressing the questions posed?
Michael
Joy Christian replied on Oct. 1, 2012 @ 13:47 GMT
Hi Michael,
I don't want to distract you from our main discussion, but since you mention Parmenides and the issue of time, I have
a paper on the subject which may be of interest to you. It was written well before my epiphany into Bell's error. It developes a Heraclitean generalization of special relativity.
Joy
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Author Michael James Goodband replied on Oct. 1, 2012 @ 16:25 GMT
Joy,
I see you have a penchant for experimental metaphysics!
Your correlation analysis can similarly be viewed at a metaphysical level - as an experimental constraint on what the structure of physical space can be. I imagine this may not be particularly popular, but it is a view I share. The physics chapter on my 11D GR is just 1 chapter out of 23 in my book, the rest are largely...
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Joy,
I see you have a penchant for experimental metaphysics!
Your correlation analysis can similarly be viewed at a metaphysical level - as an experimental constraint on what the structure of physical space can be. I imagine this may not be particularly popular, but it is a view I share. The physics chapter on my 11D GR is just 1 chapter out of 23 in my book, the rest are largely meta-science - using science analysis of the conditions of physical systems to find constraints on the form of scientific theories throughout science (physics, biology, psychology, economics) - mainly when they would be incomplete. The
paper gives an account of this general meta-science perspective of the occurrence of incompleteness which can be bypassed, including an account of the original form of my proof that QT is not fundamental. I view this paper as succeeding where Wittgenstein failed in Tractus - but he failed in an interesting way.
With regards to your paper, note that a reality bounded by the Planck scale from below is a feature of theories with dimensional compactification - mine has it - and bounded from above is a feature of a closed universe (obviously reverse for energies). For any system of measurement units the intrinsic error of measurement is ½ the unit used, so for the Planck unit system express this intrinsic measurement error in invariant form (i.e. 2nd Casimir invariant spin) and ... hello Heisenberg uncertainty relations. This obviously implies that they are fundamentally not about QT, but about the structure of space - namely that there are compactified dimensions. This gives t_p as a lower bound on time and the main input condition for your paper, but there is another coming from a closed universe.
I never really got all the time discussion stuff, and I now realise that this was because I always conceived of the universe as being finite and closed. This may disagree with the current view of an open universe, but I contend that is because observations are interpreted through an unphysical GR. Furthermore, my results for the mapping S7 to S3 imply the following is true:
I exist, therefore the universe is closed.
With a closed universe there-exists a unique cosmological reference frame (CRF), and consequently a cosmological time can be defined. In the 4D space in which the S3 is embedded this reference frame is where there is no rotation of the S3 about the centre and the only motion is radial expansion. Such an external view is obviously unphysical, but the same conclusion can be reached inside the space. In SR, every event has a unique reference frame - the co-moving reference frame - because the velocity interval is closed at v=0 but open at c=v. For 2 objects interacting, the reference frame in which the interaction event is stationary is the unique co-moving reference frame. This can be repeated for any number N of objects, which for finite N will always sensibly give a unique reference frame, up to and including all objects in the universe - hence a unique CRF. As inhabitants of the manifold, our local reference frame is always relative to this CRF, but we cannot measure what it is when we cannot see the whole universe. So we cannot calibrate our local time in our reference frame to global cosmological time in the CRF. Our view of local time, i.e. in SR, doesn't necessarily give an accurate view of the nature of the time dimension in this CRF.
Now imagine the expanding S3 with radial scale factor R(t) residing in Euclidean 4D and consider the space-time separation of 2 events at times t2>t1. Between these times the universe expands R(t2) > R(t1) and the spatial norm (dx)^2 = (x1)^2 + (x2)^2 actually gives the hypotenuse of a right-angled triangle where the vertical is the time separation (cdt)^2 and the baseline is the spatial separation (ds)^2 within the S3 manifold at time t1. Given the definition of norm in the 4D embedding space, we find:
(ds)^2 = - (cdt)^2 + (dx)^2
For observers in the expanding S3 manifold, this gives a metric signature of (-,+,+,+). The conclusion is that we reside in the surface of an expanding closed S3 universe, and the local time dimension is our experience of sweeping along the fourth spatial dimension of the 4D embedding space - obvious modification required for S3*S7, but the same general point stands.
As you consider in your paper, such a Heraclitean view entails anomalies to current physics which could be experimentally verified.
Michael
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Joy Christian replied on Oct. 1, 2012 @ 20:05 GMT
Michael,
I got my penchant for experimental metaphysics from my former PhD supervisor, Abner Shimony (the S in the Bell-CHSH inequality). In fact he introduced the concept of experimental metaphysics into physics.
My correlation analysis can indeed be viewed as an exercise in experimental metaphysics. The experimental observations of quantum correlations dictate what the structure of the physical space must be. One would think that this much should be obvious to everyone. But most people following Bell seem to get hung up on this bizarre idea of non-locality and non-reality, rather than investigating what the correlations are actually telling us about the physical space itself. They are unambiguously pointing to the octonions.
Thanks for the interesting observations on the implications of the upper and lower Planck scale bounds on reality. There is much to think about in your comments.
I also like your maxim: "I exist, therefore the universe is closed."
Joy
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Edwin Eugene Klingman replied on Oct. 1, 2012 @ 20:07 GMT
Dear Michael,
Thanks for your clarification. It helps a lot. My interpretation of "due to" was off-base and I realize that it's impossible to speak without sometimes using expressions that can be misinterpreted.
With respect to your scheme: physical => symmetry => measurement
I believe that any non-chaotic universe (where a chaotic universe never repeats anything!) will allow a
pattern recognition process to identify "things" and if these things can be transformed into each other in any way, shape, or form, then a 'symmetry' is automatically defined. Since that appears to be the type of universe we live in, then I agree with your sticking symmetry in the middle of it.
Also, with regard to your "unique cosmological reference frame", if you have not read Daryl Janzen's current essay, I suggest you do so.
Thanks again,
Edwin Eugene Klingman
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Steve Dufourny Jedi replied on Oct. 6, 2012 @ 12:10 GMT
In fact since the begining you also poor thinker.
You are not cramped dear badband , Edwin, Georgina, Lisi,Jonathan, Joy,Christi,Don, Florin,Mickael,Brendan,Johan,Rick,Tom,Verlinde,and several others....your team is known and also you have already lost. Frankly you are not skillings , so why you insist.In fact you are blocked in your own obliged false road.In fact I have already seen...
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In fact since the begining you also poor thinker.
You are not cramped dear badband , Edwin, Georgina, Lisi,Jonathan, Joy,Christi,Don, Florin,Mickael,Brendan,Johan,Rick,Tom,Verlinde,and several others....your team is known and also you have already lost. Frankly you are not skillings , so why you insist.In fact you are blocked in your own obliged false road.In fact I have already seen uncompetents, but there you are above the stupdity.
Just for what? a confusion due to my weak english, let me laugh !!! a ball there, a sphere there, a lisi appraoch there and what after? ironical, even in team and even with your algorythmic superimposings of hackers and even with your maths, I eat you all the days. Cramped is a weak word No? Probably that you are pseudo men, I am persuaded that you are even bad in the bed band of pseudos. Your hate increases, you are going to discuss and continue your strategy.Let me laugh band of comics.If you and your team you understand the generality of sciences, me I am the queen of england dear pseudo mathematicians and scientists.
Entropy, you do not understand it.
the generality, the same
the concept of evolution spherization, the same
the universality, the same, the mass and the light, the same
the serie of uniqueness, the same you confound all the limits and domains.
the geometrical algebras, aahahah let me laugh with your extrradiemsnions of 7 to 8 to 11 to 12 and what after? let me laugh with your reductionism. Kill me pseudo scientists ahahah it is better for your credibility.
now let's continue, I love to give you all courses between us with these hackings. Even like that ,I eat your sciences at my breakfast. ahahah even the amino-acids you do not understand them ahahah
I suggest really that you return at school you know dear team, because in fact you repeat always the same stupidities. but you are not bad for the marketin,g and the publicity ahahaha change of topic, of orientation ahahah if you create for example a spaceship, we are not going to go very far ahahah. if your sciences are correlated with the engeniering and its laws, me I am the future president of USA ahahah pay attention they are going to invent a time machine.
If you you are scientists, theorists,frankly the hour is serious there. And you insist ahahah Perimeter questions institute of Holland ahahah return at school and forget the theory yes .People are made for that, other no simply.Each person at its place. People teaches and others learn.You are in the second meaning. Me I am in both of them band of comics.
a ball and a sphere and a S(O)n , with strings , yes of course. because 11 are necessary for the compactification in 2D of course of course.and a bridge between the aether and the physicality, we know we know, and also godel uncompleteness is rirrational of course of course.
THE THEORY OF SPHERIZATION , Steve Dufourny Belgium !!!
they turn so they are !!!
Regards
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Michael A. Popov wrote on Oct. 2, 2012 @ 13:02 GMT
Michael,
Your statement :
"there are only 4 normed division algebras over the real numbers - real numbers, complex numbers, quaternions and octonions " may suggest that you try to find physical simplification of the Frobenius theorem on the limits of pure mathematical generalizations numbers after complex numbers and quaternions.If I understand, Frobenius theorem has a proof and I know nothing about any counter-example existence for such theorem in current literature.
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Member Benjamin F. Dribus wrote on Oct. 3, 2012 @ 05:05 GMT
Dear Michael,
I just read your very interesting essay. A few thoughts come to mind.
1. Concerning your invocation of Godel’s theorem in regard to physical measurement on page one, I have a question which might be rather clumsy to state. I am thinking that perhaps two different ideas of “proof” or “derivation” are involved. Suppose you have a true statement about...
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Dear Michael,
I just read your very interesting essay. A few thoughts come to mind.
1. Concerning your invocation of Godel’s theorem in regard to physical measurement on page one, I have a question which might be rather clumsy to state. I am thinking that perhaps two different ideas of “proof” or “derivation” are involved. Suppose you have a true statement about natural numbers, which is undecidable. It seems that you could always test the statement for a particular choice of natural numbers: just substitute in the chosen numbers and see if you get an identity. The undecidability comes from the fact that you can’t prove the statement is true in general; i.e. for an arbitrary, unspecified choice of numbers.
In your terms, you couldn’t derive it from the axioms of the theory. Now the “scientific,” or “physical,” proof of the statement is just the inductive reasoning (in the sense of Newton) based on the experiment. So I suppose what you are saying is that no matter what the axioms of your physical theory, there will be statements which are “scientifically provable” in the sense of measurement that don’t follow from the theory?
2. Does this imply that it is impossible to have a physical theory with a finite number of physical laws to which other, independent, true laws cannot be added?
3. You mention of using “successor, predecessor, zero and projection functions” to build up number theoretic functions and a “growing network of object reactions that include processes which implement arithmetic increases in the numbers of some objects.” You also mention the “path integrals of quantum field theory” in a similar context. This reminds me of “quantum causal theories” of quantum gravity. Examples are causal set theory and causal dynamical triangulations. This is interesting here because such theories often involve countable “classical universes,” and this appears to make a difference in light of your discussion on pages 3-4. For more perspective on this viewpoint, see my essay
here.
4. Your discussion of black holes and mass reduction is very interesting. Janko Kokosar speculates about a “black-hole” theory of fundamental particles in his essay, but he believes that the Higgs mechanism ruins this. I don’t know if your ideas change this consideration.
5. The essays of Torsten Asselmeyer-Maluga and Jerzy Krol might be interesting in the context of your discussion on pages 7-8.
Your essay gives me many more ideas to think about. Thanks for the great read! Take care,
Ben Dribus
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Author Michael James Goodband replied on Oct. 3, 2012 @ 15:31 GMT
Dear Ben
Thanks for your comments and your thoughtful questions.
My comments to Hector Zenil and my general meta-science paper set the context for considering Godel's theorem in scientific theories to be far more general than the one instance I discuss in my essay. The general scenario is that of a network of sets of different objects that are linked through causal changes A -> B...
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Dear Ben
Thanks for your comments and your thoughtful questions.
My comments to Hector Zenil and my general meta-science
paper set the context for considering Godel's theorem in scientific theories to be far more general than the one instance I discuss in my essay. The general scenario is that of a network of sets of different objects that are linked through causal changes A -> B in object type, where the notion of "object" here is extremely generic: any identifiable unit that can be classified into sets and counted. Godel's conditions for his theorem to be reproduced within a theory of this object causation correspond to an indefinitely growing network where some nodes cause further nodes to be added and linked to the network. The final condition corresponds to the network phase transition of a random graph where a highly connected giant network component appears. The known undecidable statements (e.g Godel and Rosser sentences) are of the form of self-referential whole system statements, which in network terms would correspond to statements about closed causal-cycles residing on the giant network component.
This sets the general context for answering your questions:
1) The self-referential whole-system form of the known undecidable statements means that your suggested number testing strategy won't work, you would have to test with the whole system. The problem is that undecidable statements are general whole-system statements that cannot be reached from the axioms of the theory, BUT they are present *within* the theory nonetheless. This means that it is wrong to simply dismiss incompleteness or give up - we still have observation, and changing the terms.
The lengthy meta-science analysis I give in the
paper is necessary to identify when Godel's conditions would be met for a physical object system that could be observed. The conditions are very physically constraining, but surprisingly frequent in the real world. In such cases, an undecidable statement present *within* the theory could correspond to an observable statement of the physical system, giving a form of scientific proof of a statement that is beyond mathematical proof. So yes, there can exist physical systems for which there will be statements which are "scientifically provable" in the sense of measurement that don't follow from the theory - the wave-property of a particle in classical physics is the archetypal example.
2) The underlying reason for Godel's incompleteness is the discrete character of logical deduction over natural-number terms (with the associated axioms). Derived forms of incompleteness, such as non-computability in Turing Machines and Kolmogorov complexity, share this discrete character. It's a corollary of Godel's theorem that adding further axioms of the same discrete form as those already present won't change the incompleteness proof - so adding further true laws can be done, but it won't make any difference to the incompleteness.
However, systems with a continuous real-number basis don't suffer from this form of incompleteness. So if you change the character of the terms in a theory from discrete integers to continuous real-numbers, then further laws *can* be added to give a "scientifically" complete theory, in that it accounts for all scientific observations - but at the price of using probability to convert the artificial real-number terms back to the reality of natural-numbers of objects.
3) The terms you quote from my essay are those required to establish the presence of causal arithmetic over object numbers in the set basis of the causal network. Given the very generic form of "object" required, the same incompleteness could be displayed in all sorts of physical systems. For example, in the particle reaction sequence case implied by the expansion in my essay, particle reaction graphs constitute a type of "object". In my Agent Physics book I use the required physical conditions to identify classes of physical system that could display incompleteness, including:
a) chemical molecular system of a living cell
b) cells of a multicellular organism
c) organisms in an ecosystem
d) neurons in a neural network - although this doesn't apply directly
e) goods in the network of a national economy
f) financial derivatives when they are allowed to form an unlimited network
All these systems appear to have some form of causal-closure where bottom-up dynamics gives a top-level of causation that propagates back down through the system, and gives the whole system collective (emergent) properties. There could well be further examples of the same effect, e.g. it could be generated in a suitably constructed software system. The form of my theory with compactified dimensions also suggests that a discrete cellular automata version of spatial structure could be constructed, such as
Vladimir Tamari's, which should also display the same incompleteness.
Michael (responses to 4,5 to follow)
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Author Michael James Goodband replied on Oct. 3, 2012 @ 15:36 GMT
4,5) The essays you mention all consider quantum gravity (QG), but this is only necessary if QT is fundamental, but it isn't and so QG is not proven to be necessary. I derive the form of QFT, which wouldn't have been possible if QT was fundamental, and Joy Christian derives the same correlation results as QT without mentioning QT, again that wouldn't have been possible if QT was fundamental.
Janko Kokosar considers black holes with singularities in a QG context, both points of which I disagree with. The black holes of my theory are the 4D GR form of 11D topological defects where space is wrapped around compactified dimensions S7, this means that the black hole has no singularity and there is no space inside - a black hole is literally a hole in space and the event horizon marks an edge of reality beyond which there is nothing.
I find the Higgs field to be a local field theory description of a global twist in the S3*S7 torus of the physical manifold of space, and the Higgs isn't the source of mass for fermions - it is for the bosons. That twist gives the topological conditions for the topological defect particles as Planck scale black holes, so it is the causal reason for the black hole form of particles.
Michael
Side-note on the first line of
Janko's section 8: 11D GR can be written on a T-shirt
Peter Jackson wrote on Oct. 3, 2012 @ 16:59 GMT
Michael
"The real foundational question exposed by this derivation of quantum field theory is, do there really exist observable features in classical physics that cannot be derived?"
Very nice essay and clear analysis, somewhat similar to Lawrence Crowell's. I'd like to suggest that, if you can speak another language, the answer to the above is 'No', as I offer a mechanism Unifying Classical physics and non commutable QFT in my essay. I hope you may read and comment or falsify the alternative logical assumptions offered and resulting ontological construction, reproducing the framework of truth function logic to derive space-time.
Best wishes
Peter Jackson
PS The 'other' language is English, but you may find familiarity with the iambic pentameter helps the flow!.
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Janko Kokosar wrote on Oct. 3, 2012 @ 20:22 GMT
Dear Michael.
Question and hint about interior of black hole (BH) I gave generaly, not linked to my theory. It seems to me, that the interior does not exist, AND that exteriors of BHs are independent from interior. That means that exteriors of BHs "(1) with interior" and "(2) without interior" are the same. Anyway, space time is emergent, thus it is not necessary to worry, what is in this hole inside horizon. I wrote still other arguments. Thus we have the same conclusion.
I DO not say that quantum BH has singularity, because I believe to Feynman's hint that "limited space contains limited information".
I have not yet read your essay, but one problem, which I suspect at you, is that you do not need quantum theory at arising at mass. I think that this is necessary. You also has 11 dimensions. I think that additonal dimensions are against Ockham's razor.
Ockham razor is also that I persist at my theory although is not compatibile with Higgs boson. The reason is, because my theory is very simple.
But I will read your essay.
Best regards,
Janko Kokosar
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Author Michael James Goodband replied on Oct. 3, 2012 @ 21:40 GMT
Dear Janko,
It is interesting that we have arrived at the same conclusion about the interior of black holes and that they are the form of the fundamental particles, and yet our views of the nature of the space in which they exist are contradictory: you that space is emergent, and me that it is a real physical "fabric" (characterised by physical constants c, G, h). That perhaps makes our point of agreement more remarkable.
The point discussed in my essay is that I start from classical physics and attempt to calculate the mass of a particle as a topological defect in a real "fabric of space" and find mathematical incompleteness in the way. Changing the mathematical terms of the theory to go around this block yields the form of quantum theory. Conclusions: 1) quantum theory isn't fundamental otherwise it wouldn't be possible to derive its form 2) cannot calculate mass of fermions in classical physics, but neither can QFT.
Occam's Razor doesn't help in practise because we all seem to have different concepts of simple. My extra dimensions are in the context of a pure geometric GR theory with a physical "fabric of space", no extra fields of any form (a great piece of simplicity), quantum theory is derived, and just involves the closed spaces S0, S1, S3, S7 in the 4 normed division algebras (significant uniqueness for a metric based theory like GR).
I suspect you could present a similar argument about the simplicity of your theory.
Best regards,
Michael
Sergey G Fedosin wrote on Oct. 4, 2012 @ 07:46 GMT
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is
and
was the quantity of people which gave you ratings. Then you have
of points. After it anyone give you
of points so you have
of points and
is the common quantity of the people which gave you ratings. At the same time you will have
of points. From here, if you want to be R2 > R1 there must be:
or
or
In other words if you want to increase rating of anyone you must give him more points
then the participant`s rating
was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.
Sergey Fedosin
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Cristinel Stoica wrote on Oct. 6, 2012 @ 16:12 GMT
Hi Michael,
Please check
this link and find how five essays, including yours, were removed from the 35 finalists. I posted some messages with attachments containing the page and screenshots at 0:01.
Good luck,
Cristi Stoica
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Author Michael James Goodband wrote on Oct. 6, 2012 @ 17:32 GMT
Space-Time: real or emergent?
This may well depend upon what you think these terms mean. Nothing prevents clear understanding quite like speaking the same language, but using the same words with different meanings. So instead of using these ambiguous terms and hoping everyone chooses the same meaning, let's call the manifold of GR an "absolute" space in the sense that the "absolute" scale...
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Space-Time: real or emergent?
This may well depend upon what you think these terms mean. Nothing prevents clear understanding quite like speaking the same language, but using the same words with different meanings. So instead of using these ambiguous terms and hoping everyone chooses the same meaning, let's call the manifold of GR an "absolute" space in the sense that the "absolute" scale of physical distances in GR is not in fact defined - this is seen in the scale factor of the universe in GR not being specified.
In any model with an "absolute" space that includes compactified dimensions, e.g. M4*X (the model referred to in the essay considers local manifold M4*S7 but the point here is more general) this problem of not having an "absolute" scale in GR is resolved by measuring ALL physical distances in M4 using the compactification scale of X - virtually always assumed to be the Planck scale (the model of the essay arrives at a Planck unit system through consistency). Of course, this explicitly depends upon grasping the meaning of the word "relative" from which the name Relativity is derived, surely not a difficult conceptual point?
As I said under Edwin's thread of 30 Sept, in any system of measurement units the intrinsic error of measurement is ½ the unit used, and when this is expressed in invariant form (i.e. 2nd Casimir invariant spin) for the Planck unit system this gives the Heisenberg uncertainty relations. It should hopefully be obvious that this implies that the relations are fundamentally NOT about quantum theory, but about the structure of space - namely that there are compactified dimensions. This also has the effect of converting an assumed smooth "absolute" manifold of M4*X (in GR) into a 4D space-time manifold MX4 expressed in terms of physical units of measurement that is NOT smooth, and has Planck's constant "built-in": precisely the features of an "emergent" space-time (i.e. MX4 "emergent" from M4*X), with an exotic differential structure such as those of the 4-manifolds discussed in
Torsten Asselmeyer-Maluga's essay. The Cellular Automata view of this "absolute" M4*X manifold is one where the neighbouring spatial cells overlap each other by ½ a cell (I mentioned this in the context of
Vladimir Tamari's CA model) to give an "emergent" view of a MX4 space-time manifold that is NOT smooth.
By grasping the real meaning of the word "relative" it can be seen that the "absolute" manifold M4*X of GR will give an "emergent" space-time MX4 with critical features of QT built-in, e.g. Planck's constant, and a non-trivial differential structure. It has been said many times before by many people that most of the features of QT are due to the geometry of space itself, and NOT specifically about the field formulation of QT. It is also well-established that to get the physics that we already know, the compactified manifold X must have 7 dimensions - for a closed manifold that means S7, as in the model of the essay. The given model recovers the Electroweak model EXACTLY - ALL couplings, ALL particles, ALL bosons masses, i.e. including the Higgs boson, Weinberg angle, Electroweak Vacuum and the quadratic and quartic terms of the Higgs potential.
Quantum Theory itself is JUST about the conversion of a natural-number valued term for the number of particles, to a real-number valued term that includes the undecidable wave-property, and the conversion back again - THAT'S IT! All other results produced by QT are due to geometry - this is why the same experimental results CAN be obtained without ever using this QT representation fiddle. If the derivation of results that agree with experiment no longer matters, then theoretical physics would amount to nothing more than a pointless self-serving exercise - at tax-payers expense!
The 40 years of failure to take physics beyond the Standard Model is due to attempting to make QT fundamental when it isn't. The false assumption that QT is fundamental IS the answer to the FQXi question posed (I'm not the only one saying it here!) - the structure of reality is not a popularity contest, the answer is the answer because it's right, not because it's popular.
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Joy Christian wrote on Nov. 7, 2012 @ 10:10 GMT
Hi Michael,
I have posted
a new paper on the arXiv concerning the local origins of quantum correlations. I thought you might find it interesting. I am also attaching a PDF file of the paper below for your convenience.
I hope you are not too discouraged by the outcome of the essay contest. We must continue to fight against the prevalent ideology.
Best,
Joy
attachments:
2piSpinor.pdf
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Author Michael James Goodband replied on Nov. 7, 2012 @ 21:11 GMT
Hi Joy,
Thanks for the update. I see that this is the work you were referring to about an experimental test between SO(3) and SU(2).
I like the idea of something like a table-tennis ball (cut in half and judiciously stuck back together) being the required hidden domain containing two objects with orientation entanglement. The crux of the paper strikes me as being on page 9, since...
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Hi Joy,
Thanks for the update. I see that this is the work you were referring to about an experimental test between SO(3) and SU(2).
I like the idea of something like a table-tennis ball (cut in half and judiciously stuck back together) being the required hidden domain containing two objects with orientation entanglement. The crux of the paper strikes me as being on page 9, since for your analysis to apply to the proposed experimental scenario, the L=±1 orientation *has* to be defined by the physical configuration of the objects inside the hidden domain. I note that the orientation of the 2 simple lumps inside the hidden domain can be specified by a vector, but a vector is insufficient to express orientation entanglement. This implies that the 2 simple lumps inside the hidden domain won't give the necessary physical scenario for your analysis to apply - a physical realisation of a spinor is required. The EPR scenario works out because the two objects in question are physically spinors, and although physical objects don't have spin ½, the same 2-to-1 rotation mapping is easily revealed, e.g. the plate trick (Dirac belt trick) or tangloids. In these cases, the orientation entanglement is revealed through two objects being physically linked - by your arm and string respectively - which suggests that some sort of twisted string or spring scenario might do the trick. Given the cult-like behaviour of the ideologues, I think it is important to make sure that the physical scenario is right.
I was far more discouraged by reading Thomas Kuhn, as being ridiculed and ignored (as in my case) is par for the course of a genuine paradigm shift - which is what QT not being fundamental amounts to. And the point I made at the end of my essay still stands - QT is just the beginning. The history of science is that these things always go through, and the adherents of the prevailing ideology end up looking very silly in retrospect. The nearly 40 year failure to reconcile QT and GR was a BIG hint that a false assumption was being made. As a Kuhn paradigm is fundamentally a social paradigm, the false assumption was perhaps inevitably going to be the one that wasn't allowed to be said, and gets shouted down if it is.
Given that FQXi was initially set up by a grant from the Templeton Foundation, I do wonder how they will feel about the shut-out I'm continuing to experience when they finally discover that my book and
philosophy of science paper gives them a big something they've been looking for.
Best,
Michael
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Joy Christian replied on Nov. 8, 2012 @ 10:24 GMT
Hi Michael,
Thanks for your feedback. I view my proposed experiment somewhat differently from how you have viewed it. The two lumps are not supposed to provide the initial orientation of the 3-sphere. The lumps are there to provide different spin directions to be observed by the experimenter, along the chosen direction of her detector (s along a). For each direction s of the spin there are two hidden possibilities for the initial orientation of the 3-sphere, namely L = +1 or -1. The rotating fragments would thus behave like fermions rather than bosons because they would be rotating with respect to each other. A fermion is a fermion because it behaves like an anchored rock rather than a free rock, where the anchor (or the rope) has only abstract or symbolic meaning (it does not have to be physical). In other words, it is the *relative* rather than absolute rotation that makes a fermion a fermion. Since in my experiment each bomb fragment is rotating with respect to (or relative to) the other fragment, it will behave like an anchored rock---i.e., like a fermion. That is the hypothesis, and the experiment is supposed to test this hypothesis.
As for Kuhn's perspective on the scientific revolutions, there is even more depressing book on the subject: "The Golem", by Harry Collins and Trevor Pinch. I highly recommend this book if you haven't read it. Because of my negative experiences since my first anti-Bell paper appeared on the arXiv in 2007, I am able to relate to every episode of scientific misconduct analysed by Collins and Pinch. It is also a more entertaining book compared to Kuhn's rather dry analysis. Sociology of science seems to follow its own laws, and by now I have learned to resign to these laws without giving up the fight.
Best,
Joy
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Author Michael James Goodband replied on Nov. 8, 2012 @ 19:28 GMT
Hi Joy,
I don't know if it has occurred to you that one obvious name for your proposed experiment is "Christian's Exploding Balls", which is a bit unfortunate ;-)
The attached pdf outlines my interpretation of your experiment and why I think that it needs the simple modification of spring loading the two halves of the sphere to give an extra axis of rotation. As something like radioactive decay is the sort of source of randomness acceptable to physicists, your proposed experiment is effectively a variation on Schrodinger's Cat. Unfortunately there may still be some physicists who don't acknowledge that the QT description of radioactive decay stops at the detector. So some sort of QT nonsense could be used ideologues, or they could falsely claim that it is what your paper is about.
I have encountered references to "The Golem" a couple of times, but not yet read it - I found Kuhn depressing enough! It must be remembered that the laws of the sociology of science are not natural laws that cannot be broken, and the social conduct of science takes place within a larger society that doesn't have the same tolerance for the social laws of science - as seen in the prosecution of the Italian scientists. Taking tax payers money to pursue something that has already been proven to be impossible (or has already been done) is known in wider society as economic fraud, and is technically a criminal offence that carries jail time. Some of the social laws of science seem to be leading to illegality because the tax-payer is paying the bill, and some people are waking up to this fact.
Best,
Michael
attachments:
Exploding_balls.pdf
Joy Christian replied on Nov. 9, 2012 @ 08:51 GMT
Hi Michael,
I am happy with the name "Christian's Exploding Balls" for my proposed experiment. It might just get the attention of my critics, who are very good at advertising my work (albeit with malicious intentions).
Thank you for your careful analysis of what you think is a problem. I am, however, puzzled why it is a problem at all. When I say that the small weights are to be randomly affixed inside the two halves of the hollow sphere, I mean they are to be affixed completely randomly. You, on the other hand, are first restricting the locations of the weights to the diagonally opposite locations (as shown in your figures), and then introducing an additional spring mechanism to force the rotations about the central axis. But this is unnecessary if we keep the locations of the two weights independent of each other from the beginning---i.e., not affix them in the diagonally opposite locations. Then the two exploding halves will rotate about all possible directions. Moreover, the two fragments need not be symmetric at all. Although unnecessary, their rotations can then be parameterised by the Euler angles, as you have done.
In fact, one of my experimentalist friends has suggested that instead of exploding balls we can simply break some chemical bonds randomly, of large enough molecules, with asymmetrical fragments flying in two opposite directions. The reason why the details of the rotational symmetries of the fragments do not matter is because the observables are normalized as sign(+s.a) and sign(-s.b). The problem with my friend's suggestion, however, is that chemical molecules are not lager enough to be called classical.
Have I missed something in your analysis?
Best,
Joy
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Author Michael James Goodband replied on Nov. 9, 2012 @ 14:49 GMT
Hi Joy,
The issue I see is that for an exploding force which separates the two shells in Figure 3, the force is parallel to the axis shown. The random positioning of weights on the shells will turn that force into a torque that sets up shell rotation, but no positioning of weights will result in a torque about the central axis of Figure 3 when the exploding force is parallel to the axis. So...
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Hi Joy,
The issue I see is that for an exploding force which separates the two shells in Figure 3, the force is parallel to the axis shown. The random positioning of weights on the shells will turn that force into a torque that sets up shell rotation, but no positioning of weights will result in a torque about the central axis of Figure 3 when the exploding force is parallel to the axis. So the rotation of the shells will not be *any* direction, but only such that the tip of the shell rotation vector lies within the plane shown in Figure 3. An axial torque on the shells is also required to get the rotation vector to lie on S2 - this is the critical requirement of your analysis that I'm considering.
A lack of symmetry in the shell half sizes and weight positions won't make any difference to the general lack of an axial torque on the shells in the separation explosion. If you imagine an exploding grenade, the radial force of the explosion can similarly set the metal shell fragments rotating end over end, or side over side, but not set them rotating about a radial axis. The radial force is in the wrong direction to give a radial rotation vector, so each particular grenade fragment cannot be set rotating in *any* possible direction - despite appearances. Any purely exploding scenario will have the same issue. This is probably the reason why the sort of orientation entanglement you're looking for hasn't been experimentally seen before.
I chose to interpret your scenario in terms of symmetric arrangements as such an interpretation more closely parallels the EPR hidden domain scenario, and in terms of the view just given it doesn't seem to make any critical difference. So I view the symmetric case as reducing the experimental scenario to its purest form. The Euler angles of Figure 4 are not to parameterise the shell rotation, but define the random location of the weight inside each shell (theta, phi) and the angular rotation (psi) that sets the extent of the spring loading between the two shell halves.
A C60 buckyball is perhaps the obvious shell scenario in the molecular world, but has reputedly still been observed to display wave motion - so as you say, chemical molecules are just not big enough to be classical.
Best,
Michael
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Richard Gill replied on Dec. 26, 2012 @ 16:55 GMT
Dear Michael
You wrote "In the case of [1], this means that the shell loading and separation explosion parts of the experiment are purely classical physics".
You are right that Joy's exploding balls need a quantum input before they'll exhibit quantum correlations.This can be seen rather easily from Joy's paper, formula (86) for the experimentally measured correlation E(a,b). Mathematically, the directions s^k can be taken to represent a classical (à la Bell) hidden variable and the formula (86) can now be interpreted as a classical local hidden variables model. One can now run through any standard derivation of the Bell-CHSH inequality, to see that Joy's exploding balls experiment is predestined to disappoint him.
In order to try to convince Joy of this, I developed a new, finitary, proof of Bell's theorem: http://arxiv.org/abs/1207.5103. However, this proof failed to have any impact at all on Joy or his staunch supporters, but maybe you will find it interesting.
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T H Ray replied on Dec. 26, 2012 @ 21:49 GMT
Richard,
That would be the "proof" whose abstract claims, " ... locality, is obviously connected to causality ..."
I don't know what you find obvious about that. Neither Einstein nor Bell subscribed to your naive incomplete conclusion " ... causal influences need time to propagate spatially."
What you find "obvious" ignores the more obvious fact that Joy Christian's topological framework addresses quantum correlations, not local causal influences. That correlations that exist at one moment exist at all subsequent moments (without quantum entanglement) can be found as early as Einstein's 1919 speech to the Prussian academy of sciences. The topological basis of the Christian framework -- continuous measurement functions and initial condition -- obviate almost every objection I've ever heard you raise to the result, which in my opinion you either deliberately misrepresent or show complete innocence of what Joy has created.
You raise statistical arguments when Joy's argument is wholly analytical.
You fall for the naive "Randi challenge" model to test Joy's framework -- a program that not even Randi could endorse, without being a quantum mystic.
If your desire is to renew the debate, that's great -- Michael knows the topology.
Tom
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Fred Diether replied on Dec. 27, 2012 @ 04:37 GMT
Hey Richard,
You didn't ever apologize to Joy for the bet you lost with me. And you are still trying to impose the CHSH inequality on the experiment which is just plain wrong. You did in fact lose that bet.
Anyways, I don't think we should pollute Michael's blog here with this debate. You can reply on
sci.physics.research to a post I did there recently if you wish.
Fred
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T H Ray replied on Dec. 28, 2012 @ 08:32 GMT
Causal inference and local realism are not logically entailed by one another.
Richard Gill's paper is an excellent example, I think, of the Bell orthodoxy taken to its conventional logical extreme of a nonlocal, observer-created reality in which probabilism emerges as a physical law.
That this framework is already shot full of holes and is destined to collapse became even clearer to me in reading my new Science magazine (338, 21 Dec). Though overshdowed by the "big science" news coming out of the LHC, the quiet "small science" news is at least equally important, because it foreshadows the physical realization of topological states of matter, perfectly correspondent to Joy Christian's theoretical predictions.
Xie Chen, et al, introduce us to "Symmetry-Protected Topological Orders in Interacting Bosonic Systems," a model which preserves time-reverse symmetry (as I have been preaching for years on this forum) as well as particle number. "Our construction," they conclude, "is nonperturbative and works for strongly interacting bosonic systems. Therefore, it contributes to a more complete understanding of the topological phase diagram in strongly correlated quantum systems."
In a piece separate from the research article, Xiao-Liang Qi explains, "Chen et al's approach is powerful because it describes a large class of new topological states in general dimensions, which is a major expansion of our knowledge on SPT states in interacting many-body systems. Many interesting questions follow: Because the prototype models proposed are discrete lattice models, is there a continuous field theory description for each topological class?"
Indeed.
The writing is clearly on the wall for nonlocality and quantum mysticism, to those who can read it.
Tom
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Thomas Howard Ray replied on Jan. 1, 2013 @ 20:47 GMT
If Richard Gill wishes to debate the issue in good faith, let him try and save his personal version of local realism by refuting the local realism of EPR as interpreted by Christian and Goodband.
It won't happen.
Local reality in the EPR sense is relativistic -- and therefore all continuous measurement functions (those results that demarcate what we think of as "physical" from what...
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If Richard Gill wishes to debate the issue in good faith, let him try and save his personal version of local realism by refuting the local realism of EPR as interpreted by Christian and Goodband.
It won't happen.
Local reality in the EPR sense is relativistic -- and therefore all continuous measurement functions (those results that demarcate what we think of as "physical" from what is not physical) are not only local, they are time-conserved. The point is that topological assumptions -- which are analytical -- do not admit a nontrivial condition where t = 1 in an unbounded measure space. This error leads Gill to falsely reason:
"I state an open problem concerning the design of a quantum Randi challenge: a computer challenge to Bell-deniers." Not only is this not an open problem anywhere except in the mind of Sascha Vongehr, it isn't a problem that withstands the scrutiny of the scientific method of defining a physical problem in terms of actual physical results; i.e., the independence of calculated result and mathematical theory. A true test of local realism in terms of hidden variables does not make this mistake -- the theoretical framework proposed by both Christian and Goodband gambles on true and precise correlation of theory and experimental result, and does not hedge the bet by assuming that computer calculation and theoretical result are the same thing (thus assuming that which was to be proved in the first place). My attempt to make this point obvious is attached. It is clear from Joy Christian's work that quantum least action is measure zero, and nature has an independent choice in the outcome of a result in every finite time interval. (I interpret this to mean that every measurement function continuous from an initial condition is nondegenerate near the singularity.)
A parting thought -- among Gill's mathematically naive assertions is this:
" . . . disproof of Bell's theorem is as likely as a proof that the square root of 2 is not an irrational number."
It is also a fact that within Dedekind cuts, there exist two numbers whose product is the square root of 2. Though these numbers are unknowable by calculation, we know that they are meta-mathematically real. The same failure of Gill to recognize the meaning of discrete results in a mathematical framework involving a continuous range of variables, prevents him from realizing the metaphysical realism inherent in discrete results obtained from a range of continuous variables in a physical experiment.
Tom
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attachments:
1_Buridans_Principle_and_the_point_at_infinity.pdf
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Florin Moldoveanu replied on Jan. 1, 2013 @ 21:50 GMT
Happy New Year in 2013!
Not only local realism is false, but a stronger result : EPR realism is false http://arxiv.org/abs/1211.4270 This result is one positive outcome out of debating Joy. Another one is the Quantum Randy Challenge.
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Fred Diether replied on Jan. 1, 2013 @ 22:20 GMT
Oh! Florin, you finally did a new paper. Why don't you start a new blog for it so we can discuss it off Micheal's blog?
Fred
Happy New Year to All!
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Florin Moldoveanu replied on Jan. 1, 2013 @ 22:44 GMT
I would love to, but I am too busy. The above pre-print will be submitted shortly to PRL where it will be peer reviewed.
I also have much much stronger results. I started a Nature submission a paper which obtains QM from simple physical principles. I expect the publishing process to be completed sometime in between February and April this year. I'll upload the first draft on the archive sometimes in February.
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Thomas Howard Ray replied on Jan. 2, 2013 @ 01:43 GMT
"To summarize, EPR reality criterion demands the objective existence of spin independent of measurement."
My last attachment refutes your result.
No physical phenomenon is independent of measurement, and neither does EPR so demand. "All physics is local" means that all measurement functions are local and limited only relativistically (i.e., no privileged frame). This renders all measurement functions continuous in the local inertial frame.
Sorry, Florin, but the moon really is there - faithfully occupying that middle value of measure zero. That's a quantum value, not classical. That no classical theory of motion can be derived from quantum mechanics does not therefore imply that quantum correlations cannot be derived from classical mechanics, as the above simple example illustrates.
The "Quantum Randi challenge" is postmodern code for the old quantum mysticism. Plus ca change, plus c'est la meme chose.
Tom
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Paul Reed replied on Jan. 2, 2013 @ 06:37 GMT
Tom (all)
Sorry to chime in with my apparently simplistic comments, but, yet again, if people started from what the generic form of physical existence (ie that which is potentially knowable to us, and not what we can dream up), then this philosophical debate would never have occurred, ie:
-physical existence is limited (ie a closed system) because it must have detectability (either...
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Tom (all)
Sorry to chime in with my apparently simplistic comments, but, yet again, if people started from what the generic form of physical existence (ie that which is potentially knowable to us, and not what we can dream up), then this philosophical debate would never have occurred, ie:
-physical existence is limited (ie a closed system) because it must have detectability (either actual or hypothetically verified on the basis of that), as this is the only form of existence we can be aware of. We cannot externalise ourselves from it, except with belief, as we are part of it. Hence without proper pre-conditions and due process, as we can only ever comparing awareness with other awareness, it is easy to conflate knowledge and belief.
-there is no relativity in physical existence, which is an existential sequence. The entirety of whatever comprises it can only exist within that sequence in one definitive physically existent state at a time. And the predecessor must cease to exist so that the successor can exist, there is no physically existent ‘future’.
-there is no time (or more precisely, change) in any physically existent state, this concerns the measurement of the rate at which change occurs between physically existent states
-all physics is local, a physically existent state can only be a physical cause in certain specific conditions in respect of spatial position and sequence order, as physical influence cannot ‘jump’ physical circumstances
-any form of sensing (ie receipt of physical input by virtue of being in the line of travel and interacting therewith) is independent of physical existence, both in terms of what was physically received and what caused that
-similarly measurement, which is the subsequent comparison of what is identified as existent against a conceptual constant, ie an abstraction of any given manifest feature
-what is sensed is a physically existent representation (in the context of the recipient sensory system) of what physically occurred. There is a timing delay between physical existence and receipt of that representation.
Paul
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Paul Reed replied on Jan. 2, 2013 @ 07:32 GMT
Florin
“If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity”.
The point is that this condition is false, although it does allude to a better understanding of physical existence than the metaphysical concept it is commenting on.
Whether we can predict or not, whilst disturbing or not, is irrelevant to physical existence. That occurred before we can do anything. Furthermore, what we physically interact with, both in order to identify physical existence and then to effect some calibration (measurement), is not physical existence. It is a physically existent ‘representation’ (ie from the perspective of the sensory system) of that (aka light, etc). Which, incidentally, by receiving (ie being in the line of travel) we do not affect either, except that that particular physical effect ceases upon receipt. Physically, receipt of this ‘representation’ by a human, or any other sentient organism, is no different from receipt by a brick, or any other inanimate entity. The difference lies in the capability to subsequently process, which is not physics.
Physical existence (or what you refer to as nature) is not determined by what we can sense, etc, etc. It occurs independently. What existence might ‘really’ be is irrelevant, because we can only be aware of it, and only in one form (ie physical existence), which is characterised by detectability. For hypothesis to be valid it must conform to this, ie not enable belief. Put simply, hypothesis must only be concerned with identifying what could have been known had the physical systems involved been perfect. Not with whatever we can dream up.
The physical existence we can be aware of is existential sequence, which involves a number of features I have described above.
Paul
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Joy Christian replied on Jan. 2, 2013 @ 09:54 GMT
Hi Michael,
A brief note to say that---since both the roughnecks and peanut gallery have finally found us---it is best we continue our dialogue in private in the New Year. You have my email address just in case you want to discuss something.
By the way, I hope you know that you can delete unwanted posts from your blog.
Best,
Joy
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Joy Christian wrote on Nov. 11, 2012 @ 11:01 GMT
Hi Michael,
It took me a while, but now I see your point. I did a little calculation to see that the angular momentum vectors of the two shells will indeed remain confined to the vertical plane, as shown in your Figure 3. The reason for this has to do with how torque is defined in mechanics: tau = r x F. Torque thus has a vanishing component along the direction of the applied force F. In other words, the torque, and hence the angular momentum of a shell will remain confined to the plane orthogonal to F. The overall picture of the experiment will thus be identical to that in the usual EPR-Bohm type experiments (see, for example, the attached PDF).
So I am with you so far. Next, you want to introduce a spring mechanism to unconfine the two angular momenta from the vertical plane (as you show in your Figure 4). Theoretically I have no problem with this. But it may lead to some practical difficulties. Moreover, I am not convinced that the spring mechanism is necessary. The issue you discuss just below your Figure 4 arises only if we restrict to the diagonally symmetric assignments of weights on the two shells. For asymmetric assignments the issue disappears, as far as I can see. Do you agree?
I am simply trying to minimise complications, because each additional contraption may increase the danger of a systematic error in the experiment.
Best,
Joy
attachments:
CHSHpage.pdf
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Fred Diether replied on Nov. 11, 2012 @ 22:19 GMT
Hi Joy,
Yes, I was going to suggest exactly what you are saying since in EPR scenarios, the polarizers (analyzers in the figure) or Stern-Gerlach device constrains the particles to give results in parallel planes. I am wondering if your experiment could be simplified by just have two flat discs with random masses on opposing sides be exploded apart?
Best,
Fred
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Joy Christian replied on Nov. 12, 2012 @ 02:04 GMT
Hi Fred,
Yes, two flat discs with randomly attached masses on the opposing sides may also work in principle. But then how would one explode them apart?
In the case of a snapped ball we can explode the two shells apart simply by heating the ball, because there would be air trapped inside.
Best,
Joy
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Fred Diether replied on Nov. 12, 2012 @ 07:26 GMT
Hi Joy,
Some kind of exploding third disc inbetween? That would explode when the temperature got high enough. Perhaps you could have holes in the center of the discs and have them slide on a taught small wire when moving apart. Maybe you could do that with the hemispheres also? I am sure some clever experimenters can figure out how to do it.
Best,
Fred
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Joy Christian replied on Nov. 12, 2012 @ 12:29 GMT
Hi Fred,
A very thin exploding third disc in-between the two main discs could do the job. We are indeed venturing into territory where the opinion of an experimentalist would be more valuable compared to our own. But the idea of two flat discs does seem to have its own appeal from the perspective of air resistance. I mean air resistance would be symmetric for the rotating flat discs compared to that for the rotating hemispheres.
Best,
Joy
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Author Michael James Goodband replied on Nov. 12, 2012 @ 13:22 GMT
Hi Joy,
I don't see asymmetric weight placement as making any difference, because the issue is turning an explosive force into a rotation vector parallel to the force vector. I tried a demonstration of this infront of the rugby on Sunday - the basic principle works but my camera isn't fast enough to see it (1 sec video). I halved a table-tennis ball, added asymmetric weight placements,...
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Hi Joy,
I don't see asymmetric weight placement as making any difference, because the issue is turning an explosive force into a rotation vector parallel to the force vector. I tried a demonstration of this infront of the rugby on Sunday - the basic principle works but my camera isn't fast enough to see it (
1 sec video). I halved a
table-tennis ball, added asymmetric weight placements, glued the halves together with chocolate (an odd material for a physics demonstration I'll admit),
placed it on an air-pump and
exploded it. The air pump nozzle would obviously have prevented any axis rotation if there were any, but I don't see how there would be. An alternative demonstration without the nozzle would be to pour some fizzy drink into the ball and then drop-in a crushed mint to nucleate bubbles - the pressure would hopefully build faster than it leaked out the hole, and so explode the ball.
The symmetric weight arrangement and spring loading I referred to in the PDF gives the basic form for a thought experiment, which then needs to be turned into a practical experiment. Finding a suitable joining mechanism to give axial rotation appears to be the main issue, and is why I think that this orientation entanglement hasn't been seen before in classical physics. The above fizzy drink example could give axial rotation if there were angled vents for some of the escaping gas pressure to rotate the shell halves. Instead of just relying on heating the ball in your experiment, the ball could contain a propane/air mixture that is ignited by an induction coil with a spark gap (inside the ball).
A related issue about the S2 defined by the tip of the rotation vector is how spherical does the surface have to be for your analysis to apply and the predicted correlation results to be experimentally identifiable?
Best,
Michael
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Joy Christian replied on Nov. 12, 2012 @ 17:20 GMT
Hi Michael,
O.K., I am beginning to appreciate the issue.
What is needed is something like what is shown in the picture below. The angled vents (nozzles) can be stuffed differently (say, with chocolate) for each trial so that the escaping gas pressure would rotate the shells differently each time. I think something like this would be much better than a mechanical device like spring. The nozzles may be kept as small as possible to retain the spherical symmetry.
Best,
Joy
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Author Michael James Goodband replied on Nov. 12, 2012 @ 18:41 GMT
Exactly!
The setting of the weights and such nozzles could be parameterised by the 3 angles (theta, phi, psi) for each shell, which must determine the orientation of the spin basis {1, L_mu(lambda)} with respect to the detector basis {1, D_mu}. I think this physical setting of the orientation lambda=±1 needs to be made explicit, so it is clear that lambda is a physically set variable which is being hidden by closing the shells. Otherwise it seems to me there is room for mischievous misunderstanding.
Best,
Michael
Joy Christian replied on Nov. 12, 2012 @ 21:05 GMT
In fact, if your interpretation is correct, then the entire experiment can be done in two different ways. One with the nozzles blocked completely so that the rotation triplets are identified, and the other with the nozzles filled only partially, so that the rotation triplets remain distinct. The first case would then correspond to the dashed blue lines in my Fig. 4 and the second case would correspond to the solid red curve (linear versus cosine correlation). So I am now warming up to your analysis.
Best,
Joy
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Joy Christian replied on Nov. 14, 2012 @ 08:17 GMT
Hi Michael,
I am afraid I am still having trouble understanding your argument. I think I follow up to the first four lines just below your Figure 4, but I do not understand the last four lines of that paragraph. In particular, I do not understand how you replaced +psi with -psi when theta is replaced with theta + pi. The difficulty I am having is with the conservation of angular momentum. If your argument is correct, then it should not conflict with any conservation laws. In fact we should be able to derive your argument from the conservation of angular momentum. But I am unable to derive it using ordinary mechanics. What I get instead is that the two rotations defined by the sets like (theta, phi, psi) would be indistinguishable even with the axial rotation added. What am I doing wrong?
Thanks,
Joy
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Author Michael James Goodband replied on Nov. 14, 2012 @ 15:22 GMT
Hi Joy,
Just to clarify that we are on the same page:
1) Individual objects are rotationally invariant under SO(3) - generator J angular momentum - whereas the relative rotations of two or more objects are rotationally invariant under SU(2) - generator S spin.
2) It is easy to see in classical physics that the true relative rotation group is SU(2) spin and not SO(3) angular...
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Hi Joy,
Just to clarify that we are on the same page:
1) Individual objects are rotationally invariant under SO(3) - generator J angular momentum - whereas the relative rotations of two or more objects are rotationally invariant under SU(2) - generator S spin.
2) It is easy to see in classical physics that the true relative rotation group is SU(2) spin and not SO(3) angular momentum e.g. plate trick and tangloids
3) For the EPR scenario of a spin singlet eigenstate S=0 of two spin ½ eigenstates, the collected papers in your book prove that the spin correlations found by two observers (Alice and Bob) can be due to this SU(2) orientation entanglement.
4) There are two critical physical conditions for this:
a) the tip of each spin vector of the pair lies on S2
b) the spins of the pair are correlated to be equal and opposite by being part of an initial singlet state of spin group SU(2).
5) Because the two spheres S2 of the spins of the singlet state are subspaces of S3, the S3 orientation of the initial correlated spin state can given by variable L=±1.
6) As we discussed earlier, the variable L can either be hidden by not being measurable by any means, or just by not being measurable in a correlation experiment - it makes no difference to your analysis.
7) This means that there could also be a third option of knowing what the value of L was, but then forgetting it - still will make no difference. In thought experiment terms, the initial state with known value of L can be prepared by a third person (say Simon) who then just doesn't tell Alice or Bob what the value of L is.
These points intuitively convince me that the underlying proposition of your paper is true:
There-exists a purely classical physics scenario of orientation entanglement where rotation/spin correlation measurements by two independent observers display the same correlation results as the spin measurements of the EPR scenario.
The only question is what exactly is this classical physics scenario. Are we agreed so far?
We have been blowing things up for a few hundred years without noticing this effect, from which I conclude that the sought-for scenario must require a non-trivial twist of some kind. Are we agreed that the rotation given to the weighted halves of an exploded sphere only lie on a plane and not the required S2?
The next point is that an explosive force on asymmetrically weighted shell halves means that angular momentum is *not* conserved. Even for the symmetric weight positioning of my Figure 1 angular momentum is *not* conserved: J=0 before the explosion, but net angular momentum afterwards. It is only in the scenario of Figure 2 that the angular momentum of the shell halves is equal and opposite after the explosion. Angular momentum conservation is a constraint that has to be added by hand through the weight placement because of the explosive force. Agreed?
To have a S=0 singlet state before and after the explosive separation, where the rotation vectors of each half lie on a sphere S2, requires the two halves to be set spinning on their axis in *opposite* directions by the explosion somehow. At the though experiment level this could be by a spring mechanism that spins the two halves about their axis in opposite directions as it exploded the shell halves apart. This gives a thought experiment scenario of a correlated S=0 singlet state before and after the explosive separation - this singlet condition seems to me to be required for your correlation analysis (point 4b above). Are we agreed on this?
Turning such a thought experiment into a practical experiment is a different matter. As is whether it does actually physically meet all the required conditions or not.
Best,
Michael
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Joy Christian replied on Nov. 14, 2012 @ 18:08 GMT
Hi Michael,
I completely agree up to your statement: The only question is what exactly is this classical physics scenario. You have understood my argument correctly and impressively clearly. The nontrivial twist you refer to is the twist in the Hopf fibration of the 3-sphere discussed on the page 200 of my book. I agree that the rotation given to the weighted halves of an exploded sphere...
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Hi Michael,
I completely agree up to your statement: The only question is what exactly is this classical physics scenario. You have understood my argument correctly and impressively clearly. The nontrivial twist you refer to is the twist in the Hopf fibration of the 3-sphere discussed on the page 200 of my book. I agree that the rotation given to the weighted halves of an exploded sphere only lie on a plane and not on the required su(2), Lie-algebraic, 2-sphere. I had not realized this before, because I was blindly following Peres's analysis of the bomb explosion without thinking it through myself. His analysis now appears to be inadequate in more than one way (cf. my chapter 3). So I agree that an additional axial rotation is needed in the experiment for it to be a viable classical analogue of the singlet experiment. I also appreciate that angular momentum is not conserved in general. Moreover, I have no problem with the spring mechanism at the level of a thought experiment. It would indeed set the two halves spinning in the opposite senses (and in the opposite directions).
So it seems that I agree with everything you have written. My confusion comes from the fact that when theta is replaced by theta+pi we are actually switching the two halves. The replacement of theta with theta+pi would detach the weight from one hemisphere and attach it to the other hemisphere (at least conceptually). Is this what you have in mind, or am I misreading what you have written in your notes? For one thing you are not using the standard notation for the polar angles. Also, psi in my paper is the rotation angle whereas psi in your notes is the angle by which the two halves are initially rotated with respect to each other. This adds to the confusion I am having (but by now I have understood your notation).
My remaining uneasiness is then still with what you say in the last four lines in the paragraph just below your Figure 4. The question is: Is the distinguishability of two rotations equivalent to the changes in the S3-orientation (L=+1 to L=-1) I have been considering? Or are we confusing two different things? I will be at ease only when I am able to translate your intuitive argument into the mathematical framework I have set out in my latest paper.
Best,
Joy
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Author Michael James Goodband replied on Nov. 14, 2012 @ 19:56 GMT
Hi Joy,
Sorry about my use of non-standard notation - I did it quickly and didn't stick to convention. The +PI point after Figure 4 is about what is *needed* to distinguish SO(3) from SU(2) in setting up each ball for explosion so that the correlations are given by SU(2) and not SO(3) - my fault, this wasn't particularly clear. My simple modification to give a twist doesn't automatically...
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Hi Joy,
Sorry about my use of non-standard notation - I did it quickly and didn't stick to convention. The +PI point after Figure 4 is about what is *needed* to distinguish SO(3) from SU(2) in setting up each ball for explosion so that the correlations are given by SU(2) and not SO(3) - my fault, this wasn't particularly clear. My simple modification to give a twist doesn't automatically deliver this without reversing the psi twist setting by hand. My awkwardness on this was due to an unease that I think I've now identified.
On the big picture overview of 2PI or 4PI periodicity, what do the known examples of the plate trick, tangloids and EPR have in common, that 2 coffee cups sitting on a table do not? The answer is connection, and moreover a connection that supports the transmission of rotational twists: your arm in the plate trick, string in tangloids and the gauge field between two charged electrons. Although a spin singlet state of photons has no such connection in quantum mechanics, in the full QFT each photon can give rise to virtual electron/positron pairs which do have a gauge field connection with the other pair. I mentioned using string earlier because I had a suspicion that inserting a physical connection between the two halves of the split sphere may be significant. A connection between the two halves in terms of an electrostatic or magnetic field may work but introduces an added complication, so it is probably better to just consider a mechanical connection.
This connection requirement would seem to explain why coffee cups - only coupled by gravity which doesn't transmit rotational twists - don't display physical orientation entanglement in everyday usage. I note in passing that in a theory with compactified dimensions, gauge fields are the dimensionally reduced description of physical rotational twists in the compactified dimensions. I can't yet tell whether this answers my earlier question about whether there is a simple way to disprove teleparallel gravity using correlation results: as in no physical orientation entanglement of solely gravitational objects means no teleparallel gravity.
I have also been having difficulty relating the physical set-up of the experiment to the S3 orientation, which I think has to be explicitly shown because the set-up determines the value of the variable L=±1 that is then hidden. The physical set-up also has to be shown to *require* a spinorial basis, as this requirement is the basis for the relative orientation L=±1 between the physically determined basis of the individual ball set-up and the detector basis.
I am very aware that the point is to actually conduct the experiment - and not just find a nice thought experiment - to obtain the same correlation results explicitly in an unequivocally classical physics experiment.
Best,
Michael
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Joy Christian replied on Nov. 15, 2012 @ 13:19 GMT
Hi Michael,
There are several things that need to be cleaned up before we can make any progress.
(1) Your notation for the triplet (theta, phi, psi) is confusing for me because they have nothing to do with the polar coordinates of the spin vectors (or bivectors). Your theta, phi, and psi are spimply parameters that determine the spin vectors, which is a different matter. So let me...
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Hi Michael,
There are several things that need to be cleaned up before we can make any progress.
(1) Your notation for the triplet (theta, phi, psi) is confusing for me because they have nothing to do with the polar coordinates of the spin vectors (or bivectors). Your theta, phi, and psi are spimply parameters that determine the spin vectors, which is a different matter. So let me replace your notation by the notation (t, p, s), where t and p specify the location of the weight in the given shell and s quantifies its spring action, per your mechanism. We can now define the spin vectors a and b as functions of this triplet: a = a(t, p, s) and b = b(t, p, s). The corresponding bivectors I.a and I.b can now be parameterized by the standard polar coordinates, theta and phi, and their product (I.a)(I.b) can be further parameterized by the relative rotation angle psi.
(2) Now I don't think the additional axial rotation is needed for the experiment (yes, I am changing my mind about this). I agree that without the axial rotation the spins would be confined to the vertical plane, but that is fine, because the corresponding spin bivectors are still elements of the su(2) 2-sphere, where su(2) is the Lie algebra of SU(2). What is more, since the Lie algebra structures of the groups SU(2) and SO(3) are identical, we have the identity su(2) = so(3), and hence the bivectors I.a and I.b themselves cannot distinguish between the groups SU(2) and SO(3). It is the *relative* rotation angle psi between these bivectors that matters, and this is brought out by the product
(I.a)(I.b) = -a.b - I.(a x b),
where psi is twice the angle between the vectors a and b. Now we can see that when b is set equal to -a (which is equivalent to replacing your theta with theta+pi) the RHS of the above product changes sign, and hence it represents the antipodal point of the 3-sphere. In other words, although I.a and I.b themselves cannot distinguish the antipodal points of the 3-sphere, their product can, and does. Moreover, none of this is affected by the fact that a and b are confined to the vertical plane. What matters is the metric tensor determining the inner product between a and b, as in my equations (55) and (85).
(3) Note, however, that in the above equation I have smuggled something in by hand---namely, the orientation of the 3-sphere. I have implicitly assumed that the 3-sphere is right-oriented. But it need not be right-oriented, and that is where I find the room for the initial state lambda. The change in lambda will change the sign of the second term on the RHS.
(4) Now there need not be a "physical" connection to reveal the truism of orientation-entanglement. What I have been arguing is that this connection already exists in the physical space we live in. The coffee cups do indeed respect this connection contrary to appearances, but we are unable to see it without the aid of a device like a flat rope. Put differently, the reason why we haven't seen orientation-entanglements in the macroscopic world so far is because no one has ever done the correlation experiment of the type I have been proposing.
I think the above points set out some differences between our respective views of the experiment. In particular, I now tend to think that the axial rotation and the spring mechanism does not add anything useful to the experiment. But I am willing to be persuaded otherwise.
Best,
Joy
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Joy Christian replied on Nov. 15, 2012 @ 15:36 GMT
Correction: I meant to say "...when b is replaced with -b..."
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Author Michael James Goodband replied on Nov. 15, 2012 @ 17:04 GMT
Hi Joy,
Our basic difference can be expressed as that you think the rotation connection of physical space applies to both fermions and bosons, whereas I think that it only applies in the fermionic sector. The conclusion of my work is that all the fermionic particles are topological defects in the structure of space, and so spin ½ particles *necessarily* have a non-trivial SU(2) spatial...
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Hi Joy,
Our basic difference can be expressed as that you think the rotation connection of physical space applies to both fermions and bosons, whereas I think that it only applies in the fermionic sector. The conclusion of my work is that all the fermionic particles are topological defects in the structure of space, and so spin ½ particles *necessarily* have a non-trivial SU(2) spatial structure about them. As discussed earlier, viewing two such particles as residing in a singlet state within a hidden domain of small radius, the spin correlation analysis should proceed *exactly* as given in your book. However in this context, the space outside of the hidden domain won't have this non-trivial SU(2) structure and the bosonic sector will be physically SO(3).
Since classical physics is the large scale limit of the bosonic sector with the physically apparent rotation group being SO(3) - but underlying SU(2) - your proposed experiment is effectively a test between our two views. The ball as set-up in your experiment - with or without the twist - would be in an SO(3) state, for which I still cannot see how the value of the hidden variable L=±1 would be physically determined. Verification of your prediction of SU(2) correlations in the apparent SO(3) of classical physics would establish your correlation results for both sectors. However, as it is only a test in the SO(3) bosonic sector, a negative result would have *no bearing* on the SU(2) fermionic sector of EPR or particles being spatial defects. My concern is that if the experiment turns out as I predict - no SU(2) correlations - as it stands you could be open to a hostile attack claiming that a negative result shows your EPR analysis to be wrong, but this would *not* be true.
I have been trying to come-up with a physical realisation of SU(2) in a way that would be compatible with your analysis - hence the various ways of trying to tweak it. The plate trick etc. by which the Z_2 centre of SU(2) is physically revealed involves mapping SU(2) over the interval [0,1]: 0 at your shoulder and 1 at your hand. If you place a gyroscope on your hand, then you can orientate it such that the tip of the rotation vector defines S2, and it will display the 4PI rotation invariance of the plate trick. But this S2 is mapped to your stationary shoulder (at 0) and so there can be no orientation correlation with another gyro placed in your other hand.
The only other way that I can see of exposing the Z_2 centre of SU(2) is to map S3 to the spatial surface S2, i.e. my spin topological defect. For such a defect to exist in field theory requires an unbroken U(1) symmetry, and to get all the known fermions requires the mapping S6 to S2 - giving the full space as being S7. Turning it around the other way, an experimental result of SO(3) correlations in classical physics would be in agreement with the conjecture that the only way to obtain the EPR correlations in classical physics is if fermionic particles are spatial defects.
My adding a twist was my first step in trying to get a physical realisation of SU(2), but I can think of no second step that actually achieves this - without it, the first step of a twist does seem to be redundant. The experiment gives a test between our two views, but your critics may view it as a test of your EPR analysis, which it is not - it is a test of your generalisation of the fermionic sector to the bosonic sector in classical physics as well.
Best,
Michael
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Joy Christian replied on Nov. 16, 2012 @ 13:06 GMT
Hi Michael,
There is always a danger of misinterpreting any experimental result, and my proposed experiment is indeed prone to the kind of hostile attacks you fear. Given the fact that belief in Bell's so-called theorem is not a rational belief, I expect nothing less from my critics. There is a 500-pound canary sitting in the very first equation of Bell's famous paper but some people are...
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Hi Michael,
There is always a danger of misinterpreting any experimental result, and my proposed experiment is indeed prone to the kind of hostile attacks you fear. Given the fact that belief in Bell's so-called theorem is not a rational belief, I expect nothing less from my critics. There is a 500-pound canary sitting in the very first equation of Bell's famous paper but some people are flatly refusing to see it. How can we expect any rational response to my experiment from them?
On the other hand, the differences in our perspective do not seem to me to be very serious. I think they boil down to a subtle difference in what we think is a fermion. For me a fermion is an anchored particle and a boson is a free particle, where the words "anchor" and "particle" are to be understood abstractly. In particular, *any* connection between rotating objects may serve to distinguish the 2pi periodicity from 4pi periodicity. I think we agree on this definition but we have different pictures in mind about what qualifies as an anchor. This is reflected, for example, in your comment: "I still cannot see how the value of the hidden variable L=±1 would be physically determined."
The hidden variable L is precisely what provides the connection between the two shells, but you are looking for it in a slightly wrong place. Here is the correct picture according to my framework:
Let S be a spin vector of one of the shells, defined by the location of the weight and, if you wish, a twist provided by a spring mechanism. Thus, in the notation of my previous post, S is a function of t, p, and s. Thus we have S = S(t, p, s). But the parameters t, p, and s are *not* the hidden variables of the model. They are clearly not hidden. More importantly, they are not the variables that are being summed over. It is the orientation L of the 3-sphere that is being summed over. In other words, over and above the variables t, p, and s, the spin S depends on L, as follows:
S(L) = L S.
And it is this L that is being summed over to obtain the correlation. Thus, for any given L, for example L = +1, we have the sign of the spin determined as follows:
S(L=+1) = + S.
And it is such signs that are being summed over to obtain the correlation. I am stressing this because you seem to be viewing t, p, and s as hidden variables, but that is not what the model is saying. It the orientation L, which in Bell's language is the initial or complete state of the system, that is the hidden variable, and it is this L that provides the connection, or anchor, between the two shells, which are not rotating in isolation but rotating *in tandem.* This is what makes the two shells fermions, not bosons, according to my definition of a fermion above.
So I think it is misleading to view my experiment as a test of extending the fermionic sector to the bosonic sector. This would be true if my proposed experiment involved coffee cups that are *not* connected by the initial state L (which is the "common cause" for the observed spin values in Bell's language).
Best,
Joy
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Thomas Howard Ray replied on Nov. 16, 2012 @ 14:45 GMT
Joy/Michael,
"For me a fermion is an anchored particle and a boson is a free particle, where the words 'anchor' and 'particle' are to be understood abstractly."
Yes, for me that would correspond to bound and free variables. The free variable is necessarily hidden (nonlocal) while the correlated measurement of free and bound variables is necessarily local.
In other words, because in a given time interval, any number of bosons can occupy a point and only one fermion can occupy a point -- the correlation state, or real measurement, is point for point exact between particles exchanging energy (the anchor and the boat metaphorically speaking), rather than probabilistic, as if the measurement were being made between the anchor and particles of the sea.
Following this exchange with much interest ...
Tom
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Author Michael James Goodband replied on Nov. 16, 2012 @ 15:44 GMT
Hi Joy (and Tom),
Yes, I agree that our only difference seems to be when we think space qualifies as the anchor. This is why I'm looking for L to be specified by the configuration, whereas I think you view it as residing in the physical space. We completely agree for EPR because for my spatial topological defects, physical space *is* the configuration space. Furthermore, in the case of 2...
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Hi Joy (and Tom),
Yes, I agree that our only difference seems to be when we think space qualifies as the anchor. This is why I'm looking for L to be specified by the configuration, whereas I think you view it as residing in the physical space. We completely agree for EPR because for my spatial topological defects, physical space *is* the configuration space. Furthermore, in the case of 2 spin defects residing within a closed hidden S2 domain, whether they are A(Up)B(Down) or B(Up)A(Down) *does* determine the value of the hidden variable L. However, these defects possess a virtual-matter field (radiation trapped in the Planck-scale rotating black hole ergo-region) for which the field expansion includes both AB and BA, giving both values L=±1. This dynamics occurs on the order of the Planck timescale, and so all experimental measurements occur on the timescale of very many interchanges between AB and BA. This gives a physical basis (from the configuration space) for performing the sum over the values L=±1, and your EPR analysis follows through.
When we move away from this EPR scenario, I carry the cause of the correlations with the configuration space whereas you seem to place the L=±1 in physical space. If you are correct in your view that normal physical space provides the necessary anchoring for a classical object to be fermionic, then the same correlations should be manifest in the sort of experiment you suggest. In contrast, if it really is about the topology of the configuration space, then the SO(3) symmetry of your experimental configuration will give SO(3) correlations. The problem I have with L=±1 residing in physical space is causation - what causes L to be +1 or -1? In my configuration space view carried over from EPR, the answer is that the configuration causes L to take a specific value. This is what I am looking for by way of the initial conditions of the relative angle values, and you're right it isn't there. If this is not the answer, then L seems to be non-causally determined and intrinsically probabilistic - Einstein would turn in his grave, except for his brain of course, which is in a jar somewhere ;-)
As my view of EPR in terms of spin defects is deterministic in classical physics, and the averaging is due to the measurement timescale spanning many cycles on the internal dynamics within the S2 hidden domain, the same results should persist when the physical scale is increased to that of experimental classical physics. This is why I also suspect that EPR-style correlations might be found in classical physics, but my configuration space view gives much more constraining conditions. EPR-style correlations will require a spin correlation configuration with SU(2) symmetry with spin vectors lying on S2 where the configuration determines the value of L, then a flipping dynamics is required in the configuration to get both L=+1 and L=-1, and then the experimental measurement needs to be made over the timescale of many of these cycles so that averaging over L is required.
I have tried to make the exploding ball scenario fit these requirements, but I can't see how it is possible. In the thread below I suggest a gyro based class of experiments, but so far I can't make them work-out for my configuration space view either.
Best,
Michael
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Joy Christian replied on Nov. 16, 2012 @ 17:28 GMT
Hi Michael,
James Putnam permits one miracle in his theory of the world. Aristotle permitted one unmoved mover. I too do not want my Buridan ass to starve to death. L = +/- 1 is a perfectly random number. It is an initial state offered to the ass. But mine is a smart ass, so it always breaks the symmetry at the moment of each explosion by randomly making a choice between L = +1 and L = -1. This is the best answer I can offer (and it is actually Bell's answer).
Best,
Joy
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Thomas Howard Ray replied on Nov. 16, 2012 @ 18:55 GMT
It has to be the right answer, Joy. Perfect randomness is perfectly symmetric -- if it were possible that t = 0, h-bar would also be zero, and we wouldn't be having this disccusion; the world would be obviously classical, and there would have been some specific time when the universe was at rest (at rest relative to what?) Because t is not zero, however, nature has a choice. Excellent.
Tom
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Author Michael James Goodband wrote on Nov. 16, 2012 @ 12:05 GMT
Hi Joy,
After my mentioning the rotation group map S3 to S2 for my spin defects, it occurred to me that there is a second class of experiment that might be worth considering: those involving two coupled gyroscopes, either mounted side-by-side or concentrically.
Unlike in the exploding ball case, the permanent mechanical connections allow for extra mechanical trickery. Your new paper...
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Hi Joy,
After my mentioning the rotation group map S3 to S2 for my spin defects, it occurred to me that there is a second class of experiment that might be worth considering: those involving two coupled gyroscopes, either mounted side-by-side or concentrically.
Unlike in the exploding ball case, the permanent mechanical connections allow for extra mechanical trickery. Your new paper considers the metric of the configuration space - not including the physical space about the configuration so our differing views on this are perhaps secondary - where the issue is whether opposite points on the S3 manifold of the configuration space can be distinguished - SU(2) - or not - SO(3). This difference seems to me, to ultimately feed through to the value of the hidden variable: L=±1 for the distinguishable case of SU(2); but L=+1 is identified with L=-1 for the indistinguishable case of SO(3). If the physical ability to distinguish between 2PI and 4PI rotations is just the issue, then can't that just be given by flipping a toggle switch? Fist 2PI rotation the switch is flipped into its set position, second 2PI rotation the switch is reset - so 2PI rotations are physically distinguishable from 4PI rotations. This sort of thing can be physically implemented for mounted gyros, but not the exploding balls.
The concentric gyro case seems to me to be the closest mechanical realisation of the S3 to S2 mapping of my spin defects - although I still can't see how to implement the required mechanical trickery to give the configuration the desired SU(2). Each gyro wouldn't be the normal disk, but the inner ring of a ring-bearing where the outer ring was mounted on gimbals to give the required S2 surface for the gyro rotation vector. With a hollow shell inside the first gyro, a second gyro could then be mounted inside it. Inside the inner gyro is a hollow shell to which the rotation group does not act because there are no mechanical objects there - hence a mapping from S3 rotation group space to physical S2. The difficulty here is that the homotopy group PI_3(S2) sees a clash between the Hopf fibre bundle with PI_3(S2)=Z and the general homotopy group relation PI_N(S^(N-1))=Z_2 for all N>2. This is the same issue between SO(3) and SU(2), where the Hopf fibre bundle configuration has 2PI invariance, whereas the configuration for PI_3(S2)=Z_2 has the desired 4PI invariance. The simple mechanical version has 2PI invariance, but the desired relative 4PI invariance could possibly be produced through suitable mechanical trickery.
If purely mechanical trickery isn't possible, then all the concentric rotating metal rings gives the possibility of using magnetic induction with suitably mounted magnets. How to do this currently eludes me, but it might be possible. Does this gyro version seem to be a potential option to you?
Best,
Michael
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Joy Christian replied on Nov. 17, 2012 @ 10:20 GMT
Hi Michael,
I am not quite following the details of this two gyro experiment. What is the initial state here? In the case of exploding balls the explosion naturally sets the initial state, which in my picture is the orientation of the 3-sphere. What is the analogue of an initial state in the gyro case? If it is purely mechanical analogue, then it can be described by the standard bivector subalgebra, defined by
(I.a)(I.b) = -a.b - I.(a x b).
There is then no room for a stochastic sign change in the second term on the RHS. So, although it would be nice to be surprised, I think you will never find the kind of mechanical trickery you are looking for. In other words, fundamentally the difficulty here is the same as in the exploding balls case.
Best,
Joy
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Author Michael James Goodband replied on Nov. 17, 2012 @ 15:36 GMT
Hi Joy,
The 2 gyro arrangement is me thinking out loud trying to find a classical mechanics scenario that dynamically realises the SU(2) I'm looking for with my configuration space view. But I can't find the correct initial state or mechanical trickery, and so I'm also coming round to the view that it isn't possible. In which case, the spherical symmetry of this sort of scenario should allow for a mathematical proof that it isn't possible. Turning that round the other way suggests that it would then be possible to prove that my spin defect scenario is the *only* possible configuration that gives a classical physics realisation - because it does - which is what I would then be looking for here. If true that would then mean in my configuration space view, that super-linear correlations between particle spins implies that particles are my spin defects.
I do have a concern about the ensemble sum in your new paper as the sum over lambda^k has a different physical basis in section V compared to the lambda sums/integrals in your book. In all the proofs of your book the sum over lambda is for one instance of correlation between two particles - physically meaning that the one instance explores all the global structure of S3, including the critical twist which is the source of the super-linearity - whereas in your new paper the sum is over an ensemble, where each instance doesn't globally explore S3, but they collectively do. These two scenarios are physically inequivalent. I've just registered this difference, and it strikes me as being significant enough to effect whether your experiment works out as you expect or not.
Best
Michael
Joy Christian replied on Nov. 17, 2012 @ 18:40 GMT
Hi Michael,
I don't think there is any difference between the sums/integrals over lambdas in my book and in my latest paper. All sums are understood to be over individual "micro" states, giving super-linear correlation in the large N limit. If there are any differences in the treatments, they are purely notational, introduced for clarity only. So I am not quite sure what you mean by "sum over one instance of correlation" versus "sum over an ensemble, where each instance doesn't explore all of S3." What am I missing?
Best,
Joy
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Author Michael James Goodband replied on Nov. 18, 2012 @ 19:22 GMT
Hi Joy,
It is in thinking about this explicit physical example in comparison with my view of how your analysis applies to my spin defect scenario that I see a technicality associated with Bell's assumption about lambda, which your analysis inherits. This is not explicitly present in your sums/integrals, but I would argue that it is implicitly present and if it is made explicit then it will...
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Hi Joy,
It is in thinking about this explicit physical example in comparison with my view of how your analysis applies to my spin defect scenario that I see a technicality associated with Bell's assumption about lambda, which your analysis inherits. This is not explicitly present in your sums/integrals, but I would argue that it is implicitly present and if it is made explicit then it will give the difference I describe.
In my spin defect case, they are such that in a S=0 state the directions of the two spins will dynamically explore the full S2 of orientations, which (because of the S=0 state) will be correlated and lie on S3 of the SU(2) rotation group. When an experimental measurement of spin direction is made, this dynamics is effectively stopped at some random point. Using the analogy of a coin-toss, the toss itself is intrinsically deterministic and the heads/tails oscillation is stopped at some random point. It is the randomness of the stopping point in relation to the deterministic dynamics which inserts the random element, and it is the same for a spin measurement of my spin defects in a dynamic S=0 state.
Now in the case of a deterministic coin-toss with a random stopping point, the common practise is to adopt a probabilistic description of the coin-toss being 50/50 and completely ignore the deterministic dynamics. In the language of Bell, the deterministic dynamics is hidden but can be described by a hidden variable lambda that determines the toss, given the initial state. Then to calculate an expectation value for a coin-toss, the hidden variable is assumed to probabilistically give heads/tails. When repeated for N coins this will give an ensemble of heads/tails. Now the classical mechanics description of coin-tosses in terms of the ensemble and in terms of the hidden probabilistic variable lambda are equivalent. But then the rotation group in this case is SO(2) with an S1 manifold, and your analysis shows the S1 case to be trivial.
For my spin defect scenario, the same hidden variable approach as for the coin-toss can be applied to give a Bell-like scenario, but in this case the manifold is S3 and all is not trivial. The dynamics explores the full S2 of possible spin orientations in the correlated S=0 state within S3 in a deterministic fashion, which is then randomly stopped at some point to give measured spin directions. It is my interpretation of your analysis that it is this exploration of the global structure of S3 which gives the super-linear correlations for these spins. This has the consequence that the same ensemble interpretation of lambda as for the coin toss will fail to produce super-linear correlations. The reason being that the exploration of L=+1 and L=-1 by one instance of the spin system is required for super-linear correlations, so interpreting them as applying to separate system instances fails to capture the exploration dynamics of the classical hidden physics. It is in this context that there would be a distinction between an integral over lambda applying to one system instance - giving super-linear correlations - and an integral over an ensemble of system instances - not. This distinction is hidden within Bell's assumptions in the formulation of his probabilistic hidden variable.
The physical assumption about space that you gave in terms of Buridan's ass as "... a smart ass, so it always breaks the symmetry at the moment of each explosion by randomly making a choice between L = +1 and L = -1", identifies an ensemble view for which the above interpretation predicts no super-linear correlations. In Buridan terms, the above interpretations says that super-linear correlations require a dumb ass that cannot make up its mind and oscillates between the two.
Furthermore, as natural-numbers are defined by way of set cardinality - such as in an ensemble - and probabilities are real-numbers, the part of my work which is being assiduously ignored identifies this change to a probabilistic hidden variable description of hidden deterministic classical dynamics as being the origin of quantum theory. In this context, I interpret your analysis as proving that such probabilistic classical mechanics is trivial - i.e. equivalent to an ensemble formulation - for all internal symmetry spaces, except for, and only except for, S3 and S7. Consequently the experimental success of quantum theory - non-trivial probabilistic classical mechanics - in describing particle reactions establishes that the internal particle symmetry space can *only* be S7. Physics can then only end one way ... and Einstein is happy ;-)
Best
Michael
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Joy Christian replied on Nov. 19, 2012 @ 10:05 GMT
Hi Michael,
I understand the physics you have described, but it largely goes beyond the operational requirements of respecting what is predicted by quantum mechanics and what is observed in the laboratory. It is the latter two aspects of the problem that Bell was concerned about.
Now in his picture the hidden variable lambda IS the initial state. Thus, for example, L = +1 would...
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Hi Michael,
I understand the physics you have described, but it largely goes beyond the operational requirements of respecting what is predicted by quantum mechanics and what is observed in the laboratory. It is the latter two aspects of the problem that Bell was concerned about.
Now in his picture the hidden variable lambda IS the initial state. Thus, for example, L = +1 would completely determine the final outcome at the detector, which in Bell's language is represented by the number A(a, L) = +1 or -1. What you have described, on the other hand, seems rather strange to me. You write: "It is the randomness of the stopping point in relation to the deterministic dynamics which inserts the random element." But there is nothing random happening at the stopping point in relation to the deterministic dynamics. At the stopping point, which is specified by the detector direction a, what is determined is a matter of analytical calculation. This calculation does not involve any random process and yields the result A(a, L) = +1 or -1. There is no random oscillation between heads or tails at the detector that needs to be "stopped." Put differently, the function A(a, L) is fully determined by the initial condition L and the final condition a. One can imagine a classical differential equation of which A(a, L) is a solution for an initial condition L and a final condition a. Thus, I think, contrary to what you seem to be thinking, Einstein would have absolutely no problem with this picture.
To be sure, there is indeed randomness involved in the determination of A(a, L). But this randomness stems from the randomness of the initial condition L, not the final condition a. So it seems to me that you have got the physical picture upside down. Far from ignoring the deterministic dynamics, Bell is saying that let it be anything you like. It does not matter what the dynamics is. In other words, deterministic dynamics in Bell's picture is not hidden at all, once L and a are specified. It is simply wrong, I think, to say that one is randomly stopping the dynamics at some point to give the measured spin directions. There is nothing random about the stopping point. The experimentalist is indeed making a choice of the measurement direction at will, but there is nothing random about her choice, and hence there is nothing random about the outcome of her measurement. In fact, one can fix the directions a and b of Alice and Bob for the entire course of the experiment and that would not make any difference in either Bell's analysis or mine.
The question then is: Would my use of Bell's analysis affect the classical observation of super-linear correlations? The answer is no, because the global structure of S3 is already captured by the Euclidean (or teleparallel) metric of S3. This is because S3 is parallelized (or flat) in my picture, not round. This is the key reason why the sweeping of all of S3 is not necessary.
Best,
Joy
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Joy Christian replied on Nov. 19, 2012 @ 10:24 GMT
Hi Michael,
In fact, by shifting the randomness from the initial condition L to the final condition a, and by making the Buridan's ass to be intrinsically indecisive, you are simply re-describing the quantum mechanical superposition principle and the projection postulate at the two ends of the dynamical process. This is what I mean by getting the physical picture upside down from Bell's perspective.
Best,
Joy
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Thomas Howard Ray replied on Nov. 19, 2012 @ 12:16 GMT
"In fact, by shifting the randomness from the initial condition L to the final condition a, and by making the Buridan's ass to be intrinsically indecisive, you are simply re-describing the quantum mechanical superposition principle and the projection postulate at the two ends of the dynamical process. This is what I mean by getting the physical picture upside down from Bell's perspective."
Excellent. I think Michael's explanation is exactly dual to yours, Joy. As you pointed out, a classical differential equation which has the solution A(a,L) in which L is the initial condition and a the final condition, does not differ from the "upside down" version in which L-future is the initial condition determining a-past final condition.
It took me quite a while to grasp that the choice of experimenter direction of observation in your framework is indifferent to the arrow of time -- the future condition is correlated with the final condition deterministically; IOW, there is but one non-random correlation of state for every random choice of vector (which obviates superposition of states). The kicker is that though the experimenter can randomly choose to observe in any direction, she can receive information from but one direction -- explained in my essay as a point at infinity.
This accords with a fully relativistic theory in which the point of Minkowski space describing the initial condition of the universe is everywhere -- and therefore local -- independent of arbitrary notions of past and future states.
Tom
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Author Michael James Goodband replied on Nov. 19, 2012 @ 13:35 GMT
Hi Joy,
Actually, I'm saying that Bell's perspective is upside down with respect to what he did, and I'm just expressing what he actually did - not what he said he did. To point out what I mean I've attached Bell's paper for convenience. Now after a nice preamble about what he intends lambda to mean, Bell decides upon expressing lambda as a single continuous parameter with a probability distribution, and writes the expectation value for the product of two spin components in eqn (2). Now he may have intended that to be an integral over an ensemble of spin correlation measurements, each with a different lambda value, but that is not what eqn (2) actually says. As written, it is an integral over lambda for the correlated spins of *one* spin singlet state, i.e. it *is* the integral over the possible values of lambda in the hidden domain of *one* system state that I described above.
My big picture point is that between the preamble and eqn (2) there is a change in the description given by lambda, and that descriptive change *IS* quantum theory. It seems an innocent change, and most of the time it is, but for configuration spaces S3 and S7, it isn't. It represents a change from an ensemble description - Bell's apparent intention - to a probabilistic description of a single instance - what he actually did in eqn (2) - that is in-equivalent to the ensemble case. So from my perspective, you successfully reproduce QT results because your analysis includes Bell's change in meaning of lambda [Ch1 pg16 eqn(1.43) , Ch2 pg31 eqn(2.7) , Ch3 pg40 eqn(3.2)...] that gives the basis for the descriptive framework of QT. You then essentially prove that this change is only non-trivial for S3 and S7.
Best
Michael
attachments:
Bell_Compact.pdf
Joy Christian replied on Nov. 20, 2012 @ 17:41 GMT
Hi Michael,
I see now what you meant.
John Bell was the enchanting Pied Piper of Hamelin. :-)
Best,
Joy
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Thomas Howard Ray replied on Nov. 20, 2012 @ 18:15 GMT
" ... Bell decides upon expressing lambda as a single continuous parameter with a probability distribution ... "
Bingo.
"It represents a change from an ensemble description - Bell's apparent intention - to a probabilistic description of a single instance ..."
And that fatally seals the case for local realism against nonlocality. Those metaphysically real "experiments not done" require only a change of initial condition, given the orientable space.
A couple of years down the road from having first been introduced to it, I am still impressed with the brilliance of Joy's replacing a nonorientable measure space of equally likely outcomes with topological orientability.
Tom
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Author Michael James Goodband replied on Nov. 20, 2012 @ 18:51 GMT
Hi Joy,
On your experiment, it has occurred to me that for your intended interpretation, the spherical symmetry of the shells doesn't need to be restored after they have been divided. The feature your interpretation seems to be looking for is a spatial connection between the two shells which selects between L=±1 when the shells start rotating in their correlated SO(3) rotational state -...
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Hi Joy,
On your experiment, it has occurred to me that for your intended interpretation, the spherical symmetry of the shells doesn't need to be restored after they have been divided. The feature your interpretation seems to be looking for is a spatial connection between the two shells which selects between L=±1 when the shells start rotating in their correlated SO(3) rotational state - the postulated hidden spatial linkage makes this SU(2). (I accept that my attempts to find an initial SU(2) configuration that transitions to a dynamic SU(2) state won't succeed.)
In which case, the two shell halves could be joined by a thin cylindrical segment that is attached to an air pump. The halves are put in place and the air pressure in the segment lowered so that the two shells are held in place by the reduced air pressure, and a valve closed to give the initial state. This dispenses with any shell fixings. The air pump pressure is increased and then the valve opened to give an explosive pressure on the shell halves. Furthermore, if these air nozzles in the cylindrical segment are smaller than the shell diameter, then there is space for separate air nozzles to act upon radial vanes inside the shell halves to give them axial rotation in the explosive separation. So the rotation vector of each shell halve could be made to lie on S2, and the initial shell state and air nozzle arrangement can give a S=0 singlet state - all to within the accuracy of the experimental kit.
Your analysis for your postulated interpretation applies for N shells with different weightings being placed sequentially on the pressure rig and exploded. This set-up is more controllable than your heater arrangement, and gives S=0 singlet states for rotation vectors on S2 - so seems to meet all your practical requirements. It seems to me that the ambiguity in the interpretation of the maths calculation - your and my views - would be resolved by this experiment - SU(2) or SO(3) respectively.
Tom, I'm also impressed with Joy's work, but I think there is more here. All the way to fixing the particle symmetry space for the QFT of the Standard Model to having to be S7 - but this would lead to further conflict ...
Best
Michael
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Thomas Howard Ray replied on Nov. 20, 2012 @ 19:15 GMT
Hi Michael,
" ... I'm also impressed with Joy's work, but I think there is more here. All the way to fixing the particle symmetry space for the QFT of the Standard Model to having to be S7 - but this would lead to further conflict ... "
I agree. I think that our discussion of the subtle distinction between measure space and physical space is far from over. It's difficult to break through preconceptions about extra dimensions in the current state of the art, though I do think the "Disproof ..." book and your book break new ground. And I also predict that these ideas will hook up with complexity and information theory in interesting -- and even perhaps unexpected -- ways.
Tom
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Joy Christian replied on Nov. 21, 2012 @ 13:38 GMT
Hi Michael,
I don't quite follow all the details, but I like the idea of an air pump instead of a heater. It would be much more controllable and stable, in terms of both time and space of the experimental arrangement. It would also be a lot safer than a heater. What I don't follow, however, is how you propose to produce a large number of variations in the spin directions. In my proposal the possibilities for different mass locations in the shells are, in principle, of the order of a million. This means one can arrange, in principle, to have the two shells rotating in a million different directions. I don't see how this can be possible within your proposal.
The point I do appreciate clearly---thanks to you---is the need for experimentally assuring the singlet condition: S=0. I had not realized that this may require a nontrivial experimental arrangement.
Best,
Joy
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Author Michael James Goodband replied on Nov. 21, 2012 @ 17:29 GMT
Hi Joy,
Your random weighting of the shells would give the same rotation variation in the plane, which would then be supplemented by using different pressure settings for the rotation pressure nozzles (including reversing their direction) to give variations in axial rotation - thus any rotation vector lying on S2 could be randomly set.
I was wondering whether in your view of a rotational connection of physical space, you would view the linkage as being between each rotating shell and the stationary pressure rig, instead of being between the two rotating shells, and whether this would make any difference to the result in your view of the spatial connection. It makes no difference in my configuration space view - always SO(3).
Unless the physics is explicitly pinned down - such as by the string etc. of the 4PI invariance examples - I can't see the underlying SU(2) being openly exposed for all to see. In my topological defect case, the spherical hole in space is effectively an object which is literally pinned down relative to the "fabric" of physical space, and so in this case our views are the same.
Best
Michael
Joy Christian replied on Nov. 21, 2012 @ 19:50 GMT
Hi Michael,
It is precisely because the role played by SU(2) in linking the two shells is not so obvious that we need to perform this experiment.
Here is what is happening in my view: After the explosion the two shells are rotating relative to each other---i.e., rotating in tandem. The component of the angular momentum of one of the shells along the direction "a" is represented by...
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Hi Michael,
It is precisely because the role played by SU(2) in linking the two shells is not so obvious that we need to perform this experiment.
Here is what is happening in my view: After the explosion the two shells are rotating relative to each other---i.e., rotating in tandem. The component of the angular momentum of one of the shells along the direction "a" is represented by the bivector I.a, and similarly the component of the angular momentum of the other shell along the direction "b" is represented by the bivector I.b. Thus I.a and I.b are elements of the Lie algebra su(2), and can be thought of as representing two equatorial points of a parallelized 3-sphere. In other words, the set of all points such as I.a and I.b is a unit 2-sphere within the 3-sphere. The product of I.a and I.b, however, is a *non*-equatorial point of the 3-sphere:
(I.a)(I.b) = -a.b - I.(a x b).
Thus---and this is the key point---what connects the numbers I.a and I.b is the orientation of the 3-sphere. Had the orientation been left-handed rather than right-handed, we would have had a different product:
(I.a)(I.b) = -a.b + I.(a x b).
Now the correlation is given by the covariance of the standard scores I.a and I.b, and is the mean of their geometric product. Thus the underlying SU(2) is indeed "openly exposed for all to see."
In the above picture the linkage is clearly best viewed as being between the two shells rather than between a shell and the stationary rig (or the stationary laboratory). I think it would make a big difference in my case if we took the latter linkage (which too exists) to be primary. The reason for this is that the strong (or quantum) correlations, in my view, are correlations among the points of the 3-sphere itself, not among the points the 3-sphere and something else. So, as you noted above, the proposed experiment would indeed adjudicate between our respective views, not to mention between my view and that of the rest of the world.
Best,
Joy
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Author Michael James Goodband replied on Nov. 22, 2012 @ 18:38 GMT
Hi Joy,
From your reply, I see that the pressure-rig scenario is acceptable as the rotation of the shells relative to the rig is the same as that to the walls of the lab etc., all of which is irrelevant as what matters is the rotation of the shells relative to each other. Given that it would decide between our views, and consequently the direction to pursue, I was wondering what plans you have for the experiment? It is basically just a novel measurement in a simple scenario that could possibly even be set as a physics (or engineering) (grad?) student project - thus sneaking it in under someone else's budget and having it done :-)
Best
Michael
Joy Christian replied on Nov. 22, 2012 @ 19:43 GMT
Hi Michael,
I have very serious plans for the experiment. I prefer not to spell out the details, because there are people out there who are determined to frustrate my every effort, in every which way possible (have you not surfed the Internet to see what I have been putting up with for the past five years?).
In any case, I am very serious about the experiment. I am in touch with a serious experimentalist, who is willing to hire a team to perform the experiment once all the details are sorted out. It cannot be a simple student project. That will not do, because it has to be a precision experiment that can withstand the scrutiny of a prominent physics journal. In fact it will not be an easy experiment to do (although according to David Wineland---this year's Nobel Laureate---"it is doable"). There are many practical factors we haven't discussed; such as air resistance, gravitational effects, wobbling of the two shells, and other moment of inertia effects. All these side effects can potentially destroy the strong correlation, or introduce large enough error bars to render the experiment meaningless.
We also must not forget the sociological discoveries made by people like Kuhn, Collins, and Pinch. Even if the experiment is successful, the result would be disputed tooth and nail. So we cannot afford to take any chances.
Best,
Joy
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Author Michael James Goodband replied on Nov. 22, 2012 @ 23:03 GMT
Hi Joy,
That's excellent news! I look forward to the result with interest.
Yeh, I've seen stuff on the internet, which is kind-of how Kuhn said these things go - plus some. I've experienced the shut-out this year - arxiv, journals etc. - which is the other side of how it goes. It is interesting to contrast with Bell's paper which was taken to confirm what was believed to be true, and assigned the status of "theorem". Just imagine if Bell had contradicted what was believed to be true, he would have been ripped to shreds in the internet era - in addition to your points, there is the change in meaning of lambda I pointed out above.
I see your EPR result as having an unequal relation to your experiment with regards to verfication and falsification - would be verified by the experiment, but not actually falsified if it goes the other way. It must be said that finding QT-style correlations in classical physics would be a big-grin result :-)
Best,
Michael
Fred Diether replied on Nov. 23, 2012 @ 07:45 GMT
Hi Michael,
That's right. If Joy's macroscopic experiment beats Bell's inequality, then we know for sure that Bell was wrong. If the experiment doesn't beat Bell's inequality, then Joy's model could still be right for the microscopic quantum domain. Well... it still could be right also for the macroscopic domain if it is just not the correct experiment.
I was initially a bit skeptical that Joy's model would apply also to the macroscopic domain but after more research, I think it does need to be fully tested in all ways possible. I have no doubt whatsoever that Joy's model is the correct model for microscopic domain correlations.
Best,
Fred
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Author Michael James Goodband replied on Nov. 23, 2012 @ 12:24 GMT
Hi Joy,
Just to clarify, you're not the only one in the world to think that the shell possesses a hidden SU(2) orientation-based variable which is, at the thought experiment level at least, physically measurable. I have been thinking about whether I would be able to account for a positive experimental result - this is my line of reasoning:
Start with the EPR singlet state of up-down...
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Hi Joy,
Just to clarify, you're not the only one in the world to think that the shell possesses a hidden SU(2) orientation-based variable which is, at the thought experiment level at least, physically measurable. I have been thinking about whether I would be able to account for a positive experimental result - this is my line of reasoning:
Start with the EPR singlet state of up-down SU(2) spins. Because they anti-commute UD=-DU the 2 spin orientations are distinguishable, giving a hidden variable L=±1 that is related to the S3 orientation. To simplify notation, these 2 SU(2) spin states can be labelled as S=+0 and S=-0, which are physically distinguishable by separation into their fermion components. Now imagine two such SU(2) singlet states next to each other forming a combined S=0 singlet state: they could form 1 of 4 possibilities (+0,+0), (-0,-0), (+0,-0), (-0,+0), which are all physically distinguishable by separating into fermion components. But as all the singlet states commute (±0)(±0)=(±0)(±0) in all 4 cases, they are indistinguishable when they are not separated into their parts, i.e. the SU(2) singlet states behave as expected for bosonic states. The two values of L=±1 are indistinguishable at the bosonic level, corresponding to the identification of opposite points in S3 that gives the group manifold of SO(3) - the boson rotation group.
However, if we take the product of SU(2) singlet orientations we get a hidden variable M=L1*L2=±1 which is physically measurable by breaking each of the singlet states into its fermions. The same will conceptually hold for any number of singlet combinations of fermions, up to the macroscopic scale of the shell halves. When the halves are combined, the SO(3) S=0 singlet state can be labelled with the SU(2) hidden variable M=±1 denoting the product of the SU(2) L=±1 orientations of all the SU(2) components, which at the thought experiment level is physically measurable. So the SO(3) S=0 singlet state can be labelled with the *physical* hidden variable M=±1 to give the two possibilities, S=+0 and S=-0. The randomness of L=±1 for a single SU(2) singlet state propagates through to make M=±1 a random variable.
Your proposition is then that in a transition from a classical physics static S=±0 state to a dynamic S=±0 state, the physical hidden variable M=±1 of the underlying SU(2) will be manifest in rotation correlation of the shell halves in an otherwise apparently SO(3) macroscopic singlet state.
Our difference of view then lies in the interpretation of the hidden variable calculation, which revolves around the point I made earlier about Bell's paper.
Best,
Michael
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Joy Christian replied on Nov. 23, 2012 @ 18:12 GMT
Hi Michael,
Your reasoning seems quite reasonable to me. It fits in well with my preferred rule of composition: A composite object is a fermion if and only if an odd number of its components are fermions; otherwise it is a boson.
My only question about your reasoning concerns the following equation of yours:
M = L1*L2 = ±1.
Can you please provide more details how you got this (just to avoid any misunderstanding)?
I agree with both you and Fred about the unequal relation of my experiment with regard to verification/falsification. My model for EPR would be verified by my experiment, but cannot be falsified by *any* experiment, because it simply reproduces already established results. This is why there are desperate attempts by some to find a mathematical error in my argument.
Best,
Joy
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Author Michael James Goodband replied on Nov. 24, 2012 @ 00:29 GMT
Hi Joy,
The value of L for a closed surface around two singlets would be that for SO(3), i.e. L=1. So M is simply a product of the orientations of each SU(2) singlet (+0 or -0):
(+0,+0), (-0,-0) have M=+1*+1=-1*-1=+1
(+0,-0), (-0,+0) have M=+1*-1=-1*+1=-1
As a measure it fails to distinguish between (+0,-0) and (-0,+0) which should also be physically distinguishable by...
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Hi Joy,
The value of L for a closed surface around two singlets would be that for SO(3), i.e. L=1. So M is simply a product of the orientations of each SU(2) singlet (+0 or -0):
(+0,+0), (-0,-0) have M=+1*+1=-1*-1=+1
(+0,-0), (-0,+0) have M=+1*-1=-1*+1=-1
As a measure it fails to distinguish between (+0,-0) and (-0,+0) which should also be physically distinguishable by breaking each fermionic singlet state in two, but I just wanted a reliable orientation-based measure that would be physically measurable and scale up in deterministic classical physics. That way macroscopic J=0 (SO(3) rotation) states can be labelled with the two M states as being S=+0 and S=-0 (SU(2) rotation).
So my coffee cup on the desk in a static J=0 state has a hidden variable M=±1, which is revealed by placing the cup on my open hand (or by making any other form of physical connection which captures relative rotations), as I now have the plate-trick where a 2PI rotation turns S=+0 into S=-0, and vice-versa. So experiment reveals that there is a physical 2 value hidden variable that is related to the orientations of SU(2), and the product rule for M gives such a variable.
It is probably worth remembering that your 500-pound canary is quite an embarrassing thing to miss - I know, I read Bell's paper years ago and didn't spot it. Unlike you, the rest of us can feel a bit silly for having missed it. Since Bell's paper appears to tell people what they want to hear, there seems to be a reluctance to admit there could be simple errors. The point I made earlier about the change in meaning for lambda is also fairly simple, and I've met the response that it is too simple, it can't be true. All the focus on the C, H and O number systems overlooks the other two: real numbers and natural numbers. The change in meaning for lambda is directly related to a shift between these 2 number systems, and my work shows this to be the basis for what QT is actually about. This is why I totally agree that your EPR result simply *cannot* be experimentally falsified - it has reproduced QT because it has captured the essence of what QT is about in the probability interpretation of lambda - implicit in the integrals I gave earlier.
I would expect the probability interpretation for lambda in your framework to reproduce the results of QT, and this gives me a conflict with your prediction for your experiment. The QT prediction is for SO(3) correlation, which I would expect to be reproduced in your framework with the correct interpretation for lambda - and with the probability description I gave earlier, it would be. I think that your experiment could instead be posed as being a test of Bell's interpretation of lambda - the experimental test of Bell that has yet to been done. Put Bell in the frame instead of you, so if there is any brown-stuff flying around, deflect it towards Bell.
Best,
Michael
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Joy Christian replied on Nov. 24, 2012 @ 09:21 GMT
Hi Michael,
What is shocking about the 500-pound canary sitting in Bell's very first equation is not the canary itself but some people's determined refusal to see it even after it has been repeatedly pointed out to them (for example in my Chapters 1, 4, 6, 7, 8, and 9). A(a, L) = +1 or -1 and B(b, L) = +1 or -1 are supposed to be mathematical functions. As such, they take values from their...
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Hi Michael,
What is shocking about the 500-pound canary sitting in Bell's very first equation is not the canary itself but some people's determined refusal to see it even after it has been repeatedly pointed out to them (for example in my Chapters 1, 4, 6, 7, 8, and 9). A(a, L) = +1 or -1 and B(b, L) = +1 or -1 are supposed to be mathematical functions. As such, they take values from their domain and churn out numbers that live in their co-domain (which is of course different from the actual image points, or measurement results such as +1, -1, etc.). It is then abundantly clear that any correlation between the numbers A(a, L) and B(b, L) is entirely determined by the topology of their co-domain. Now one may insist that the co-domain of A(a, L) and B(b, L) is simply the binary set { +1, -1 }. But then the completeness criterion of EPR can never be satisfied, as I have demonstrated in my book. Even if we disingenuously pretend that Bell's argument is somehow meaningful independently of the EPR argument, the set { +1, -1 } is by no means the only possible choice of a co-domain that can satisfy all the other requirements of Bell. One such set is a parallelized 3-sphere, which is a simply-connected collection of the zero spheres { +1, -1 }. The topology of this set then *necessitates* that the correlation between A(a, L) and B(b, L) cannot be anything but -a.b. One does not have to be Einstein to recognize this elementary fact. But instead of recognizing it some people's reaction is to reach out for the gun and shoot the messenger: How dare you point out the 500-pound canary in Bell's argument?
The above observation is actually not unrelated to your observation of a shift in the meaning of lambda in Bell's equations (1) and (2). The zero sphere { +1, -1 }, or even a collection of all such zero spheres, can only be a *totally disconnected* set. The set S3, however, is a simply-connected set, and hence more akin to the real number system rather than the natural number system. It is therefore not surprising that EPR correlations are entirely determined by the topology of S3. The shift from a frequency interpretation of lambda in Bell's equation (1) to the probability interpretation of lambda in his equation (2) goes hand-in-hand with the shift from a totally disconnected co-domain { +1, -1 } to the simply-connected co-domain S3. This shift is then the 500-pound canary in his equation (1).
Your advice to put Bell in the frame is very wise, but if diplomacy were my strong point I would not be in this position of having to defend my work and career (you are aware of the kind of names I have been called by the lesser minds). Besides, I did try to put Bell in the frame (see, for example, my Chapter 3), but that only produced kneejerk reactions and shut-outs from the mediocrity (the public attempts to crucify me is only a fraction of what has been going on behind the scenes since 2007).
More importantly, it is not surprising that QT predicts SO(3) correlation for my experiment. In fact I am counting on that. I am counting on the fact that most people would not expect to see strong correlation. What my work (and your work) shows, however, is that QT is an incomplete theory of nature (in the EPR sense). What is more, in my view quantum correlations are the evidence that the physical space we "live in" respects the geometry and topology of a parallelized 3-sphere (more generally, 7-sphere). If so, then we should expect strong correlations between objects rotating in tandem even in the macroscopic domain. And that is what I am expecting to see in my experiment.
Best,
Joy
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Thomas Howard Ray replied on Nov. 24, 2012 @ 11:38 GMT
"Even if we disingenuously pretend that Bell's argument is somehow meaningful independently of the EPR argument, the set { +1, -1 } is by no means the only possible choice of a co-domain that can satisfy all the other requirements of Bell. One such set is a parallelized 3-sphere, which is a simply-connected collection of the zero spheres { +1, -1 }."
Right on, Joy. I think furthermore the fact that S^0 is a 2-dimension nonorientable space reinforces the important role of orientability in any measurement function -- (in your words, "No observation was ever made except in some direction") -- which is tantamount to an order already built into the function's initial condition, that cannot be realized in any spherical dimension < 4, where S^3 is the simplest Riemann sphere oriented by a point at infinity. Which of course, leads to your conclusion:
"The topology of this set then *necessitates* that the correlation between A(a, L) and B(b, L) cannot be anything but -a.b. One does not have to be Einstein to recognize this elementary fact."
One does have to think like Einstein, however -- that continuous function physics is independent of the observer's choice of measurement direction. This could only be true if the physical space is orientable.
Tom
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Joy Christian replied on Nov. 24, 2012 @ 13:33 GMT
Thanks, Tom.
Indeed, one does have to think like Einstein. Or more modestly, one has to remember not to forget the lessons learned by Einstein.
Best,
Joy
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Constantinos Ragazas replied on Nov. 24, 2012 @ 17:43 GMT
Joy Christian, et al
I cannot comment on the pros and cons, proofs and disproofs, of Bell's Theorem and its Pied Piper tune key in Quantum Physics. But if the question is
"A World Without Quanta?" the results contained in my chapter,
"The Thermodynamics in Planck's Law" may be of some interest and relevance. Specifically,
1) "Planck's Law is an exact mathematical tautology." And not a physical law as such, requiring the existence of energy quanta. This explains the exact fit of the experimental data with theory.
2) "If the speed of light is constant, then light is a wave".
Best regards,
Constantinos
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Joy Christian replied on Nov. 24, 2012 @ 19:18 GMT
Hi Constantinos,
The question we are addressing is not quite whether there can be a world without quanta, but whether such a world can be locally causal, if it is realistic (and deterministic). Bell and his followers claimed that it cannot be, and some of us are claiming that Bell and his followers were as wrong as 2+2=5.
Your essay is nevertheless interesting. You may find the essay by Eirc Reiter in this year's contest interesting as well, if you haven't already checked it out.
Thanks for your remarks.
Best,
Joy
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Constantinos Ragazas replied on Nov. 25, 2012 @ 03:27 GMT
Joy,
Thanks for your response. I know Eric Reiter. We have corresponded many times in the past. His 'energy loading' is my 'accumulation of energy'. I support his experimental work. And hope he wins a prize!
Constantinos
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Author Michael James Goodband replied on Nov. 25, 2012 @ 17:56 GMT
Hi Joy and Tom,
On thinking like Einstein, it is worth updating the EPR argument from quantum mechanics to quantum field theory (I've re-attached a copy of the original EPR paper for convenience so you can see that it is a QM based argument). Dirac's equation of 1928 raised a warning flag about the effect of relativity on QM before the EPR paper, and the first quantum field theory (QED) was...
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Hi Joy and Tom,
On thinking like Einstein, it is worth updating the EPR argument from quantum mechanics to quantum field theory (I've re-attached a copy of the original EPR paper for convenience so you can see that it is a QM based argument). Dirac's equation of 1928 raised a warning flag about the effect of relativity on QM before the EPR paper, and the first quantum field theory (QED) was in place by the time of Bell's 1964 paper (the Nobel prize for QED was 1965). But despite this, Bell's choice of manifold S0={-1,+1} is effectively based on the assumption of a non-relativistic classical physics analogue of non-relativistic QM. BUT this is wrong because the required classical physics analogue should be of relativistic quantum field theory.
In QFT - and this applies even in the deceptively non-relativistic case of stationary electrons - the electrons interact by virtual photons that can become virtual electron-positron pairs. In this QFT expansion, positrons can annihilate the original electrons, turning their electron partners in the created pair into the new correlated electrons. In this process, the spins of the real electrons - i.e. not the virtual ones - are constrained to be in the same S=0 singlet state. If each spin was also constrained to remain in the same direction THEN the manifold would be S0, BUT each spin is actually free to lie on any point of S2 within S3. Any physically correct classical physics analogue - i.e. what Einstein was after - MUST reproduce this, which Bell's does NOT, but Joy's does - ergo, the former is wrong and the latter is correct.
But in addition to the S=0 condition, the QFT dynamics is also constrained for there to be 2 real electrons - it is easy to forget this, but in QFT a virtual photon can produce a particle/anti-particle pair for any of the charged fermion types. These virtual pairs must annihilate to leave 2 real electrons, and this QFT constraint MUST also be reproduced in the hidden variable classical physics analogue of the QFT dynamics. In analogy to the correlated spins effectively exploring the global structure of S3 through the classical physics analogue of the QFT dynamics, the changes in particle type also effectively explore the global structure of the "particle space". The constraint of S3 or S7 should similarly apply, implying that the internal particle symmetry space MUST be S7.
The scenario given in my essay (and paper) is of the correct form for a classical physics analogue for QFT of the EPR scenario, but it is also the predicted scenario of a pure geometric 11D GR without additional fields.
Best,
Michael
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EPR.pdf
Fred Diether replied on Nov. 25, 2012 @ 20:57 GMT
Hi Michael,
You said, "In this QFT expansion, positrons can annihilate the original electrons, turning their electron partners in the created pair into the new correlated electrons."
Yes, real electrons can just swap with their virtual counterparts all the time. Of course it doesn't matter so much as the properties will remain the same in ordinary circumstances. But I am not quite getting the point of this related to what you say further about "If each spin was also constrained to remain in the same direction THEN the manifold would be S0,..."?
Also, in the EPR-Bohm scenario, the Stern-Gerlach device for detection, does further constrain the spins to be either up or down.
Best,
Fred
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Joy Christian replied on Nov. 25, 2012 @ 21:45 GMT
I think Fred is right. Bell's insistence on using S0 is fully justified on the operational grounds. What he missed, however, was the distinction between the image of his functions A(a, L) within their co-domain, which has to be S0, and their co-domain itself, which has to be S3 in general, as I have argued. But once the co-domain is taken to be S3, the correlation -a.b follows at once.
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Author Michael James Goodband replied on Nov. 25, 2012 @ 23:31 GMT
Hi Fred,
The point about S0 is in constructing a classical physics analogue of QT in terms of hidden dynamics - "thinking like Einstein" and looking for the physical dynamics. If the direction of a classical spin is set in one direction and there is no dynamics to change it, then it remains the same - this gives the condition for Bell's S0={-1,+1}. But in the QFT of EPR, it is not the...
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Hi Fred,
The point about S0 is in constructing a classical physics analogue of QT in terms of hidden dynamics - "thinking like Einstein" and looking for the physical dynamics. If the direction of a classical spin is set in one direction and there is no dynamics to change it, then it remains the same - this gives the condition for Bell's S0={-1,+1}. But in the QFT of EPR, it is not the direction of each spin which is conserved, but the spin of the singlet state S=0. The virtual particle dynamics can give any electron pair state with S=0, which will include the individual electron spins as possibly being any point on S2. Any classical physics hidden dynamics must reproduce this feature, which only exists because of the virtual pair creation of QFT.
Joy, you said: "But once the co-domain is taken to be S3, the correlation -a.b follows at once." But it doesn't follow *at once*, it follows via an integral over lambda, which in Bell's paper is the previously mentioned eqn (2) for a SINGLE electron pair, NOT an ensemble (the meaning of lambda in this integral is different from its meaning in the preamble). This integral over lambda is only justified in *physical terms* - the Einstein standard of EPR - IFF the dynamics explores the extent of this lambda domain. This is the dynamics required to reflect the spin features of the QFT dynamics. Otherwise it is an ensemble integral, for which there is no *physical* dynamics correlating different points on S3, as in this case these points are *physically* experienced by different electron pairs. Thus there would be no causal *physical* dynamics involving the global structure of S3, and consequently no super-linear spin correlation.
This is not an issue of mathematical constraint, but an issue of the hidden *physical* dynamics required to satisfy the condition. The *physical* hidden dynamics for a SINGLE electron pair must explore S3 to *physically* justify integrating over it, i.e. eqn (2) and the equivalents in your analysis. It is this uncompromising focus on the *physicality* of the hidden dynamics which is why I phrased it: "thinking like Einstein".
Best,
Michael
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Joy Christian replied on Nov. 26, 2012 @ 06:56 GMT
Hi Michael,
I am afraid you are going too fast in your reasoning in the middle paragraph above. Let me explain:
For completeness, let me begin by stressing that in my very first paper I introduced two trivectors, mu and I, which are related as
mu = +/- I.
Thus there are two trivectors in my model for EPR, mu and I, and they are related by the orientation L = +/-1 of a...
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Hi Michael,
I am afraid you are going too fast in your reasoning in the middle paragraph above. Let me explain:
For completeness, let me begin by stressing that in my very first paper I introduced two trivectors, mu and I, which are related as
mu = +/- I.
Thus there are two trivectors in my model for EPR, mu and I, and they are related by the orientation L = +/-1 of a unit parallelized 3-sphere. The twelve or so papers that followed are my continuous attempt to explain this basic fact to some of my critics, who are unable to grasp that fixing the orientation L = +1 or L = -1 *a priori* amounts to smuggling something in by hand.
In the present company we are not confused about this, but what I want to stress is the discreteness of the hidden variable L (in my entire model, for ALL possible quantum correlations). Thus, although your observation of the shift in the meaning of lambda (or L) in Bell's equations (1) and (2) is entirely correct, it is not as relevant as you seem to think when it comes to my model. In particular, because L is discrete in my model, the continuous integral in Bell's equation (2) reduces to the discrete sum evaluated in equation (104) of my latest paper (which I am attaching here for convenience). To be sure, one can treat the trivector mu as a continuous geometrical object (a volume form) of the physical space and then integrate over the functions A(a, mu) as I do in my earlier papers, but that does not change the fact that the basic hidden variable L of the model is a discrete number. This is especially transparent in the second to last step in the derivation of the correlation (104).
Thus, I think, you are too hasty in your conclusion that "...there would be no causal *physical* dynamics involving the global structure of S3, and consequently no super-linear spin correlation." You can certainly argue in favour of the propensity interpretation of probabilities ("single instance") as opposed to the frequency interpretation ("ensemble integral"), but that is a different debate altogether. The correlation (104) itself follows robustly from the co-domain S3(L) regardless of the choice of interpretation of the stochasticity involved in the calculation.
Best,
Joy
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4_2piSpinor.pdf
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Author Michael James Goodband replied on Nov. 26, 2012 @ 15:40 GMT
Hi Joy,
I can appreciate that after 5 years of critics, I might be confusing you as I think there is more to your work, not less - a kind of an anti-critic. I have no doubts about the application of your model to EPR, and its mathematical status as a counter-example which disproves the generalised claim made on the basis of Bell. And I'm also aware that in your model it is physical space...
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Hi Joy,
I can appreciate that after 5 years of critics, I might be confusing you as I think there is more to your work, not less - a kind of an anti-critic. I have no doubts about the application of your model to EPR, and its mathematical status as a counter-example which disproves the generalised claim made on the basis of Bell. And I'm also aware that in your model it is physical space which provides the connection between spins, and that without this there would be no *physical* causal dynamics involving the global structure of S3. But I'm not convinced that the metaphysical result of your proof - has to be S3 or S7 - is directly dependent upon this spatial connection condition, and I'm also not convinced that the basic mathematical structure is only true for the spatial connection condition either. I think it is largely a physical interpretation issue on the hidden variable and its integration over the hidden domain.
In the general metaphysics of the hidden variable (L) framework, L is specified by the functions A(n, L), the factorisation rule and the L integral (eqn (2) in Bell). The hidden variable rhetoric of Bell is a red-herring as he contradicts himself in the calculation - the bit that actually matters. This metaphysical framework leaves a great deal of freedom in the choice of L, a freedom that you use to find a model that disproves the generality of Bell by counter-example. My interest is in metaphysical proof, specifically a proof that it has to be S3 or S7 within the generic hidden variable framework for there to exist the super-linear correlations of QT.
I think that the freedom of choice for L can be used to choose your framework as a specific instance to prove the general metaphysical result. Your model does this for the EPR scenario (S3) and the general spin case (S7). But your spatial connection condition leads to further predictions - such as for your experiment - which are not metaphysics. The distinction being that without this spatial connection condition, the result would be backed-up by the whole weight of experimental particle physics - because it is just a hidden variable formulation of QM and QFT - and so could not be wrong. This would make it a metaphysical result that constrained what physics could be. In contrast, the spatial connection is a model specific feature which can be wrong.
The physical dynamics I described above is what is required to be captured by the hidden variable model for the proposed generic metaphysical proof to be possible. Just as the spin singlet state can be characterised by S0 on the S2 equator of S3, a positron-electron state - the QFT particle/anti-particle equivalent of the EPR spin state - could be characterised by S0 on the X equator of Y. If you accept that my change in interpretation of the hidden variable is significant enough for your framework to be applied without the spatial connection, then your work amounts to a metaphysical proof that Y - the particle symmetry space - has to be S7. My change in interpretation would mean that your work amounts to a metaphysical proof that QT only applies in physics to the particle symmetries (S7) and spin (S3) - the second Casimir invariant of the Poincare group. This would mean that there was NO proof that QT applies to interactions only involving mass - the first Casimir invariant - and so this metaphysical existence proof for QT would not include quantum gravity (implying that there is no such thing).
In combination, my change in hidden variable interpretation raises your results from being model specific to generic metaphysics that constrains physics on the origin of QT, no quantum gravity, and the particle symmetry space. All which agree with my results, no doubt because the constraints come from the same place - the 5 number systems (N, R, C, H, O). The price to pay for this would be the loss of the physical spatial connection, and consequently your prediction of SU(2) correlations in your classical physics experiment. As I said, I don't see your results as requiring the physical interpretation you give it of a physical spatial connection. If I'm wrong and they do, then I can't believe that there isn't a very closely related model without this physical interpretation that can be used for the generic metaphysical proof instead.
Best,
Michael
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Edwin Eugene Klingman replied on Nov. 26, 2012 @ 21:20 GMT
Dear Michael, Joy, Fred, Jonathan, and Tom,
A truly fascinating discussion. Congratulations to all. While I do not accept either Joy's specific model or Michael's S7 particle model, it is absolutely fascinating to follow the reasoning in these remarks.
Thanks, Michael, for bringing QFT and virtual particles into the discussion. As Fred noted, you said, "In this QFT expansion,...
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Dear Michael, Joy, Fred, Jonathan, and Tom,
A truly fascinating discussion. Congratulations to all. While I do not accept either Joy's specific model or Michael's S7 particle model, it is absolutely fascinating to follow the reasoning in these remarks.
Thanks, Michael, for bringing QFT and virtual particles into the discussion. As Fred noted, you said, "In this QFT expansion, positrons can annihilate the original electrons, turning their electron partners in the created pair into the new correlated electrons." Are you implying that the positrons are exactly correlated with the original pair, and hence should introduce uncorrelated change to the original pair? Is this what you refer to when you state "This integral over lambda is only justified in *physical terms* - the Einstein standard of EPR - IFF the dynamics explores the extent of this lambda domain [the ensemble?]. This is the dynamics required to reflect the spin features of the QFT dynamics." My own opinion is that virtual particles are *the* primary fudge factor of QFT. As you noted, it is based on *every* species of particle [which raises interesting questions about SUSY, which would double the number of species!] In raising QFT issues of this sort you have taken the discussion in new directions.
Joy has reiterated that his model began by introducing two trivectors, mu and I, and his subsequent twelve papers are based on these. In my opinion it is this introduction of these trivectors into physics that is Joy's greatest accomplishment. My model uses volume forms in ways different from Joy and I am making nice progress in this regard, but here is not the place to present this.
Michael's last comment 26 Nov 2012 @15:40 has taken yet another major turn, a hard turn into metaphysics. In this [if I understand him] he is finding new common ground between his model and Joy's model [that I earlier denied existed] in yet another new conception. While I don't follow all of his reasoning I greatly admire both his grasp of issues and his originality.
I would also like to observe that Michael's points about Bell changing horses in midstream, halfway betwixt his preamble and his eqn [2], is of potentially major significance, and I hope this point does not get lost in the new twists and turns this conversation is following.
Thank you, Joy and Michael, for stretching my brain. It feels good.
Edwin Eugene Klingman
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Edwin Eugene Klingman replied on Nov. 26, 2012 @ 22:35 GMT
Michael,
An editing mistake deleted a 'not' from my above question to you.
You state above that "In QFT - and this applies even in the deceptively non-relativistic case of stationary electrons - the electrons interact by virtual photons that can become virtual electron-positron pairs. In this QFT expansion, positrons can annihilate the original electrons, turning their electron partners in the created pair into the new correlated electrons."
The question is whether these new electrons are correlated with the original pair of electrons [I assume not], and whether you are postulating that this occurs 'all the time' by virtue of the very nature of virtual processes in QFT or simply occurs occasionally, and so does not significantly affect the Bell test correlations that are actually measured. Or do you mean something else entirely?
Thanks,
Edwin Eugene Klingman
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Joy Christian replied on Nov. 26, 2012 @ 23:04 GMT
Hi Michael,
There is indeed a lot we agree about. I am not sure, however, what you mean by "the metaphysical result of [my] proof - has to be S3 or S7." The closest "metaphysical proof" of my result I can think of is actually a mathematical theorem (the theorem by Hurwitz; cf. section 1.5 of my book), which says that a certain quadratic equality holds only for the numbers 1, 2, 4, and 8....
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Hi Michael,
There is indeed a lot we agree about. I am not sure, however, what you mean by "the metaphysical result of [my] proof - has to be S3 or S7." The closest "metaphysical proof" of my result I can think of is actually a mathematical theorem (the theorem by Hurwitz; cf. section 1.5 of my book), which says that a certain quadratic equality holds only for the numbers 1, 2, 4, and 8. The rest is a physical proof, whose simplified version goes as follows: Measurement results (at least in the non-relativistic domain) are events in space at a given time. The nature of the simplest non-trivial quantum state---namely, the four particle GHZ state---dictates that the corresponding EPR elements of reality are points of a unit 7-sphere (cf. section 6.5.2 of my book). Such a 7-sphere, however, is not disciplined enough (if it is round) to reproduce the strong correlations predicted by the quantum GHZ state. The strong correlations can be reproduced if and only if the 7-sphere is parallelized. Thus the observed quantum correlations are the evidence that physical space we live in respects the geometry and topology of the parallelized 7-sphere.
There is of course a lot more to my argument than this simplified version (cf. chapter 7 of my book), but the above, in essence, is my argument why it has to be S7. Any other attempts to reproduce quantum correlations realistically and deterministically would necessarily violate local causality. This is because only manifolds corresponding to a division algebra, such as S7, can be closed under multiplication, and without that it is impossible to maintain local causality. Thus, unlike you, I do not see the spatial connection in my work as a model specific feature, but the very essence of my argument. What I am after is not just to exclude quantum gravity, but to explain quantum phenomena themselves as gravitational (or geometrical) effects, where gravity is to be understood sufficiently broadly.
So, it appears that while agreeing about a lot we continue to disagree about the most fundamental issues. At one point I thought that you could accommodate the spatial connection within your point of view. But apparently you were not entirely happy with your own attempt to do so.
Thank you, Edwin, for your input and remarks. While valid, we shouldn't get too excited about Michael's observation of the shift in the meaning of lambda in Bell's equations (1) and (2). We must remember that this was his first paper on the subject. He has much more careful presentations of his "theorem" in later reiterations, most notably in his last paper (written in 1990).
Best,
Joy
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Author Michael James Goodband replied on Nov. 27, 2012 @ 13:27 GMT
Hi Joy,
Found it! I've been having extreme difficulty with the physicality of your model. Its been annoying the hell out of me, as my physics intuition has been telling me that EPR is fine, but the classical physics extension is not. I was right on my 14 Nov post, there has to be a physical spatial connection for super-linear correlations and in EPR there is - it IS light (100% sure, no...
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Hi Joy,
Found it! I've been having extreme difficulty with the physicality of your model. Its been annoying the hell out of me, as my physics intuition has been telling me that EPR is fine, but the classical physics extension is not. I was right on my 14 Nov post, there has to be a physical spatial connection for super-linear correlations and in EPR there is - it IS light (100% sure, no doubt whatsoever). Your model doesn't explicitly include the fact that electrons are charged, and you can't reproduce EPR in physics with electromagnetically neutral particles, because none really exist. E.g. a neutron is a composite of charged particles, and has a net magnetic dipole moment - therefore there-exists a electromagnetic connection between EPR neutrons.
All other possible scenarios are the same, the particles in an EPR spin singlet state are coupled by an electromagnetic gauge field. In QFT this is described in terms of the spin 1 photon, in classical physics light is described by circularly polarised light (i.e. with rotation), and in Kaluza-Klein style theories like mine, the gauge field is a torsional metric connection along the compactified dimensions. In my model there is a direct association between spin and electromagnetism, because as topological spin defects the fermionic particles only exist because there is the unbroken U(1) symmetry of electromagnetism. So in ALL the known physical ways of describing the EPR scenario, there IS a physical spin connection between the electrons - it IS light. The spin connection of EPR definitely is NOT a new spin force aspect of gravity, but in any theory with compactified dimensions it IS definitely geometric - a torsional aspect of the extra-dimensional fabric of reality. So in a Kaluza-Klein sense, it is a gravitational effect.
Your model of EPR captures this geometric aspect in a mathematical form that does NOT include the physical fact that the particles in question are charged (and have a magnetic dipole moment) where light is the physical spin connection. Extending your model from EPR up to classical physics takes it beyond its domain of validity, and gives a false impression that classical objects in SO(3) rotation states will display QT correlations - the physics of EPR says that they will not. The success of your model in describing EPR does NOT provide evidential support for QT-style correlations in the SO(3) rotations of classical objects - it is an entirely unsupported speculation.
If you put your head on the block over this speculation, given the behind of scenes state of physics you describe, I can see you losing your head! It can get far worse yet, such as being shut-out of arxiv, journals etc. and viewed as a crank who doesn't know any physics. I know that can be the Oxford view of Cambridge and DAMPT, but physics history says otherwise.
I have already shown that QT can be arrived at by a shift from discrete to continuous description in a pure geometric theory (11D GR) - it's been in UK libraries all year. I have also shown that any attempt to construct a classical physics theory of particle reactions makes this necessary - this QT result is a metaphysics result that is independent of my GR model. The associated papers are only on vixra because journals, and arxiv, are SO closed minded as not to even read them because I have no university affiliation or endorsement (note that my PhD papers are on arxiv and were published, I know the standard). My epiphany was seeing how Godel applied to science, and it can do so in 9 difference instances, QT is just one of them. The basic proof is just undergraduate level maths - at least it was when I did my degree - so I know for a fact that it is a PROOF. A Cambridge education really isn't that pathetic, although British philosophers of science have given me the message that they think so - something I noted down to use in evidence against them at some later date that will come, it always does.
Your (parallelised) S3 and S7 results is not a metaphysical proof yet, but I think such a result is possible - it hadn't occured to me that such a thing could be possible until I saw your work. You could find it quicker than I could as I don't have your mathematical talent, but your work (almost) gives a template for how do it.
Best,
Michael
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Joy Christian replied on Nov. 27, 2012 @ 16:20 GMT
Hi Michael,
I am afraid you are mistaken. Your error lies in the following statement: "...you can't reproduce EPR in physics with electromagnetically neutral particles." This statement contradicts quantum mechanical prediction for entangled neutral particles such as neutral kaons and neutrinos. You may be able to discount the case of neutral kaons (as you have discounted the case of neutrons), but your argument falls apart for the case of
entangled neutrinos. No light there, I am afraid.
Best,
Joy
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Author Michael James Goodband replied on Nov. 27, 2012 @ 16:47 GMT
Hi Edwin,
In QFT, don't forget that the virtual photons provide a connection between the original electrons and the virtual electron-positron pair. QFT also says that this dynamics is happening all the time, and so QFT predicts that the spin of an electron in the singlet state isn't confined to stay pointing in the same direction, but dynamically takes every possible value on S2. My point...
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Hi Edwin,
In QFT, don't forget that the virtual photons provide a connection between the original electrons and the virtual electron-positron pair. QFT also says that this dynamics is happening all the time, and so QFT predicts that the spin of an electron in the singlet state isn't confined to stay pointing in the same direction, but dynamically takes every possible value on S2. My point is that to fulfil Einstein's original intention for his EPR scenario, the hidden variable framework in classical physics needs to reproduce the net result of this dynamics. This would seem to necessarily entail an integral over the physical S2 given by QFT - the integral over the hidden variable is that integral, and my IFF condition expresses the corresponding physical dynamics.
On virtual-particles being the primary fudge factor of QFT, my work shows the shift in descriptive language from natural-numbers (N) for the numbers of particles to real-number (R) valued fields - i.e. matter fields - to be the critical fudge of QFT, but the physical reason for this fudge, IS virtual-particles. The distinction is because despite the critical role of virtual-matter in QFT, it is fundamentally a feature of Relativity and not QFT per se. GR predicts that normal matter becomes virtual-matter when it enters the ergo-region of a rotating black hole, and such a black hole of 4 million solar masses is predicted to lie at the centre of our galaxy (the chances that it isn't rotating are nil). The Kerr metric for this black hole gives an ergo-region just outside the event horizon where the in-falling matter and radiation becomes virtual, but this would be on the macroscopic scale of classical physics and not QFT scales.
On SUSY, note the dependency of reasoning that leads to the speculation of SUSY:
It is a super-symmetry between fundamental bosonic fields and fermionic matter fields
1) Fermionic matter fields are a continuous field description of discrete particles
2) The discrete numbers of particles are recovered by a number operator acting over the fermionic fields
3) This relationship between discrete (N) and continuous (R) is fundamentally QT - this is why I'm picking up any attempt to try and sneak in this shift (such as Bell)
4) These matter fields are necessary because QT is fundamental
QT not being fundamental implies that matter fields are not fundamental, so how could there be a super-symmetry between something fundamental (bosonic fields) and something that isn't (fermionic fields)? The obvious answer is that there is no super-symmetry.
Best,
Michael
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Author Michael James Goodband replied on Nov. 27, 2012 @ 16:57 GMT
Hi Joy,
Neutrinos are electrically neutral, but they are not entirely neutral because they have a non-zero isospin charge. The analogous QFT story as for electron pairs still stands for neutrinos but with the spin 1 photon replaced by the spin 1 W and Z bosons. The physical spin connection is still the gauge fields, where there is also a corresponding description in terms of classical gauge fields and KK compactified dimensions. So my point still stands for neutrinos.
The flavour entangled element of neutrinos is where it gets interesting, but does require my point about S7 being the internal particle symmetry space. I raised this flavour issue earlier if you remember in the context of the non-associativity of the octonions.
On the relation between the parallelisation of the spheres S3, S7 and my desire for them to correspond to symmetry group spaces, the spaces of SU(n) are flat are they not? So my assertion that the unified symmetry "group" is actually the symmetry group quotient SU(4)/SU(3) gives the differntial manifold S7 which MUST be flat - the parallised sphere S7 - mustn't it?
Best,
Michael
Joy Christian replied on Nov. 27, 2012 @ 17:41 GMT
Hi Michael,
I am afraid I remain unconvinced. How big is the non-zero isospin charge compared to their gravitational interaction? And how strong a link such a short-range interaction could provide in a long-range correlation such as EPR correlation? The parameters of neutrinos are not known precisely. What is known for sure is that neutrinos have non-zero masses, and hence they are gravitationally non-neutral. So it is gravity, and gravity alone---not light---that is common in all known examples that exhibit long-range entanglement, including my macroscopic fermions.
I am sure the manifold S7 you derive is flat, or could be made flat by parallelization. But one cannot account for even the simplest three-particle GHZ correlations local-realistically without recognizing that these correlations are correlations among measurement events in space-time, not in a symmetry space. The simultaneous clicks of six detectors are events in space-time, not points in a symmetry space. The GHZ correlations are thus correlations among events in space-time, not symmetry space. This is the point of our disagreement.
Best,
Joy
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Thomas Howard Ray replied on Nov. 27, 2012 @ 17:56 GMT
Joy wrote: " ... your argument falls apart for the case of entangled neutrinos."
I think this underscores the importance of our being able to show that strong quantum correlations do not differ from weak classical correlations, given any case of particles sharing an initial condition.
A classical correlation -- such as the prediction that a fair die producing one value correlates...
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Joy wrote: " ... your argument falls apart for the case of entangled neutrinos."
I think this underscores the importance of our being able to show that strong quantum correlations do not differ from weak classical correlations, given any case of particles sharing an initial condition.
A classical correlation -- such as the prediction that a fair die producing one value correlates perfectly to one of five other values -- is as dependent on perfect information (i.e., knowledge of the complete state of the die's six faces) as the probabilistic quantum mechanics. The trouble with QM, though, is that by assigning perfect information (by the equally likely hypothesis) to an incomplete state, nonlocality sneaks in the back door as a fundamental physical principle. One then leaps to the assumption that "the experiment not performed" has no basis in reality, and then takes the short step to conclude that we live in an observer-created world.
This nonconstructive argument (and its proof) neglects that the equally likely hypothesis applied to incomplete information is a shot in the dark. One is reminded of the parody:
"I shot an arrow into the air;
It fell to Earth I know just where.
Though aimed at a buck who stood afar,
It pierced the radiator of my car."
(No idea of whom to attribute this dimly remembered ditty.)
Point is, QM brings the target to the arrow. Whatever probability the arrow has of hitting the car when the bow is drawn, the probability is 100% that it hit the target.
Classically, the arrow either hit the target or missed (the outcome is heads or tails) -- and whether or not it hit or missed, there is a lot of complicated but local physics between the state preparation (drawing of the bowstring) and the measurement result. In QM, state preparation is disconnected from the measured outcome; Bell-Aspect type experiments only end up proving what they assumed in the first place, i.e., that correlated events remain correlated to infinity. The explanation: nonlocality. That's like saying that because EM and gravitational field influences are infinite, physical laws on one side of the universe do not differ from those on the other side -- true, but trivial.
What QT proponents *really* want from entanglement, is to be able to show that
quantum correlations are independent of classical correlations .
Vlatko Vedral never replied to my response to his challenge, though some time ago in these FQXi forums he said he was willing to bet a bottle of Bollinger champagne that quantum entanglement would remain a part of fundamental physics. I am willing to take that bet.
Tom
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Joy Christian replied on Nov. 27, 2012 @ 18:25 GMT
Vlatko Vedral is absolutely correct. Quantum entanglement will remain a part of fundamental physics just as assuredly as metempsychosis will remain a part of fundamental Hinduism.
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Thomas Howard Ray replied on Nov. 27, 2012 @ 18:30 GMT
LOL! Joy, are we getting a wee bit cynical? :-)
Tom
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Fred Diether replied on Nov. 27, 2012 @ 18:52 GMT
Hi Joy, Tom,
Well, the physical effect certainly won't go away. But hopefully the wrong explanation of non-locality will go away.
Best,
Fred
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Author Michael James Goodband replied on Nov. 27, 2012 @ 19:38 GMT
Hi Joy,
In Electroweak theory: isospin charge ½, hypercharge -1, hypercharge and isospin couplings related to electric charge by the Weinberg angle and so of the same order of magnitude. The weakness of the force is just due to the range being limited by the W/Z boson masses. The electron neutrino mass if of the order 1eV, so not much gravity there. But the crucial factor is that neutrinos only occur in left-handed state, so the correlation addressed in the paper is between left-handed electron neutrinos and left-handed muon neutrinos. The correlation considered in the paper is NOT spin correlation, but flavour correlation. They are NOT in an EPR singlet state, so your model doesn't apply as it is. I'm not mistaken on this one, I know my basic QFT.
It is precisely because this flavour correlation doesn't seem to be readily accounted for in EW theory, that I raised the issue of the non-associativity of the octonions earlier in connection with flavour. In a space with compactified dimensions, the topology of the compactified space is part of the topology of the full space and impacts space-time events. The dimensional reduction procedure of KK theory shows that the compactified dimensions give a torsional component to the "gravity" between objects - it IS the gauge fields. The S7 is a physical part of space at every point, and not just a symmetry space. Proving that such a space MUST be a flat S7 would be metaphysical result.
In a loose mathematical sense, the gauge fields of my compactified S7 gravitational theory can be viewed as being associated with the non-commutativity of the octonions. This begs the question as to whether their non-associativity is also manifest in terms of a physical "force". My theory naturally generates the 3 family flavours of particles, so flavour dynamics would naturally be associated with the non-associativity of the octonions in my theory - as some sort of gauge effect.
Best,
Michael
Joy Christian replied on Nov. 28, 2012 @ 10:55 GMT
Hi Michael,
I have thought some more about your recent posts. The jargons of our approaches seem to be obscuring the contrast between our positions. Let me summarize this contrast in simple terms:
You seem to be suggesting that what is responsible for entanglement---at least in the singlet state---is *light*, or more precisely the electroweak interaction. Without electroweak interaction there would be no strong quantum correlation between the singlet constituents.
Is this correct?
I have been arguing, on the other hand, that what is responsible for entanglement---at least in the singlet state---is *the geometry and topology of the physical space*, or more precisely the gravitational interaction. Without gravitational interaction there would be no strong quantum correlation between the singlet constituents.
Do we agree that these, in essence, are our respective positions on the singlet correlation?
If so, then we can move on to the next step. You wrote: "...S7 is a physical part of space at every point, and not just a symmetry space. Proving that such a space MUST be a flat S7 would be metaphysical result."
If I understood this statement better, then proving the "metaphysical result" may be possible. The mathematics, if needed, is already in place, but I am not quite following what it is that you want to be proved. The first step towards the proof would a precise mathematical statement of what needs to be proved. Can you formulate such a statement?
Best,
Joy
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Thomas Howard Ray replied on Nov. 28, 2012 @ 11:55 GMT
Joy wrote to Michael:
" ... the next step. You wrote: '...S7 is a physical part of space at every point, and not just a symmetry space. Proving that such a space MUST be a flat S7 would be metaphysical result.'
"If I understood this statement better, then proving the 'metaphysical result' may be possible. The mathematics, if needed, is already in place, but I am not quite following...
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Joy wrote to Michael:
" ... the next step. You wrote: '...S7 is a physical part of space at every point, and not just a symmetry space. Proving that such a space MUST be a flat S7 would be metaphysical result.'
"If I understood this statement better, then proving the 'metaphysical result' may be possible. The mathematics, if needed, is already in place, but I am not quite following what it is that you want to be proved. The first step towards the proof would a precise mathematical statement of what needs to be proved."
Last January, I formulated the theorem: "For every observation of a classical state, there exists at least one correspondent quantum state."
This was based on the assumption noted earlier here, that weak classical correlations do not differ from strong quantum correlations (no boundary between quantum and classical domains). That there is at least 1 quantum state correlated to the classical state is sufficient to show that the classical record corresponds 1 to 1 with the quantum record for 1 measurement in 1 time interval. All other unmeasured events in the same interval could therefore be characterized as metaphysically real.
My notebook from 17 - 20 January 2012 contains a crude proof outline that begins with "lemma: Joy Christian's framework for quantum pair correlations implies geometric uniformization for 3-manifolds.."
12 proof steps follow. I want to offer for discussion here, the first five:
1. By Myer's theorem, a complete, compact Riemann manifold M has finite fundamental group.
2. Every point of the Joy Christian manifold has finite fundamental group. Therefore:
3. Any singularity arbitrarily chosen for surgery, or as the initial condition of a local continuous measure function, is a metric -- i.e., a nondegenerate curve that on a Riemann manifold can be represented as a metric tensor of infinitesimal length.
4. The Ricci metric, described as
d/dt g_ij(t) = - 2 Ric
is independent of time, meaning that even though the measure is expressed over a time interval, the measure may be rescaled for *any* time interval.
5. The Joy Christian framework is scale invariant, such that quantum correlations apply over spacetime intervals of any length or duration, quantum or classical domain.
Tom
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Thomas Howard Ray replied on Nov. 28, 2012 @ 13:28 GMT
To supplement my last post, I came across a
1979 paper by G. Galloway that reinforces the initial perception I had a couple of years ago that Joy's framework is powerful enough to solve the cosmological horizon problem. This follows from the framework's implied independence of time scale.
Tom
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Joy Christian replied on Nov. 28, 2012 @ 13:29 GMT
Hi Tom,
Thanks for the summary, but I am not sure how it is related to what Michael wants to prove. Let us wait and see what he has in mind, because so far I haven't understood what he wants to prove, or why it is not already proved in Chapter 7 of my book (or in the attached paper).
Best,
Joy
attachments:
7_1101.1958v1.pdf
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Thomas Howard Ray replied on Nov. 28, 2012 @ 13:46 GMT
More recently from
Professor Galloway And seeing that this paper was communicated by no lesser light than S. T. Yau, I get the goosebumpy feeling that topology in physics is on the verge of a golden age.
Tom
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Author Michael James Goodband replied on Nov. 28, 2012 @ 19:27 GMT
Hi Joy (and Tom),
Yes, nothing quite stands in the way of clear communication like using the same language, but with different intended meanings. So on the point:
"You seem to be suggesting that what is responsible for entanglement---at least in the singlet state---is *light*"
This is not a suggestion, but the standard QFT view of the interacting particles in a spin singlet...
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Hi Joy (and Tom),
Yes, nothing quite stands in the way of clear communication like using the same language, but with different intended meanings. So on the point:
"You seem to be suggesting that what is responsible for entanglement---at least in the singlet state---is *light*"
This is not a suggestion, but the standard QFT view of the interacting particles in a spin singlet state. For most singlet cases in QFT, there is a virtual-particle connection between the particles in terms of the gauge bosons - photon, W/Z, gluons - depending upon the particle charges, and no fermionic particle is genuinely chargeless (unless you find a right-handed neutrino!). So in the QFT view, it is the spin of these bosons which is ultimately responsible for the strong quantum correlations between the spins of the particles in the spin singlet state. For the hidden variable framework to say that QT correlations come from somewhere else - i.e. not QT - it must successfully capture this QFT view in order to go beyond it.
The exception to this general QFT view is the neutrino correlations you pointed out, as the strong correlations in this case are between 2 left-handed neutrinos with different flavours. So the strong QT correlations are flavour correlations which aren't accounted for in QFT because they are not due to the spin of a photon, W/Z or gluon connection. This marks a weak point of the Standard Model - I'm suggesting this points to the non-associativity of the octonions, because my model with an octonion space reproduces particle flavours.
Then there is my suggestion, which comes from the fact that dimensional reduction of a pure geometric 11D GR yields the Standard Model Lagrangian (up to colour group only) with S7 gauge space - this can be read straight from the attached paper (sec 2.3-2.4 eqns 2.20 and 2.22 of attached paper give my eqns 14 and 18 in sec 4 of
my paper) which is a review of the state of KK in 1987, before Witten falsely claimed KK couldn't give EW chirality - i.e. the dimensional reduction is standard stuff. As for all KK-theories, the 4D gauge connection is a *gravitational* connection in the full 11D - that is why KK can unify gravity with particle forces. So I have NO disagreement over the wording:
"I have been arguing, on the other hand, that what is responsible for entanglement---at least in the singlet state---is *the geometry and topology of the physical space*, or more precisely the gravitational interaction."
There is no "other hand" in my suggestion, the gauge connection of 4D field theory - i.e. QFT - IS about the *geometry and topology of the physical space*. What I'm looking for is a metaphysical proof in 3 parts (the highlighted words make it metaphysics):
1) Strong QT correlations *must* be due to the topology of physical space
2) That necessarily *requires* the existence of compactified dimensions - then the connection IS a form of gravitational interaction in its most general sense
3) The compactified dimensions *must* be S7
On first reading of your Ch 7 it seemed to me that you had already proven this, but you have been disputing this in our discussion - I still think that in the mathematical framework you have the core of the proof I'm seeking. In your proof, it is the expression of causation as a factorisation condition which gives the critical condition of mathematical closure that selects the fundamental number systems C, H, O - the C case being trivial.
In my case, I have causation expressed as GR. The topological condition for the existence of topological monopoles demands a mapping from S7 to S3, and then the causal dynamics of GR also gives S1. So the essential physics of our two approaches is the same - expressions of causation - and the topological conditions pick out the same fundamental number systems - C, H, O. In my case there is a very open issue between N and R, whereas I pointed out the same issue is implicitly present within the hidden variable framework. It seems to me that between us we have a round peg and round hole, and I can't see them not fitting. Because we have the same very basic underlying physics and maths, the claim that they are in contradiction strikes my as being similar to claiming that we have a proof that in physics 1=0. That is very unlikely!
Best,
Michael
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Author Michael James Goodband replied on Nov. 28, 2012 @ 19:37 GMT
Attachment failed as is 4.4MB. Reference was Rep. Prog. Phys. 50 (1987) 1087-1170. IOP journal behind a pay-wall, can't find where my pdf came from. Can e-mail if query my statement that it's standard stuff in a review article.
Michael
Joy Christian replied on Nov. 28, 2012 @ 20:54 GMT
Thanks, Michael.
I actually know the report by Bailin and Love. I studied it some years ago. I have downloaded it again just in case, but I don't doubt your word for a second. I am more concerned about understanding the apparent incompatibilities in our views. I will reflect on your comments above and get back to you.
Joy
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Jonathan J. Dickau replied on Nov. 29, 2012 @ 07:05 GMT
Intriguing developments.
This thread has been white hot with interesting ideas to compare. I can barely keep up with reading the parts I like, but this twist in the compatible or incompatible debate is a bit surprising - and it gives me a lot of food for some very intense thought. Whether to consider your two theories as possibilities that might be real or realities that might be possible is part of the issue, I think. I still have the gut feeling that your ideas can be blended, or that nature's reality incorporates aspects of both your models, but digesting all of the comments above will take time.
I keep returning to the notion that size is relative, and so is interiority/exteriority among forms, when non-commutativity and non-associativity enter the picture, so that the physical interpretation of geometric realities may differ from their intrinsic arrangement. We do not possess a God's eye view, as inhabitants in a physical reality. So there are still legitimate questions about what constitutes a privileged viewpoint, and what an ordinary observer would see in a given setting.
All the Best,
Jonathan
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Author Michael James Goodband replied on Nov. 29, 2012 @ 15:29 GMT
Hi Jonathan,
Full appreciation of the depth of Relativity is critical, where it can be viewed as having third orders of meaning:
1) First order meaning is the relative measurement of rotations - i.e. fermionic spinors - and speeds - as in the speed of light is the same for all local observers at the same cosmological time. It is one of the themes of this year's essay contest, that...
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Hi Jonathan,
Full appreciation of the depth of Relativity is critical, where it can be viewed as having third orders of meaning:
1) First order meaning is the relative measurement of rotations - i.e. fermionic spinors - and speeds - as in the speed of light is the same for all local observers at the same cosmological time. It is one of the themes of this year's essay contest, that even this level of Relativity isn't being properly grasped in the mainstream. It is quite trivial in SR that there is a unique reference frame for every event in the universe, namely the co-moving reference frame. Apply this fact to a closed expanding universe, and it has a unique co-moving reference frame - a global cosmological reference frame with a uniquely defined cosmological time, and all our local measurements are relative to this. As the stars are being dragged along by the expanding fabric of reality, we have a realisation of Mach's principle. So it's fairly trivial to show in GR that many of this year's essays, and the 'process physics' paper you mentioned in your thread below (plus more) are correct about the mainstream presentation of Relativity being screwy. Other essays have objected to the mainstream cosmological constant, which is an oxymoron in Relativity (the clue is in the word). That the cosmological term is defined to be 'constant' relative to the metric is even clearly evident on
Wikipedia - the term has to be 'constant' within the surface defined by the metric. But for a closed expanding universe where the metric is parameterised by radial scale factor, because it is an extra-dimensional parameter, the cosmological term can also be parameterised by the same factor and still be 'constant' as demanded - as could the speed of light and the gravitational coupling constant. Again, it is trivial to show that the mainstream presentation of GR is screwy, as many of us saying.
2) Second order meaning is what you referred to, which is physically realised in the case of all space-time measurements being relative to the physical scale of compactified dimensions. The simple relativism of this solves the apparent mystery of compactified dimensions being of 'constant' size - ALL physical measurements are relative to the size of the compactified dimensions, and measuring their scale in terms of themselves gives a constant relative size. In an absolute sense, they're not of a constant size. When the compactified dimensions are octonion in character, then as you imply, this relativism gets really interesting. As I mentioned in your thread below, when the scale measurements used in the construction of space-time differentials are relative to octonion compactified dimensions, it is not unreasonable to expect the resulting differential structure for the 4D space-time manifold to be 'exotic'. My KK-theory indicates that the non-commutivity gives a gauge structure, whereas the non-associativity gives a family structure to the 'emergent' 4D space-time. The left/right split in the octonion representation could well be associated with the different chiralities of the EW vacuum - this appears as though it would be the case from my work. The various ways of expressing the octonions after this left/right split does seem to raise legitimate questions about the existence of privileged viewpoints.
3) Third order meaning of Relativity is that the definitions of some physical quantities are defined relative to the number of dimensions of the space. This will be irrelevant, except when there is the compacification of dimensions, which seems to be the case. Just assuming that a black hole has a compactified surface is all that is needed to derive Hawking's expression for black hole entropy in basic thermodynamics. But the derivation reveals that the definition of entropy for radiative modes involving compactified dimensions depends upon the number of spatial dimensions left uncompactified. This changes from 3 in normal space, to 2 in the compactified surface of a black hole, which implies that the black hole 'information paradox' is simply due to an entropy anomaly of not comparing like definitions of entropy. The classical thermodynamics derivation also gives black hole radiation - with the correct inverse relationship between temperature and radius - which implies that radiation in a compactified surface exerts an outwards radiation pressure. This agrees with the cosmological 'constant' not being constant, and solves the mystery of where the motive force for spatial inflation and dimensional compactification comes from.
With a full appreciation of Relativity, a lot of the apparent mysteries surrounding the mainstream view of Relativity just disappear. It is probably worth noting that many of the mysteries disappear if we assume that the universe is closed. I show that this assumption also solves the mystery of what the fermionic particles are, and why EW theory is chiral. The relativism of space-time to an octonion structure seems to be a significant feature that remains to be explored.
Best,
Michael
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Rick Lockyer replied on Nov. 29, 2012 @ 18:32 GMT
Michael,
Nice to hear acceptance of the fact there is a right and left character for octonion algebra. You would not know this from most of the available literature. Curious about your actual position on the difference between the 8 algebraic structures of like chirality you brought up. Do you think it is reasonable to think one may be preferable to another? Clearly I do not think so, for it is the cornerstone of my work on applying octonion algebra to physics. The ramifications of acceptance that NONE of the 16 ways to roll out octonion algebra is preferable to another is the voice behind the algebra telling us precisely how nature must look. It is not a coincidence that all of these old school things like observable currents, force, work, energy density, energy flux, momentum, and conservation of energy and momentum, etc. all fall in line with my law of algebraic invariance when properly represented in an octonion analytic framework.
I would be wary of any mathematical construction that requires a subset of octonion algebraic constructions to work out.
I do not know if Tevian Dray still favors one over another, but you might look
here as a starting point if you are unfamiliar with the work.
Rick