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CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: Unitarity, Locality and Spacetime Geometry: Foundations That Are Not Foundations by Lawrence B Crowell [refresh]

Author Lawrence B Crowell wrote on Aug. 12, 2012 @ 17:16 GMT
Essay Abstract

This essay discusses a possible route towards the removal or deformation of existing physical postulates. This is looked at in light of history. The foundations of interest are unitarity and locality. How these principles are changed or abandoned is first examined in light of previous changes in the understanding of physical foundations. These foundations are examined to question their firmness, and if they give way then unto what do they submit to as emergent properties. Suggested approaches are then proposed within light of the AdS/CFT correspondence, nonlocal BCFW amplitudes in QCD, cosmological quantum phase structure and ultimately the replacement of unitarity by deeper principles of modularity.

Author Bio

My graduate work was at Purdue University. I have worked on problems of clock synchronization with general relativity, spacecraft navigation, quantum optics and more recently with IT/programming. I spend much time thinking about issues concerning foundations.

Yuri Danoyan wrote on Aug. 12, 2012 @ 23:21 GMT
Hi,Lawrence

What mean unitarity is emergent?

Correct quote of Ludwig Wittgenstein

"Whereof one cannot speak,thereof one must be silent"

Major Works: Selected Philosophical Writings p.82

2009 by HarperCollins Publishers

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Author Lawrence B Crowell replied on Aug. 13, 2012 @ 01:09 GMT
If you look in P. gibbs' page you will see I break this out in a bit more detail. Unitarity is a limiting case where wave functions are analytic everywhere. Physics based on modularity and nonlocality has no reference to spacetime. Causality in physics is based on propagators or Greene functions that push a field from (x, t) to (x’, t’). Without spacetime this simply does not exist. The removal of the pole or singularity occurs when there are no black holes or in a region of spacetime that excludes big bang singularities.

One of the things I think comes from this is the universe contains only one of each particle. The universe has only one electron, one up quark, one muon, one photon, one Z, one higgs one… . What we observe as individual particles are the same particle within different configuration variables, whether spacetime or momentum-energy. Spacetime is in effect a sort of emergent property, in many ways an illusion, where particles we observe are mirror images of the same particles with different configurations. Baruch Spinoza wrote about something like this, which he called monads.

Cheers LC

Yuri Danoyan replied on Aug. 13, 2012 @ 01:51 GMT
1.The "Monads" belong to Leibniz, The "Modes" coined by Spinoza.

2.The Universe has:

Fermions 12(6 quarks+3 leptons+3 neutrino).

Bosons 12(8 gluons+3 vector(2W+1Z)+1photon).

Numerical supersymmetry not broken.

3.From other side the Universe has:

Fermions 3(proton,electron,neutrino),neutron non-stable

Boson only 1 photon.

See my essay http://www.fqxi.org/community/forum/topic/946

Metasymmetry is broken

In this case Lawrence B Crowell is right.

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Author Lawrence B Crowell replied on Aug. 13, 2012 @ 13:40 GMT

I write more on this below. If I am right the any particle, say an electron, in some wave function ψ(r, t) at some point in spacetime (r, t), is a projection of a single electron onto those configuration variables. The same holds if the particle is described in momentum-energy variables in a Fourier tranforms

φ(k,ω) = sqrt{1/2π}∫d^3xdt ψ(r, t)e^{ikx – ωt}.

This projection occurs due to the nonlocality of fields, and their physics is described not by analytic functions or unitarity, but rather by modularity.

Cheers LC

James Putnam wrote on Aug. 12, 2012 @ 23:44 GMT
Dr. Crowell,

In reaction to a message I just read posted in Dr. Gibb's blog, your essay is listed. Glad to see you enterred and are sharing your expert opinions again in discussions.

James

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Author Lawrence B Crowell replied on Aug. 13, 2012 @ 01:11 GMT
I hope you find this essay not too much to your disliking.

Cheers LC

Pentcho Valev wrote on Aug. 13, 2012 @ 05:00 GMT
Lawrence,

Do you still believe that Banesh Hoffmann and John Norton are wrong in their claim that the Michelson-Morley experiment CONFIRMED the variable speed of light predicted by Newton's emission theory of light?

http://www.pitt.edu/~jdnorton/papers/companion.doc

John Norton: "These efforts were long misled by an exaggeration of the importance of one experiment, the Michelson-Morley experiment, even though Einstein later had trouble recalling if he even knew of the experiment prior to his 1905 paper. This one experiment, in isolation, has little force. Its null result happened to be fully compatible with Newton's own emission theory of light. Located in the context of late 19th century electrodynamics when ether-based, wave theories of light predominated, however, it presented a serious problem that exercised the greatest theoretician of the day."

http://philsci-archive.pitt.edu/1743/2/Norton.pdf

John Norton: "In addition to his work as editor of the Einstein papers in finding source material, Stachel assembled the many small clues that reveal Einstein's serious consideration of an emission theory of light; and he gave us the crucial insight that Einstein regarded the Michelson-Morley experiment as evidence for the principle of relativity, whereas later writers almost universally use it as support for the light postulate of special relativity. Even today, this point needs emphasis. The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/d
p/0486406768

"Relativity and Its Roots" By Banesh Hoffmann: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

Pentcho Valev pvalev@yahoo.com

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Author Lawrence B Crowell replied on Aug. 13, 2012 @ 13:24 GMT
Banesh-Hoffman are right that a particle, even a photon, emitted by a moving frame relative to a stationary frame has more energy than the same particle emitted in the stationary frame. In the case of a photon the photon emitted from a moving frame in the same direction is blue shifted with more energy. These matters concerning the measurement of light speed are old and clearly demonstrated.

To be honest I did not write this essay with the intention of debating century old physics that is well established. I doubt I am going to seriously get around to reading these papers, for they are long and not likely very enlightening. I am not sure why people decide that some aspect of physics is all wrong and devote their lives and work doing battle. This happens with biology in the ongoing reaction to Darwin, but at least the deniers are upholding some theology, which gives some sense for why they do this. There is no such motivating ideology for denying some physical theory that is well established.

The point of my essay is not that relativity is all wrong. It is more that in a quantum field setting at small scales it becomes incomplete. This pertains to black holes that are smaller than a nucleus or within the first 10^{-30} seconds of the big bang and so forth. This does not mean that relativity is overthrown and what I advocate here is found in basic measurement, such as the Michelson-Morley experiment.

Special relativity is not just a subject to be researched, but it really is more of an application these days. It is so well established within its proper domain of experience that its validity is beyond reasonable doubt. General relativity is a subject of research, but it is pretty well tested with no empirical evidence that it fails.

Cheers LC

Pentcho Valev replied on Aug. 13, 2012 @ 14:13 GMT
In 1887 (FitzGerald and Lorentz have not yet advanced the ad hoc length contraction hypothesis) the Michelson-Morley experiment unequivocally confirms the assumption that the speed of light varies with the speed of the light source (c'=c+v) and refutes the assumption that the speed of light is independent of the speed of the light source (c'=c). That is what John Norton and Banesh Hoffmann suggest. Do you agree, Lawrence?

Pentcho Valev pvalev@yahoo.com

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Author Lawrence B Crowell replied on Aug. 13, 2012 @ 14:35 GMT
To be honest I would prefer that my essay page not be filled with posts over this imagined controversy.

LC

Author Lawrence B Crowell wrote on Aug. 13, 2012 @ 14:44 GMT
There have been some developments along these lines which may give support for my thesis here. The paper Black Holes: Complementarity or Firewalls? by Almheiri, Marolf, Polchinski, Sully raises an important point. This points out an inconsistency with the holographic principle. They focus on the suggestion that postulate #2; Outside the stretched horizon of a massive black hole, physics can...

view entire post

James Putnam wrote on Aug. 13, 2012 @ 15:40 GMT
Dr. Crowell,

Nice work! Just the right amount of historical and introductory theoretical information to help the educated non-physicist have a reasonable opportunity to follow the logic of your essay. That extra information is clearly not filler material or added in an author's attempt to appear to be well informed. Not at all! Your professional viewpoint is made accessible while presenting advanced theoretical concepts. Thank you for the lift-up.

James

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Steve Dufourny wrote on Aug. 13, 2012 @ 16:05 GMT
Hi Lawrence,

here are some ideas ...

Hello thinkers,

Very interesting these extrapolations. But I am insisting about the finite groups. Furthere more a photon in my line of reasoning possesses the serie of uniqueness.So a serie begining from the main central sphere.After the serie is a fractalization with specific spherical volumes. the serie is between 1 and x. So a photon is so complex in fact because its quantum number is very important.See also that this numbers the same than our cosmological number of spheres(without the quantum spheres of course).So it is very relevant about the broken symmetry indeed due to informations correlated with volumes and the rotations spinal and orbitals.The tori of stability take all their meaning. See that the system is a fusioned system.The desnity is relevant correlated with mass, and the polarity m/hv due to evolution. So the exchanges is probably a fusioned system and not a binar system in its pure generality.

See also that the informations are very relant when we consider the VOLUMES OF SPHERES !!!The informations can be bosonic or fermionic.Personnaly I beleive that the volumes of fermions are more stable due to the encoding of evolution.The bosonic encoding is more subtle due to its quantum number and its fractal cited above. The sortings and synchros appear with a universal proportionality.

Regards

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Author Lawrence B Crowell replied on Aug. 13, 2012 @ 22:11 GMT
Thanks guys for the response. I think the situation we face with quantum gravity may mirror something in the past. The solution might in part be under our noses.

LC

Steve Dufourny replied on Aug. 13, 2012 @ 23:00 GMT
You are welcome.

Regards

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Steve Dufourny replied on Aug. 16, 2012 @ 16:32 GMT
not guys !!!but Steve or Mr Dufourny.

It is a kind of respect above the strategies !

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Ted Erikson wrote on Aug. 13, 2012 @ 19:16 GMT
1st timer submission, not yet submitted, while reviewing selected works for possible End Notes.

Good history and very interesting paper but got lost in the heavy math, wish I was abreast of all covered…but love your ideas "G implying 1/mass and QFT as unit less coupling, have different times" (if I interpret correctly)

First I see E/f = h and Power = E/t. Dividing one gets, t/f, so IF t = 1/f it implies either t squared of 1/f squared. Square roots generate plus and minus, a past and future with no present?

Second, mass and energy, respectively, as the inscribed sphere, tangent to the face of a regular tetrahedron where sphere and tetrahedron have equal surface-to-volume ratios at ANY size, e.g. equivalent "activity" as free energy.

Comment? (may use in end notes)

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Author Lawrence B Crowell replied on Aug. 13, 2012 @ 22:09 GMT
The gravitational constant in naturalized units is "area," so it is sqrt{G} that is ~ length or reciprocal of mass.

Verlinde has a proposal that the work done by gravity W = ∫F•dr is equal to entropy S = nkT. There has been some controversy over this. However if we look at an increment of work done through some increment of time δt, I will not worry about the relativistic issues with this definition of time for now, then the increment of work is

δW = F•(dr/dt)δt = Pδt.

Power has in natural units reciprocal length squared L^{-2}, or ~ 1/G. Consequently, this increment in work can be written as δW = δt/G ~ n/G. We interpret G as the fundamental Planck unit of area, and n = # of Planck units of area generated by this work. This would then correspond (roughly) to the Bekenstein bound or entropy S = kA/4L_p^2. This is why I think his entropy force of gravity pertains to moving the holographic screen.

Cheers LC

Ted Erikson replied on Aug. 15, 2012 @ 17:12 GMT
Thank you. My approach is perhaps simply too naive, but suggests work for confirming Dr. Tykodi's approach and a preliminary definition of consciousness, aka panpsychism..

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Edwin Eugene Klingman wrote on Aug. 14, 2012 @ 00:29 GMT
Dear Lawrence Crowell,

You begin your essay with a well written summary of physics history, beginning with "the motion of particle executes little variations to find the proper path", then undergoing a "radical shift [from] variation of the least action in classical physics [to] the path integral in the quantum mechanics of fields." Like some others in this essay contest, I am more inclined to attempt to derive quantum theory from classical fields than vice versa, so I particularly liked your explanation that "constructing a propagator for a field on that very same field" leads to problems.

In analyzing the limits of space-time, you point out that we are limited by the fact that beyond a certain point, our probe creates black holes that hide the information from us. [That's one reason I treat non-relativistic quantum mechanics and weak field gravity, where we know, at least potentially, whereof we speak.] Thus you point out, "space-time itself is a barrier to the complete specification of an observable." You then say "information conservation demands...". If you'd care to comment on the grounds on which you base a belief in "information conservation" I would be interested. I know it is often assumed nowadays, but I'm not sure on what it is based. I assume you do not begin with quantum error correcting code to achieve this.

While I don't buy either quantum gravity or supergravity, nevertheless your observations about "the breakdown in the ability to measure everything about the universe" are quite interesting, as is your conjecture that this implies time, unitarity, locality, and causality to be emergent. You seem to agree with Philip Gibbs, so I suspect these are the waters the "math beyond physics" school swim in today. In my previous essays and in my dissertation, "The Automatic Theory of Physics", I presented logic and mathematics as emergent, so I tend to question any ultimate conclusions based on math that go beyond physical barriers to observation. Frank de Meglia may have as much claim to this territory as anyone.

Nevertheless, having chosen to play the game of 'math beyond physics', you do a bangup job of it, ending up with one electron, one quark, one photon in a universe based on underlying quantum error correction codes.

Best of luck in the contest,

Edwin Eugene Klingman

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Author Lawrence B Crowell replied on Aug. 14, 2012 @ 13:54 GMT
It is not difficult to quantize weak gravity. This is usually written as a bimetric theory g_{ab} = η_{ab} + h_{ab}, where η_{ab} is a flat spacetime (Minkowski) metric and h_{ab} is a perturbation on to of flat spacetime. We may write a theory of the sort g_{ab} = (e^{ω})_a^c η_{cb}, where the bimetric theory is to O(ω) in a series expansion

g_{ab} =~ (δ_a^c + ω_a^c) η_{cb}.

Gravitons enter in if you write the perturbing metric term as h_{ab} = φ_aφ_b, or ω_a^c = φ_aφ^c. The Ricci curvature in this weak field approximation is

R_{ab} - (1/2)Tg_{ab} = □h^t_{ab},

with h^t_{ab} the traceless part of the metric, and □ the d’Alembertian operator. Which in a sourceless region this computes plane waves. The two polarization directions of the graviton may then be interpreted as a form of diphoton, or two photons in an entanglement or a “bunching” as in Hanbury Brown-Twiss quantum optical physics.

If we now think of extending this to a strong field limit there are the square of connection terms Γ^a_{bc} in the Ricci curvature, or cryptically written as R ~ ∂Γ + ΓΓ where there is the appearance of the nonlinear quadratic term in the connection. This nonlinear term indicates the group structure is nonabelian, so the photon interpretation breaks down. The graviton in this case is a form of di-gluon, or gluons in a state entanglement or chain that has no net QCD color charge. This connects with the AdS_n ~ CFT_{n-1} correspondence, where for n = 4 the conformal field theory is quark-gluon QCD physics. Further D-branes have QCD correspondences and this takes one into the general theory I lay out. One does need to look at the references to learn more of the specifics. The quantum phase transition to entanglement states is given in the paper I write in ref 11 L. B. Crowell

The simple fact is that as physics develops it will invoke new mathematics. I don’t think I am overly mathematical in this essay, and I leave most of those details in the references. A theoretical physicist I think is wise to have a decent toolbox of mathematical knowledge and thinking. Physics invokes ideas of symmetries, remember Noether: symmetry corresponds to conservation law, and invariant quantities can also have connections with topology and number theory. I think the more one is familiar with advanced mathematics the more capable one is of thinking deeply about these matters.

It is true that my work is commensurate with P. Gibbs’. If field theoretic locality and spacetime are emergent structures then so is causality. This emergence is connected with a quantum phase transition, or a quantum critical point (tricritical point of Landau), and something occurring on a scale much larger than the string length.

Cheers LC

Edwin Eugene Klingman replied on Aug. 14, 2012 @ 17:11 GMT
"Physics invokes ideas of symmetries, remember Noether: symmetry corresponds to conservation law, and invariant quantities can also have connections with topology and number theory."

"Invokes" is an excellent choice of word. My impression is that many physicists today would go farther and claim that symmetry is the basis from which the universe 'emerges' -- a very questionable assumption.

I also agree that "the more one is familiar with advanced mathematics the more capable one is of thinking deeply about these matters." But that doesn't address the issue that "mathematics hangs on logic." And to assume that when space and time are abolished (coming "close to what we might call nothingness") somehow logic and math still exist, is to assume a lot. I believe it is a wrong assumption.

Edwin Eugene Klingman

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Author Lawrence B Crowell replied on Aug. 14, 2012 @ 19:00 GMT
Large symmetries are clearly important. The more general a symmetry group is, say with a larger Lie group, the transformations of that group can maintain a more general vacuum as a vacuum. In other words, symmetry preserves the ground state (vacuum), and broken symmetry does not, or maintains a more restricted ground state. There may of course be other elements to the foundations of physics than simply using ever larger Lie groups, such as removing certain postulates like locality of field data.

A lot of this about mathematics and logic relies upon the philosophy of mathematics, which I have read about and find somewhat interesting. However, I am not that steeped in the subject, nor does it concern me that deeply. Some mathematical subjects have no reference to geometry, such as most of number theory. Of course we humans have to exist with all our causal structure in spacetime to study it. However, a mathematical realist would say that number theoretic proofs are true whether we know them or not.

Cheers LC

Christian Corda wrote on Aug. 14, 2012 @ 09:37 GMT
Fantastic Essay LC, I hope to send my entry within this week.

Cheers,

Ch.

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Author Lawrence B Crowell replied on Aug. 14, 2012 @ 13:51 GMT
Thanks for the thumbs up. I seem to be falling downwards in the community rankings, though my paper has only been up about 36 hours. I am not sure what is going on there, for I know the physics I present is better than a whole lot of the papers ranking higher.

Cheers LC

Steve Dufourny replied on Aug. 14, 2012 @ 14:50 GMT
hello to both of you ,

Mr Corda,

Happy to see you again.

Regards

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Eckard Blumschein wrote on Aug. 14, 2012 @ 22:04 GMT
Dear Lawrence Crowell,

While you now correctly spelled annus, I see you wrong again: "The introduction of the Monad, as Leibniz conceived it, is a direct result of his disagreement with Descartes and Spinoza." (http://www2.sunysuffolk.edu/schievp/file22m.html)

You wrote on p. 3: "This would not quantum mechanics in any natural or realistic

way." I do not understand this sentence.

According to the title of your essay, unitarity is a foundation that is not a foundation. I wonder why you did not anticipate readers like Yuri and me who do not feel forced to immediately understand such play with words just because you mentioned the nebulous word "emerging". Having searched for "unitarity" in the text of your essay, I did not get the due explanation but only two hits.

The abstract promised replacement of unitarity by modularity, a word that is not at all mentioned in the text.

We merely learn: unitarity "might be emerging". In "abandonment of locality and unity" you did perhaps also mean unitarity, not unity; because the next sentence speaks of the loss of unitarity.

I do not just criticize some imperfections but I am also ready to factually question it if you are willing to deal with my admittedly quite different view.

Sincerely,

Eckard

Eckard

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Author Lawrence B Crowell replied on Aug. 15, 2012 @ 00:17 GMT
My response is below. I didn't put it in a response.

LC

Author Lawrence B Crowell wrote on Aug. 15, 2012 @ 00:03 GMT
The matter over Leibniz is not in my essay. I appear to be wrong with respect to Spinoza in my blog post.

The sentence is missing the word be, which is unfortunate. it should read, "This would not be quantum mechanics in any natural or realistic

way."

I discuss modularity towards the end. I was planning on breaking this out further, and in fact did so more. However, I exceeded the word/page limits for the essay. So this got rather scant mention at the end.

The word unity is supposed to be unitarity.

The emergence of unitarity is complicated. The existence of singularities means that quantum wave functions are not analytic functions. They are meremorphic, which define modular function or forms. I wrote a bit more on this in a post above on Aug. 13, 2012 @ 14:44 GMT. This is a deep subject, which gets into Borel groups, Leech lattices and so forth. The length restriction on this essay prevents me from breaking this out. Besides most of this that I have worked out is on notebook paper and not published. Yet analytic functions or unitarity occurs in the special case the singularity is removed or has minimal nonlocal connection to a region outside the event horizon in the case of a black hole. This occurs for large black holes.

I am not sure what the main objection is you want to raise. I am not likely to respond much if your objection is about the foundations of mathematics or set theory.

Cheers LC

Anonymous replied on Aug. 17, 2012 @ 02:27 GMT
Lawrence,

Meromorphic (not meremorphic) means analytic with exception of singularities. For instance Joy Christian made the singularity of Riemannian sphere at infinity an issue in physics. Used to write C U {infty}, mathematicians are treating only the "north-pole" of it as a singular point while they do not take care for the "south-pole", i.e., for the zero. For EEs like me it is common practice to operate with poles and zeros almost as naturally as with north and south.

If we assume that the singularity alias actual infinity is just a mathematical fiction, then this might also hold for zero and the ideal (Peirce) continuity; and those who ascribe physical correlates to singularities are simply victims of their inability to realize that even the most advances mathematical tools are just tools that must not be misused in an intuitive pre-mathematical manner. Weren't you unable to refute Ernst Fischer's essay?

Eckard

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Author Lawrence B Crowell replied on Aug. 17, 2012 @ 02:57 GMT
Fischer’s essay is a case of how one gets out of something what one puts in. He uses equation of state for static matter to show that there is no singularity. This is of course to be expected. The matter is composed of particles on nongeodesic paths in spacetime, which if these are meant to modelgeodesic flow corresponds to a violation of the equivalence principle. Otherwise this is just a model of a star or some bulk material object which has no singularity by construction. I am a bit amused that his essay is in the top slot.

Check out Gibbs’ blog entries, he spells very colorfully. I wont misspell meramorphic again, or is it merumorphic or … :)

Cheers LC

Eckard Blumschein replied on Aug. 17, 2012 @ 21:08 GMT
Lawrence,

Concerning singularity, I decided to add new arguments here.

Anyway, I appreciate your insight that pre-mathematical assumptions are decisive.

Eckard

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Author Lawrence B Crowell wrote on Aug. 15, 2012 @ 23:19 GMT
I think that unitarity is a special case of modular transformations when there is no singularity, or if in the case of a black hole the singularity is hidden by a very classical event horizon that causes decoherence of nonlocal fields across it. If the event horizon is quantized, say with a very small black hole, then this breaks down. Further, the meaning of spacetime and light cones becomes lost. They are so to speak blurred out by quantum fluctuations.

If the definition of spacetime breaks down on a very small scale then the definition of time is lost. If there is no effective definition of time there is then no unitary time development of quantum states or observable by an operator, such as the Hamiltonian. This is a loss of unitarity.

The Wheeler-DeWitt equation tells us this to begin with. The Hamiltonian in classical gravity is zero, or NH = 0, for N the lapse function. This is a standard result of ADM general relativity. The reason for this is Gauss’ law, where there is no boundary sphere around the universe by which one can integrate out the mass-energy contained within. This argument can be posed according to the nature of coordinate time in general relativity, where this is a frame dependent quantity and physics should not depend upon it. So the Schrodinger equation

i∂ψ/∂t = Hψ = 0

is seen to be zero on both the left and right hand side in a consistent manner. This is the Wheeler-DeWitt equation Hψ = 0, which is the quantum form of the Hamiltonian constrant NH = 0. There is in this case no Hamltonian which acts as a Hermitian operator that define a unitary time development operator. Unitarity is gone.

What takes the place of unitary transformations are modular transformations, in particular the Eisestein series and Jocobi functions. The Jacobi functions are realizations of the E_8 and Leech lattice Λ_{24} based sporadic groups --- in particular the Mathieu group of quantum error correction.

In that case my essay does propose the removal of or change in established physical postulates.

I am less concerned with mathematical foundations. The connection to matters such as Zermelo-Fraenkel (ZF) set theory is at best very subtle, and really could be nonexistent. ZF set theory has some strange features, such as the duplication of spheres with the Axiom of Choice. There are alternatives such as Polish sets. This goes double for philosophical issues over how or whether mathematics exists independent of physical reality or the mind of a mathematician. These questions simply go far beyond the scope of what I am concerned with.

Cheers LC

Steve Dufourny replied on Aug. 16, 2012 @ 16:30 GMT
You think really that you can make what you want with my spheres and spherization Theory or What ??? :)

well a duplication of spheres with an axiom of choice , it is interesting.

and a toe also no? second :)

third :) soon at New York my friends and we shall discuss about my spheres in live.

They turn so they are...

ps eureka form belgium, the real toe.The real gut, the real spherization ! with humility of course.

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Author Lawrence B Crowell replied on Aug. 16, 2012 @ 16:51 GMT
The duplication of a sphere is called the Banach-Tarski paradox. This is the result of "immeasurable measures" that can occur with the axiom of choice.

Cheers LC

Steve Dufourny replied on Aug. 17, 2012 @ 21:46 GMT
I am going to catalyze you in live.

:) you know that I am not a fan of paradoxs.

The meiosis of a sphere, interesting.or a mitosis.interesting :)

immeasurable measures ??? Not really rational that.

You know Lawrence, I find your knowledges very relevant, but you know the aim is not to enumerate the concepts but to apply them with a pure rational and dterministic road. In fact , when there are too much pseudo convergences, so it implies an ocean of confusions.Implying an impossibility to have a true general theory.

In fact you know indeed your physics and maths.But is it sufficient for the generality. I am surprised to see how you interpret the boundaries ? You know Lawrence ,forget your chains ....and open your universal heart.

The mind of a mathematicians is the same than for physics. They must be always rational and dterminsitic.

ps you can make better :)

ps2 the unitarity, the singularity,it is these central spheres, Lawrence.

ps3 I have an idea for the serie,the fractal from the main cnetral sphere, in logic the serie is universal at all scales for the uniqueness. I ask me if the primes can help, I beleive that yes for the periodic oscillation.between 1 and x. The number of planets become relevant for our universal sphere.and we take the number 1 for the central sphere. The volumes are under this logic. The primes can help for the correct serie. It is essential to have finite groups and boundaries you know Lawrence for our quantization and our axiomatizations.If not the thermodynamics are not ok.like the proportions of our universal mecanic.

It is evident you know.

Regards and good luck, your essay is very well.

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Joe Fisher wrote on Aug. 16, 2012 @ 14:32 GMT
Dear Doctor Crowell,

Because I am an uneducated non-physicist, I was unable to fully understand many of the exquisite rational arguments you touched upon in your exceptional brilliantly written essay. I was immensely gratified by your posted contention that “One of the things I think comes from this is the universe contains only one of each particle” seems to agree with my understanding of the singular universe as posited in my essay Sequence Consequence. Could technological advancement be confusing all of us as to the true nature of the universe? Natural sunlight barely penetrates 10 fathoms into the ocean. Yet fabricated electrical flashlights are used thousands of fathoms deep. I do not understand how fabricated electrical light can overcome density while much more powerful sunlight cannot.

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Anonymous replied on Aug. 16, 2012 @ 16:57 GMT
Light is attenuated in water by particles that absorb or scatter light. The extinction of light over a distance is the same for sunlight striking the water surface and for photons leaving a flashlight underwater.

I'll take a look at your essay. Good luck.

Cheers LC

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Georgina Parry wrote on Aug. 17, 2012 @ 09:07 GMT
Hi Lawrence,

I get the feeling I understood more of this essay than last years. So it is, I think, more accessible. (I made two separate attempts.) The history was interesting. I understood a chunk of problems you pointed and the reasons for then considering each in turn, though not the mathematical explanations themselves. My own failing I know. It is probably straightforward to those with the necessary familiarity with mathematics.

As I rarely understand much of what you write I think we have both done rather well with this essay. I wish I was able to give more positive feedback. I hope you get lots of informed readers who will be able to properly understand and talk to you about the essays content, which is probably far more fascinating than I can appreciate. Good luck in the competition.

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Author Lawrence B Crowell replied on Aug. 17, 2012 @ 17:01 GMT
There is a growing understanding of a correspondence between quantum chromodynamics (QCD) and gravitation. The AdS/CFT correlation is one of them. More recently developments such as the BCFW recursion relationship indicate that calculation techniques for QCD and quantum gravity are related to each other. Gravitons are I think entanglements of gluons, or what we might call gluon chains. Certain complex self interacting states of gluons can form effective mass states. Remember that gravity interacts with mass-energy, so gluons can be self-interacting --- similar to gluons. In classical gravity there are some solution types that are intermediate to the near field solution, a black hole, and the far field solution as gravity waves. A black hole can be thought of as a condensate of particles or gravitons in a state that is completely self-confined.

Quark-gluon plasmas produced by RHIC and the lead heavy ion collisions at the LHC can produce very transient states corresponding to black holes, or with tiny quantum amplitudes corresponding to black holes. These amplitudes are not large enough to generate a full bonifide black hole, as seen in previous fears of the LHC producing an Earth devouring black hole, but they should be sufficient to test these theories.

holographic graviton

Cheers LC

Avtar Singh wrote on Aug. 17, 2012 @ 16:29 GMT
Hi Lawrence:

The fundamental question is how to determine what is the most fundamental reality or physical process that governs the Foundation of the universe. I demonstrate in my posted paper -“ From Absurd to Elegant Universe” that current crisis in physics and cosmology as evidenced by the well-known paradoxes and singularities are artifacts of the missing Foundation of the fundamental physics of the spontaneous decay and birth of particles. Hence, many of the so-called foundational assumptions or phenomena are shown to be artifacts rather than foundation of the universe or a universal theory. When this missing foundational physics is counted in, it not only successfully predicts the observed accelerated expansion of the universe and galactic star velocities but also resolves paradoxes and singularities of the Cosmic Conundrum today. It also provides understanding of the inner working foundations of quantum mechanics.

Best Regards

Avtar Singh

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Author Lawrence B Crowell replied on Aug. 17, 2012 @ 17:58 GMT
Hi Avtar,

I loaded up your paper, which time permitting I will try to read today. Singularities in one sense do reflect a failure of an existing theoretical structure. In a more general theory they becomes something else, or are removed.

There is a growing understanding of a correspondence between quantum chromodynamics (QCD) and gravitation. The AdS/CFT correlation is one of them. More recently developments such as the BCFW recursion relationship indicate that calculation techniques for QCD and quantum gravity are related to each other. Gravitons are I think entanglements of gluons, or what we might call gluon chains. Certain complex self interacting states of gluons can form effective mass states. Remember that gravity interacts with mass-energy, so gluons can be self-interacting --- similar to gluons. In classical gravity there are some solution types that are intermediate to the near field solution, a black hole, and the far field solution as gravity waves. A black hole can be thought of as a condensate of particles or gravitons in a state that is completely self-confined.

Quark-gluon plasmas produced by RHIC and the lead heavy ion collisions at the LHC can produce very transient states corresponding to black holes, or with tiny quantum amplitudes corresponding to black holes. These amplitudes are not large enough to generate a full bonifide black hole, as seen in previous fears of the LHC producing an Earth devouring black hole, but they should be sufficient to test these theories.

holographic graviton

Cheers LC

Author Lawrence B Crowell replied on Aug. 19, 2012 @ 18:05 GMT
Your essay proposes a way in which special relativity can be extended to global spacetime. Your results are departures from standard cosmology. I suppose I am not sure how the cosmological constant depends upon the velocity of a particle. The potential you compute in equation 5 PE = ∫Gmm*dr/r, where I presume there should be a dr in there, appears to be similar to the calculation of a moment of inertia. The redshift factor z diverges as v --- > c in a special relativistic type of theory, but this runs into trouble with luminosities.

Cheers LC

Avtar Singh replied on Aug. 20, 2012 @ 15:39 GMT
Hi Lawrence:

Yes, the results of my paper and book – The Hidden Factor show departure from the paradoxical and inconsistent results of the Standard Cosmology. My paper shows that when the missing physics of spontaneous decay are taken into account, it cures many ills of the standard cosmology and successfully predicts the observed expansion of galaxies and the universe.

You asked – “…… how the cosmological constant depends upon the velocity of a particle?” The cosmological constant represents the kinetic energy (velocity) of the particles residing and moving close to the speed of light within the so-called vacuum space. This kinetic energy is the mechanistic description of the mysterious dark energy still un-described by the standard model.

In response to your comment –“The potential you compute in equation 5 PE = ∫Gmm*dr/r, where I presume there should be a dr in there, appears to be similar to the calculation of a moment of inertia”, a complete derivation of the gravitational potential is provided in the attached pdf file.

Also, responding to your comment- “The redshift factor z diverges as v --- > c in a special relativistic type of theory, but this runs into trouble with luminosities”, in the GNMUE model describe in my paper and as shown in figure 3, V is never larger than C; hence the luminosity equation has no singularities or infinities.

Best Regards

Avtar Singh

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Jayakar Johnson Joseph wrote on Aug. 18, 2012 @ 05:45 GMT
Dear Lawrence B Crowell,

I think, without quantum physics we cannot describe the events of universe coherently, in that unitarily is imperative for its completeness. Thus the unitarily of the universe and the locality of its events are expected to have their outcomes as nonzero, in that the current scenario of dimensionality from point source is contradictory.

With best wishes,

Jayakar

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Author Lawrence B Crowell replied on Aug. 20, 2012 @ 18:29 GMT
I have to confess I am not having the easiest time figuring out what you have written here. Good luck on this. I will try reading again in the next couple of days.

Cheers LC

Author Frank Martin DiMeglio wrote on Aug. 19, 2012 @ 00:23 GMT
Hi Lawrence. Gravitational and inertial equivalency and balancing is fundamental to balanced and equivalent attraction and repulsion and to fundamentally stabilized and balanced distance in/of space as well. Importantly (and moreover), this fundamentally proves/demonstrates F=ma.

And, this is all consistent with instantaneity and the fact that gravity cannot be shielded. (Obviously, the fact that gravity cannot be shielded is connected with instantaneity.) Balance and completeness.

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Author Lawrence B Crowell replied on Aug. 20, 2012 @ 18:30 GMT
Thanks for the positive response.

Cheer LC

Author Lawrence B Crowell wrote on Aug. 23, 2012 @ 21:33 GMT
The Britto, Cachazo, Feng, Witten (BCFW) recursion relationship is a way in which a complex scattering process can be decomposed into tree level diagrams. The picture attached describes the process

A set of gluon momenta entering a region (we set those leaving as the negative of entering as done in the STU symmetries) may be written as the sum of products of two diagrams. To start one...

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attachments: BCFW_recursion_rule_2.GIF

Cristinel Stoica wrote on Aug. 29, 2012 @ 06:20 GMT
Dear Lawrence,

Congratulations for the essay. I like how you walked through the assumptions about space and time, showing how they changed in the history, and how you discussed the deformations of the foundations. I found the second part more difficult to me, so I had to reread it with more care. I really hope that unitarity and locality are not lost, but if they are, the implications you foresee are very interesting.

Good luck with the contest,

Cristi Stoica

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Author Lawrence B Crowell replied on Aug. 29, 2012 @ 17:48 GMT
I wrote the response in a fresh text box. So if you are getting those respose alerts by email you will be appraised.

LC

Steve Dufourny replied on Aug. 29, 2012 @ 19:47 GMT
pay attention the dream team ahahahah wait wawwwww impressing your maths ahahah.

they have the latex in their head ahahah Chriti, Florin, Georgina,Jonathan, Joy, Ray, Lawrence, Edwin,Mickael,Don,James, JCN,goodband they say hahahah wawww imrpessing the strategy in some years, wawwww ahahah make surf band of comics ! I have seen your real heart . Dark and vanitious and without consciouness.Ahahah pay attebntion, I don't see their play, pay attention, they superimpose the algorythms, waww they are so intelligent.

And what after ahahaha band of comics.

I will fight with honor, faith, universality, universal love !!!

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Steve Dufourny replied on Aug. 29, 2012 @ 19:58 GMT
ahaha and Joe and Frank and alan and ted an,d friends who insists ahaha poor thinkers

Occupied with startegies instead of studying from real innovators.ahaha ironical no,

And what after? that is all you can make ???

You can make better perhaps become there it was easy to find the players and easy to play also. But it is just a suggestion of course.ahahah ironical.

Jonathan and lawrence,them make surf in california, Don, Florin and Jonathan,them are at New York, Edwin and Eckard them speak about consciousness wit James and Brendan and Johan them travel of course.And who pay for these things, still the people of course like always.Georgina prefers the prime quaternionic bridge and of course joy implies the connection. and what after , a course of maths.

You are ironical !

Vanity of vanities , all is vanity !

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Author Lawrence B Crowell wrote on Aug. 29, 2012 @ 17:47 GMT
If locality and unitarity are not fundamental it means there is a huge reduction in the number of fundamental degrees of freedom in the universe. In fact if you read my paper referenced in my essay you see that the number of degrees of freedom on a brane are boost dependent, and are thus not fundamental. The huge number of elementary particles we observe in the universe are just the same type...

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Cristinel Stoica replied on Aug. 30, 2012 @ 04:23 GMT
"If locality and unitarity are not fundamental it means there is a huge reduction in the number of fundamental degrees of freedom in the universe."

I see now what you mean, and I think you're right. These symmetries sound like a kind of "gauge freedom".

Best regards,

Cristi

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Eckard Blumschein replied on Aug. 30, 2012 @ 05:31 GMT
With his judgment TOTLSHT LC will perhaps win less sympathies than for instance Christi who even declared non-constant numbers "great work". This comment of mine is not meant to appreciate non-factual kindness.

How many degrees of freedom has an empty sheet of paper? Call me an anus, I think LC is not even wrong if he demands a huge number of fundamental degrees of freedom in the universe. I see his gauge freedom in company with Einstein's naive observer-bound perspective.

If my own essay did not just face more attention but at least one tangible critical comment, those who might tacitly agree with my admittedly unwelcome arguments will certainly be happy.

Eckard

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Author Lawrence B Crowell wrote on Aug. 30, 2012 @ 19:21 GMT
Chris,

There is more to this, which I could not break out due to length limitations. The gauge symmetries are Yangians, or enveloping algebras. These have a duality, where the gauge symmetry in one representation is dual to another without spacetime configuration variables.

Eckard,

I argue for a massive reduction in the number of degrees of freedom. In fact if the universe has quantum states given by E_8xE_8, it means the universe has only 496 fundamental degrees of freedom, or in its supersymmetric extension 512 = 2^8.. In the Leech lattice Λ_{24}there are 4096 weights, due to the theta function representation over 3 E_8 groups, and Λ_{24} is the automorphism of the Conway group Co_1 with rank 8,315,553,613,086,720,000. The full automorphism over the Fischer-Griess group is of rank 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,
000,000,000, which is huge. Yet in this total extended picture the number of real degrees of freedom is only 4096.

The actual number of elementary particles is then very small, but they have multiple representations in configuration variables. The configuration variables are a system of entanglements, or holographic projections, which give the appearance of a large number of particles.

I don’t think the fundamental issues with physics lie with the foundations of mathematics. I might be wrong of course, but I really do not think mathematics has been on some fools errand for the last 150 years or more.

Cheers LC

Torsten Asselmeyer-Maluga wrote on Aug. 31, 2012 @ 10:09 GMT
Lawrence,

a really interesting and enlightning essay. In most cases, only "boring" agreement between us. The BCJ duality is very interesting. Before reading your essay I started to study this duality but now I understand its relevance.

At one point we maybe disagree: "...that spacetime is not a complete concept". We found a contrary point of view (see my essay) especially to express the "fuzzyness". Interestingly, modularity is also important there and locality is unimportant (by diffeomrophism invariance). In particular, the diffeomorphism group is not a Lie group (rather a pseudo-group) and the description of the local part (some substitute of a Lie algebra) used enveloped algebras in an essential way. You see "boring agreement" at wide parts.

Best

Torsten

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Author Lawrence B Crowell replied on Aug. 31, 2012 @ 18:24 GMT
I read your paper a week ago with the idea of reading it again with greater attention to detail and your references. I just reread your paper, but unfortunately not in great detail, so I have yet to dig into your paper at great length. I have to confess I have read a pretty small minority of the paper on this essay website.

I went through the Atiyah, Donaldson, Freedman work on exotic...

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Torsten Asselmeyer-Maluga replied on Sep. 3, 2012 @ 13:12 GMT
Dear Lawrence,

thanks for your answer. Yes it is not an easy problem to consider exotic 4-manifolds. Actually from the differential topological point of view, two non-diffeomorphic 4-manifolds are distinct. Therefore you have to sum over these possibilities in the path integral and for each class the measure remains the same. (see arXiv:1112.4882 and arXiv:1003.5506)

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Author Lawrence B Crowell replied on Sep. 3, 2012 @ 23:44 GMT
Dear Torsten,

Thanks for the reply. I will try to read your papers on this in the near future. I also need to review matters of the Atiyah-Singer index, Seiberg-Witten theory, Freedman- Uhlenbeck work on moduli at singular points and the rest. Back in the late 1990s I was better spun up with these matters.

The one thing which I think needs to be considered is that spacetime is...

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Member Giovanni Amelino-Camelia wrote on Sep. 1, 2012 @ 20:32 GMT
dear Lawrence

as you suggested in a post related to my essay, there are some connections between our essays, in spite of the differences of approach and goals

and now that I have studied your essay I can observer that there are closer connections between parts of your essay and some of my works, see e.g.

http://arxiv.org/abs/arXiv:1206.3805

http://arxiv.org/abs/arXiv:1107.1724

http://arxiv.org/abs/arXiv:1101.0931

best wishes for the competition

Giovanni

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Author Lawrence B Crowell replied on Sep. 2, 2012 @ 02:05 GMT
Dear Giovanni,

I just started reading Relative locality in a quantum spacetime and the pregeometry of _-Minkowski http://arxiv.org/pdf/1206.3805v1.pd. You seem to be pointing to a similar end. Noncommutative geometry and Hopf algebras are a main tool in the work with Yangians. I will write more when I complete reading your paper.

Equation 1 is interesting, for it proposes a...

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Rick Lockyer wrote on Sep. 2, 2012 @ 17:29 GMT
Lawrence,

Do you really think the variation of parameters method implies a *particle* “tries” all neighboring paths and “chooses” the one that minimizes variation of the Lagrangian?

I have always believed the mathematician or physicist does the varying as a purely mathematical process to find the *actual* path the particle takes because it has no choice in the matter, nor capacity to make any decision between choices.

This position you appear to be taking seems like a canard to justify or legitimize non-deterministic concepts.

On my essay blog you asked about the fundamental nature of Octonion Algebra, and asked me to look at your essay and particularly the response threads. My essay clearly provides the fundamental connection between Octonions and physical reality, but perhaps not in the way you were looking for. In my response to you I mentioned those of a mind (you particularly) that believe it is important to unify QM with GR might be better off trying to unify QM with Octonion Relativity, especially if there is a link between QM and Octonion Algebra. Your essay responders might find illumination on the fundamental connection between Octonion Algebra and physical reality, and what I mean by “Octonion Relativity” by reading my essay The Algebra of Everything.

Rick

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Rick Lockyer replied on Sep. 2, 2012 @ 18:34 GMT
Sorry, had a space char in link. Try The Algebra of Everything.

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Author Lawrence B Crowell replied on Sep. 2, 2012 @ 21:09 GMT
I have given you essay a read through, which means I have not yet read it a second time for greater detail and content.

The quantum path integral is a measure over the distribution of a quantum field or particle. It assigns amplitudes to each path, which in the large N limit converges to the classical variational method.

The connection between quantum mechanics and octonions is not completely clear. The associator (ab)c - a(bc) that is not zero is not as well founded according to operators as noncommutative structures are. Further, the physical meaning is not as clear. I think octonions are really a system of quaternions (7 of them) which are related to each other by a general duality principle. This duality principle may then be expressed by the associator.

Cheers LC

Jonathan J. Dickau wrote on Sep. 5, 2012 @ 04:46 GMT
Hi Lawrence,

I read through your essay, but have not returned to it yet - to read for detail. But I've noted some of your comments, and wanted to add one or two of my own. First off; I saw your EJTP paper on "Counting States in Spacetime" which you posted on Rick Lockyer's essay site, and I note several points of overlap with the following paper by Frank Potter.

Our Mathematical Universe: I

Second; as I understand it octonions can indeed be represented as a system of 7 quaternions, but then the quaternion variables must be resolved in a definite order or sequence, or handled in a consistent way, as the effect of each term is cumulative (as with procedural steps or process stages). I think Rick uses the term ensemble multiplication.

But this is not quite the same as saying that the 'octonions are really a system of quaternions.' Maybe O is more fundamental than H, as Rick asserts. But perhaps saying octonions can be treated as an ordered or nested system of quaternions would work, though.

Regards,

Jonathan

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Author Lawrence B Crowell replied on Sep. 5, 2012 @ 16:02 GMT
Hi Jonathan,

Thanks for the paper. In looking at it I see many things which are in my notes and which I have in other papers and the book “Sphere Packing, Lattices and Codes” by Conway and Sloane.

The graininess of spacetime is something which I think only comes about with the measurement of black hole states. As I indicated on Giovanni Amelino-Camelia’s essay blog site...

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Rick Lockyer replied on Sep. 5, 2012 @ 20:57 GMT
Lawrence,

Sorry you were offended by my calling you out for posting on my essay blog without the common courtesy of having read the essay first. I only meant to inform you that you might possibly find some perspective on your question about how Octonion Algebra relates to physical reality since it was the thesis of my essay. Thanks for reading it later. I am curious about your characterization that it is just a gauge theory using associators. The Lorentz gauge mention was simply to demonstrate a point of commonality between 4D and Octonion presentations of Electrodynamics, that’s it. Hardly a cornerstone of the presentation. I never once mentioned the associator, and frankly have never used non-associative brackets in any mathematical description. Octonion Algebra does indeed present a non-zero associator because it is a non-associative algebra. It MUST be so in order to be a normed composition algebra, hence a division algebra. Without this non-associativity and the remainder of O structure, it would be impossible for the algebraic invariances to match up the math to what we can measure or detect, and algebraic variances to give us clues on the math for what is hidden from us but none the less in play.

Rick

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Jonathan J. Dickau replied on Sep. 6, 2012 @ 03:49 GMT
Thanks Lawrence,

That nicely spells out where you are coming from. Glad you enjoyed the Potter paper, also. I've not looked at Giovanni's essay yet, but a quick read through of Torsten's paper has made it a 'must read' for the insights he shares. I am certainly not put off by your comments or Rick's and have found a lot of fascinating insights on the forum - even in the points of dispute.

I am glad the back and forth has kept everybody thinking. More fun lies ahead!

all the best,

Jonathan

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Author Lawrence B Crowell wrote on Sep. 8, 2012 @ 02:00 GMT
In indicated to Giovanni Amelino-Camelia there should be some connection between the theory κ-Minkowski spacetimes and the boost system he advances with twistor theory. The connection to twistor theory is I think not hard to see. The boost operator P_μ that acts on [x_i, x_0] = ilx_i such that

P_μ > [x_i, x_0] = il P_μ > x_i

The coordinates (x_j, x_0) we write in spinor form

x_j = σ_j^{aa’}ω_{aa’}

x_0 = σ_0^{aa’}ω_{aa’},

where ω_{aa’} = ξ_a ω_{a’} + ξ_{a’}ω_a. This commutator has the form

[x_i, x_0] = σ_j^{aa’}σ_0^{bb’}[ω_{aa’}, ω_{bb’}]

= iC^{cc’}_{aa’bb’} σ_j^{aa’} σ_0^{bb’} ω_{aa’}

= i|C| σ_j^{aa’}ω_{aa’}

where the magnitude of the structure matrix is |C| = l. In general this may be written for

x_j = σ_j^{aa’}ω_{aa’}

x_0 = σ_0^{aa’}ω_{aa’} + iq_{aa’}π^{aa’},

where the commutator [ω_{aa’}, π^{bb’}] = iδ_a^bδ_{a’}^{b’} and the general form of the commutator is then

[x_i, x_0] = i|C| σ_j^{aa’}ω_{aa’} + iσ_j^{aa’}q_{bb’}[ω_{aa’}, π^{bb’’}

[x_i, x_0] = ilσ_j^{aa’}ω_{aa’} - σ_j^{aa’}q_{aa’}.

The boost operation B = 1 + a^l_jP^j on the commutator [x_i, x_0] is then equivalent to the commutation between spinors [ω_a, ω’_b] for ω’_b = ω_b + iq_{bb’}π^{b’},

[ω_a, ω’_b] = [ω_a, ω_b] + iq_{bb’}[ω_a , π^{b’}]

= C^c_{ab} ω_c + iq_{ab}.

This could be explored more deeply. Ed Witten demonstrated the "twistor revolution" in string theory. If twistors are connected to κ-Minkowski spacetime there might then be a link between string theory and LQG and other "edgelink" type of quantum gravity theories. This would be potentially interesting, for this might serve to correct the difficulties with each of these.

Cheers LC

Pentcho Valev wrote on Sep. 10, 2012 @ 19:15 GMT
Lawrence,

You wrote: "Einstein changed Newton's laws by adjusting the first and third laws, motivated by the locality of electromagnetic fields predicted by Maxwell's equations."

Einstein did not adjust anything - he just introduced two postulates the second of which was false. In 1887 the Michelson-Morley experiment had refuted the light postulate and had confirmed the variable...

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Author Lawrence B Crowell wrote on Sep. 10, 2012 @ 21:39 GMT
I am not sure why you decided to make your life’s work to discredit relativity. You keep posting the same thing over and over, with the same references.

The invariance of the interval, equivalently the constancy of the speed of light, means in addition to the three rotations of space there are three Lorentz boosts. The physics of this has been tested literally thousands of times in many different ways. The empirical support for relativity is simply overwhelming. You are not going to find many people here who are well grounded in physics who agree with you.

Cheers LC

Pentcho Valev replied on Sep. 11, 2012 @ 09:55 GMT
Lawrence,

Roger Schlafly wrote in his site:

"Pentcho, you are right that the emission theory was the only known explanation [of the null result of the Michelson-Morley experiment] in 1887..."

Is Roger right? Also, Lawrence, you used to claim that John Norton is wrong when he says that:

http://philsci-archive.pitt.edu/1743/2/Norton.pdf

John Norton: "The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

Do you still believe Norton is wrong, Lawrence?

Pentcho Valev

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Author Lawrence B Crowell wrote on Sep. 11, 2012 @ 12:44 GMT
I have not yet read Schlafly’s essay or read the posts on his blog. I am not particularly interested in revisiting old stuff like this. Whether one can interpret the M-M experiment in different ways is of little interest to me. Lorentz interpreted the result as due to a length contraction that nullified the effect of the putative aether. Einstein was apparently not aware of the M-M experiment at all. Which ever is the case with interpreting the M-M experiment it is not relevant. Special relativity has been tested by many dozens of other types of experiments repeated many thousands of times. I am not sure why anybody would want to take up the cause of trying to overturn relativity this way. There were people up to the early 19th century who wanted to overturn Newton as well.

Cheers LC

Pentcho Valev replied on Sep. 11, 2012 @ 15:10 GMT
The fact is that, in 1887, Newton's emission theory stating that the speed of light varies in accordance with the equation c'=c+v (v is the speed of the light source relative to the observer) was the ONLY existing theory capable of explaining the null result of the Michelson-Morley experiment.

You find this fact unimportant and accordingly occupy the top of the community rating list. I find this fact extremely important and am at the bottom. Simple isn't it?

Pentcho Valev

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Author Lawrence B Crowell replied on Sep. 11, 2012 @ 16:01 GMT
As for the rankings, there are two possible reasons for this. The first is that relativity is all wrong and has been propped up for over a century by an international scientific conspiracy. Those involved with the conspiracy or who believe its falsehood are wrongly voting your paper down. The other possibility is that you are simply wrong in your thesis that relativity is wrong based on an interpretation of an experiment performed over 130 years ago. You are not alone in such conspiracy claims. Some people who advance local hidden variables cry how the physics world has gone astray, and more recently a certain politically motivated "alt-science" community claims there is a big conspiracy to demolish the economy with global warming concerns by climatologists.

I tend to avoid these things, along with claims the 9/11 attack was an inside job, grassy knolls with Kennedy's assassination, Princess Diana's death was an inside job, and so forth. It is not possible to absolutely prove these things false, but seriously entertaining them is probably about as productive as masturbation is with impregnating your wife.

Cheers LC

Pentcho Valev replied on Sep. 11, 2012 @ 17:18 GMT
That "relativity is all wrong" is a fact often hinted at by high-ranking Einsteinians:

http://www.perimeterinstitute.ca/pdf/files/9755
47d7-2d00-433a-b7e3-4a09145525ca.pdf

Albert Einstein (1954): "I consider it entirely possible that physics cannot be based upon the field concept, that is on continuous structures. Then nothing will remain of my whole castle in the air, including...

view entire post

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Yuri Danoyan wrote on Sep. 12, 2012 @ 02:40 GMT
Lawrence

Arnold was great mathematician,not metaphysics

but is favor observation was trinity

http://www.neverendingbooks.org/index.php/arnolds-tri
nities-version-20.html

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Member Benjamin F. Dribus wrote on Sep. 18, 2012 @ 06:07 GMT
Dear Lawrence,

I found your essay very intriguing and absolutely packed with interesting information, which will require some more thought to digest. One question: near the end of the paper you are discussing path integration involving paths in "what becomes the emergent spacetime." Now, of course in some theories that make use of path sums, the paths are in a configuration space of "universes" (geometries, triangulations, or whatever), rather than in a single lower-level structure. I am wondering if there are two different quantum notions occurring here, one involving the "spacetime" itself, and one involving paths in the spacetime? Take care,

Ben Dribus

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Author Lawrence B Crowell replied on Sep. 18, 2012 @ 17:59 GMT
Ben,

I have not gotten yet to reading your essay. There are lots of these here and it is not possible to read more than one or two in a day. I have it in mind to read yours, as it has been lofted for the most part towards the top of the ratings.

What you are asking is related to a discussion I had with Torsten Asselmeyer-Maluga . He argues that spacetime is completely continuous....

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Yuri Danoyan wrote on Sep. 18, 2012 @ 14:37 GMT

Discreteness and Determinism in Superstrings ?

arXiv:1207.3612 (replaced) [pdf, ps, other]

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Author Lawrence B Crowell replied on Sep. 18, 2012 @ 23:58 GMT
It looks interesting. It might take me a day or two to read it.

Cheers LC

Hoang cao Hai wrote on Sep. 19, 2012 @ 14:41 GMT
Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

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?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regard !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Author Lawrence B Crowell replied on Sep. 19, 2012 @ 19:37 GMT
Hi,

I am a bit uncertain about what you are saying here. Mass and weight are different things. Weight is just mass under the acceleration of gravity F = ma, where the acceleration a is just the local gravity on a planet, such as on earth a = g = 9.8m/s^2.

The Higgs field is a pair of doublets, with four components in total, where three of them couple to the Z^0 and W^{+/-} particles and the remainder is the Higgs particle recently detected. At very high energy these four components are free, where the three absorbed into the Z^0 and W^{+/-} particles are also free particles. At lower energy these are absorbed. This is the Goldstone mechanism.

Good luck in the essay contest,

LC

Hoang cao Hai replied on Oct. 2, 2012 @ 04:01 GMT
Thank you Lawrence B Crowell

Based on my research: the separation of the concept of "weight" and "mass" is a mistake stems from the failure to identify specific "gravity".

But perhaps we should not be further discussed when we each use a different argument.

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Author Lawrence B Crowell replied on Oct. 2, 2012 @ 13:43 GMT
It is often the case that mass and weight are used interchangeably in ordinary language.

Cheers LC

Patrick Alan Hutchinson wrote on Sep. 20, 2012 @ 21:34 GMT
Hello Lawrence

Thank you for your essay. It gives the clearest presentation I have yet come across of what seems to be a fundamental muddle pervading the subject. It appears in the notion which you describe very clearly on your page 3:

"The light cone at any point is subject to quantum fluctuations. Consequently the point where all null rays pass through is indeterminate; null rays...

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Author Lawrence B Crowell replied on Sep. 22, 2012 @ 01:06 GMT
A light cone is a spacetime representation of the path a spherically expanding light pulse takes in spacetime. If spacetime is noncommutative on a small scale this light cone point is not a point but a region where a set of null rays pass. Here the term ray used here is mathematical more than an geometric optical concept of a ray.

Cheers LC

Patrick Alan Hutchinson replied on Sep. 22, 2012 @ 20:41 GMT
If one is discussing physics then a "a spherically expanding light pulse" cannot start from a point but from a region. If one is discussing maths then what a light cone is depends on one's assumtions. I know nothing worth mentioning of noncommutative geometry, and take your word for it that a light cone in noncommutative geometry has some sort of a vertex which is, as you say, a region, but one can make other assumptions.

The first two pages of your essay are very nicely written. On page 3, you lose me. Do you regard "quantization of spacetime" as an assumption or a theorem or what? The essay seems to be based on some sort of premiss that spacetime must be quantized in any mathematical model of observed physics. Is that what you assume? If so, as seems on your page 4:

"Our world is on the boundary of an anti-de Sitter (AdS) spacetime, where the interior is quantum gravity ..."

there has to be justification. I think it is conceivable that physics has other models in which spacetime is not "quantized", whatever that means, but is just a straightforward manifold with a metric and connection. The metric and connection may not be as Einstein suggested, but not very different. It seems quite possible that all the noncommutative aspects of observed physics can be modelled by solutions of assumptions expressed using much more conventional functional methods.

This is not to say that noncommutative geometry and quantization of spacetime and e.g. Asselmeyer's ideas about exotic smooth structures are "wrong". It is also conceivable that all these different approaches yield equivalent models which all reflect observed physics, much as the Schrodinger and Heisenberg approaches to QT match each other. (If they are, that would suggest some fascinating theorems.) As yet, I think it is just too soon to commit to one set of assumptions and reject all others. At the very least, assumptions should be stated.

bw. Alan H.

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Author Lawrence B Crowell replied on Sep. 22, 2012 @ 23:25 GMT
I attach a picture of a light cone in spacetime. There is a hypersurface of space that is a frame of simultaneity, and the future and past cones meet at the origin of this coordinate system.

The work of Asselmeyer is complementary to the noncommutative description. There are probably deeper principles at play here. The FERMI spacecraft measured the time of arrival of photons from distant gamma ray burstars. Photons of different wavelengths arrived at the same time. If there were Planck scale grainy properties or so called spacetime foam then shorter wavelengths would couple to these more strongly. The result is there would be a dispersion of light. None was observed. This measurement is different from what an extremely high energy experiment might observe where the probe scale is near the Planck scale. In the case of the FERMI experiment the probe scale was cosmological, billions of light years to a burstar, so this reflects a different type of experiment. This may suggest a type of quantum complementarity at work here. Asselmeyer works with exotic spaces which are absolutely smooth, but this exotic structure may have some duality or categorical equivalency with noncommutative geometry.

The AdS spacetime comes in with the AdS~CFT correspondence of Maldacena. You can look this up on Wikipedia. It is a rather deep and involved topic in connection to string theory and D-branes.

Cheers LC

attachments: light_cone.JPG

Anonymous wrote on Sep. 27, 2012 @ 01:27 GMT
Dear Lawrence,

I noted the sketch you made concerning shape/causal duality on my thread, and made some remarks in response. In the future, please feel free to post at the bottom of my thread... that way I will see your comments immediately. Take care,

Ben

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Steven Dinowitz wrote on Oct. 3, 2012 @ 06:10 GMT
Hi Lawrence,

I think I made an interesting discovery. Check out my post dated 9/19/12. Let me know what you think.

Regards,

Steve

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Author Lawrence B Crowell replied on Oct. 4, 2012 @ 01:36 GMT
I will take a look at this paper. The matter of CP violation is of course interesting, and it is important to understand how this discrete symmetry is violated, presumably at lower energy. I do think that solving the problem of CP violations by breaking the equivalence between inertial mass and gravitational mass is at best converting the problem from one form to another. Think of it from a Gauss law perspective. Consider a large mass M made with matter and a smaller mass made of antimatter m. If I were to put a Gaussian surface around the two of them the gravitation at the surface would be that of a mass M - m. Now force the small mass m into M, and BOOM you are left with a mass M- m in the center and a shell of photons of mass 2m approaching the Gaussian surface. The observer on the Gaussian surface would detect this huge pulse of radiation E = 2m and from gravity would now detect a gravitating mass M - m. Now suppose this Gaussian surface is a perfect mirror that reflects the light back to the mass M - m. The Gaussian surface measure of gravity would then have a mass M + m. The interaction between matter and antimatter would increase the amount of gravitational mass.

Solving the CP violation issue with this seems to be a rather odd solution. Of course nature could turn out to be strange. Performing this experiment would be of interest, and I suspect or at least hope that nature does not turn out to be this crazy.

Cheers LC

Peter Jackson wrote on Oct. 3, 2012 @ 14:16 GMT
Lawrence

I was very pleased to be able to understand your essay, until page 6, and the problem of frame boundaries expressed in the conflict of Maxwell's equations/CSL and classical mechanics. I found your resume clear and logical, up to that point. I congratulate you for that and am sure the problem after then was mine.

I wonder if you might use your obvious deep understanding of...

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Author Lawrence B Crowell replied on Oct. 3, 2012 @ 17:43 GMT
Peter,

The loss of unitarity requires a somewhat different way of thinking. I think it is a great thing that our educations give us rigor in our thinking and abilities to solve problems. There is an unfortunate flip side where with regards to foundations this can lead to a sort of “rigor mortis.” Trying to think of physics that is outside of what is accepted is very difficult. It is...

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Peter Jackson replied on Oct. 3, 2012 @ 20:13 GMT
Lawrence

Thanks, Congratulations, and you're very welcome. Hold on tight, grit your teeth and I'll see if I can stick a pit prop up your nether end to prove Andy Warhol wrong!

Do come back when you've had a think about it. It really does take some 'dynamic' thought and research, and the dropping of deeply rooted assumptions to test the axioms. It helps a lot if you're familiar with the structures of logic, both TFL, and Propositional Modal Dynamic or PDL. It IS rather a different language.

There are still a couple of bits missing, plus lots of dressing, but you've only seen the tip of an ice cube off a glacier that won't stop pouring out physics!

Very best Wishes

Peter

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Author Lawrence B Crowell replied on Oct. 4, 2012 @ 13:05 GMT
I would need to read you essay, which I read a while back. I was reminded that Oct 5 11:59EDT is the end of voting. I was thinking for some reason that it went on until near the end of October. So I have to read and vote a fair number of these.

Cheers LC

Author Lawrence B Crowell wrote on Oct. 3, 2012 @ 16:57 GMT
My reference [11] L. B. Crowell, ”Tricritical quantum point and inflationary cosmology,” http://arxiv.org/abs/1205.4710 used in my essay have been accepted for publication. This won an honorable mention in the GRF essay contest earlier this year. The acceptance letter is below.

I see that for some reason I am top of the community rating list. That will probably prove Andy Warhol's 15 minutes of fame, but it is curious that it happened.

Cheers LC

CC: dharamvir.ahluwalia@canterbury.ac.nz

Ref.: IJMPD1055

"Tricritical quantum point and inflationary cosmology"

Dear Dr. Crowell,

I am pleased to tell you that your essay has now been accepted for publication in the International Journal of Modern Physics D.

The proof of manuscript will be e-mailed to you within 2 weeks. For any questions related to publication of your essay, please e-mail to: ijmpd@wspc.com

Thank you for submitting your work to this journal.

Sincerely,

Chee-Hok Lim

for D V Ahluwalia (Editor)

Pentcho Valev wrote on Oct. 3, 2012 @ 18:16 GMT
Lawrence,

I remember criticizing the following statement of yours but you (or some guardian angel) deleted my comment:

You write in the essay: "Einstein changed Newton's laws by adjusting the first and third laws, motivated by the locality of electromagnetic fields predicted by Maxwell's equations."

Could you please elaborate? When and how did Einstein do that?

Pentcho Valev

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Author Lawrence B Crowell replied on Oct. 3, 2012 @ 20:37 GMT
Newton’s first law tells you that to observe physics you must do so from an inertial frame. Einstein generalized this with the equivalence principle. Newton’s third law indicates the laws of physics are invariant with respect to displacement and orientation. Einstein supplanted that with Lorentz boosts. In doing to Maxwell equations are invariant in all frames.

LC

Pentcho Valev replied on Oct. 3, 2012 @ 21:33 GMT
Strange (euphemism) formulations of Newton's first and third laws. "Anything goes" would say Paul Feyerabend.

Pentcho Valev

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Vladimir Rogozhin wrote on Oct. 3, 2012 @ 20:02 GMT
Dear Lawrence,

Unfortunately, I did not see in your essay ontological justification of your basic assumptions. A physics today requires a fundamental revolution. But can it be done without ontology? Mathematics is also not ontologically grounded science. Sincerely, Vladimir

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Author Lawrence B Crowell replied on Oct. 3, 2012 @ 20:42 GMT
I did not spend much time on philosophical issues. I tend to procede in a more operational way. When it comes to ontology and quantum wave functions the basic results of Bell and Kochen-Specker hold, which indicates the wave function is either not ontological or is in some way minimally ontological.

Cheers LC

Vladimir Rogozhin replied on Oct. 4, 2012 @ 09:33 GMT
Dear Lawrence!

Fundamental physics was always together with philosophy, ontology. Especially, when it comes to Space-Time geometry. And this is not just a problem of physics and mathematics, but of human culture, the problem of the knowledge base. "Trouble in physics" just to have a source in the absence of the ontological foundations of geometry of Space-Time. Sincerely, Vladimir

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Sergey G Fedosin wrote on Oct. 4, 2012 @ 07:04 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
$R_1$
and
$N_1$
was the quantity of people which gave you ratings. Then you have
$S_1=R_1 N_1$
of points. After it anyone give you
$dS$
of points so you have
$S_2=S_1+ dS$
of points and
$N_2=N_1+1$
is the common quantity of the people which gave you ratings. At the same time you will have
$S_2=R_2 N_2$
of points. From here, if you want to be R2 > R1 there must be:
$S_2/ N_2>S_1/ N_1$
or
$(S_1+ dS) / (N_1+1) >S_1/ N_1$
or
$dS >S_1/ N_1 =R_1$
In other words if you want to increase rating of anyone you must give him more points
$dS$
then the participant`s rating
$R_1$
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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Author Lawrence B Crowell replied on Oct. 4, 2012 @ 12:55 GMT
That is the trick, for one does not know R_1. The only way to insure you increase a person's community ranking, or not drop it, is to give them a 10.

LC

Peter Jackson wrote on Oct. 5, 2012 @ 09:46 GMT
Lawrence

You too seem to have been targeted by Trolls. Do you think Brendan can identify the conspirators giving out mass 1's? - giving ridiculous drops of

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Author Lawrence B Crowell replied on Oct. 5, 2012 @ 12:32 GMT
I wrote about this to Brendan Foster yesterday. I dropped suddenly 106 points and everything was jumbled up. He says there is a computer glitch that is messing things up. Things are still a mess, and I was averaging around 20 or so for a while and am still down the list. It appears possible that any objective aspect to this contest has ended. I don't know if they have records of where authors were ranked before this happened, but if not it appears this contest might be humpty dumpty.

LC

AndyM replied on Oct. 5, 2012 @ 18:29 GMT
After the contest, in the interests of eliminating any possibility of contest score-fixing, I think that the community scoring of each reviewer should be made public. No where in the rules does it state that the scoring is or should be anonymous.

Note that I am not a participant in the contest, but feel that there is a good chance that there is manipulation.

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Author Lawrence B Crowell wrote on Oct. 5, 2012 @ 19:16 GMT
A number of things could be done. I really think there needs to be a better initial screening of these essays. By at least skim reading them essays that have stuff about the speed of light being dependent on the source, or nonlocal communication in quantum mechanics, or some puerile ideas about how some physics 101 idea “explains all,” or an action principle that is clearly contrary to known physics (there is an essay with this), and so forth can be eliminated. The pure crackpot crank stuff should be weeded out right away.

The problem is that you can’t just write to these authors that their work is nonsense. They rate your essay as much as you rate theirs. So you have to do this ridiculous condescending nonsense to them.

The ranking needs to be based on a total score, not on whether they average some score. An essay with 5 rating of 8 should be ahead of an essay with 1 rating of 10. At least this should be the case until they reach some “critical number” of total scores, say 10 of them.

Clearly the system was compromised in some way, and I suspect it was hacked into. The person doing the hacking then had liberties to either give certain contestants multiple voting powers or they themselves gave multiple votes. The whole contest is supposedly set back “right,” but now I see lots of nonsense essays towards to top, mine is still way down. Alves wrote a fine essay that I gave a 9 or 10 and he is way down. I doubt the damage has not really been fixed.

The whole thing has been hopelessly corrupted and is frankly a wash. Those who remained at the top will doubtless make the cut. Those who were in the > 35 rating who are now down the list are out in the cold. There are a number of essays in this top region that are not worth the paper they are printed on.

Cheers LC

Author Lawrence B Crowell replied on Oct. 5, 2012 @ 19:28 GMT
PS, On the screening of essays, I think essays that are just some loose or post-modernist screed should be prevented from being hosted here as well.

LC

Pentcho Valev replied on Oct. 5, 2012 @ 21:37 GMT
"essays that have stuff about the speed of light being dependent on the source (...) can be eliminated. The pure crackpot crank stuff should be weeded out right away."

Be more careful, Lawrence. Crackpots, cranks, trolls etc. are easy to eliminate but VIP people might look badly at you:

Joao Magueijo: "Lee [Smolin] and I discussed these paradoxes at great length for many months, starting in January 2001. We would meet in cafés in South Kensington or Holland Park to mull over the problem. THE ROOT OF ALL THE EVIL WAS CLEARLY SPECIAL RELATIVITY. All these paradoxes resulted from well known effects such as length contraction, time dilation, or E=mc^2, all basic predictions of special relativity. And all denied the possibility of establishing a well-defined border, common to all observers, capable of containing new quantum gravitational effects."

Pentcho Valev

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Author Lawrence B Crowell wrote on Oct. 5, 2012 @ 22:42 GMT
You clearly do not understand what you are talking about. The ideas of Joao Magueijo and Lee Smolin have to do with relatvity on a small scale near the Planck length. In no way could I imagine they would agree with your whole assessment that relativity in the proper domain of application is completely false. I am sorry, but that is all there is to this. You keep pestering people with your stuff on this, and we have to condescend to your nonsense to keep from getting one-ratings from you.

This is a major flaw with the whole contest format.

LC

Pentcho Valev replied on Oct. 5, 2012 @ 22:54 GMT
Don't worry about one-rating. I have only given 10's, once 8. One-rating contradicts my ethical principles.

Pentcho Valev

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Author Lawrence B Crowell replied on Oct. 5, 2012 @ 23:58 GMT
I have given up on the contest. After this October surprise there is no point in it, and frankly if I get a string of 25 ones at this point I could frankly give a damned.

LC

Pentcho Valev replied on Oct. 6, 2012 @ 06:50 GMT
"I have given up on the contest."

Obviously you haven't. Such a spectacular jump after voting was stopped and the "final" results were posted!

Pentcho Valev

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John Merryman wrote on Oct. 7, 2012 @ 03:33 GMT
Lawrence,

Going through comments this afternoon, I came across this exchange you had with Peter and couldn't help responding:

"It is strange to think spacetime might have a wild and chaotic structure on a small scale, and then at the same time a structure that is perfectly smooth. The Yangian system constructs a dual geometry, and this is reflected here. Experimentally it has been found that gamma ray burstars that are billions of light years away have no dispersion of light. If spacetime is grainy on a small scale it is expected that short wavelength light would interact more strongly with this “foam” and would be slower. However, the observational data does not bear that out."

Math may only be concerned with the message of measure and quantity, not whether the medium is apples, oranges, or inches, but physics is concerned with the medium. Just because space and time are measured as units doesn't mean they are equivalent. When we measure space, be it distance, area, or volume, we are measuring space. When we measure time, we measure change caused by action.

Action occurs in space.

Space and action might be inseparable, but are they really indistinguishable?

Centrifugal force is the interaction of spin and inertia. Spin is action, but what is inertia?

Isn't it at least possible space is smooth because it is distinct from physical activity, yet at any scale of space, there will be some level of dynamic activity? That way, there would be both smoothness and foam.

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Anonymous replied on Oct. 7, 2012 @ 23:13 GMT
John and Lawrence, inertia is resistance to acceleration, and it is only equivalent with gravity/acceleration given instantaneity and balanced attraction and repulsion, as gravity cannot be shielded.

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John Merryman replied on Oct. 7, 2012 @ 23:51 GMT
Anon,

The point is that if you have a spinning object, with no outside reference, such that this spin cannot be defined by some other physical frame, but is only spinning in effectively empty space, what is the basis of the inertia, other than space as an absolute frame?

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Frank Martin DiMeglio replied on Oct. 8, 2012 @ 08:04 GMT
John and Lawrence, the point is that there is necessarily a balance between invisible and visible space that involves balanced inertia/resistance to acceleration and gravity/acceleration. This sits at the heart of physics.

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Author Lawrence B Crowell wrote on Oct. 7, 2012 @ 21:58 GMT
General relativity pretty clearly shows that spacetime is an aspect of dynamics. The smoothness vs noncommutative fluctuation or graininess is a dual aspect of quantum principles or nonlocality between different regions.

Cheers LC

Anonymous replied on Oct. 7, 2012 @ 22:28 GMT
No wonder you could not make the final 35.

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John Merryman replied on Oct. 8, 2012 @ 00:35 GMT
Lawrence,

Couldn't we use ideal gas laws to show "volumetemperature" "is an aspect of dynamics?" Just as acceleration or gravity slows clock rates, increasing or decreasing the volume of a particular quantity of gas will cause a fairly precise change in its temperature, so it would quite easy to formulate a mathematical model where temperature is another parameter of volume, much as time is modeled as a fourth dimensional vector.

In terms of waves, time is frequency and temperature is amplitude. They are quite obviously aspects of dynamics. Treating space as an aspect of dynamics is another matter. We are subjective, so we need an dynamic process to measure space, but that is obviously due to the subjectivity of perspective. When we measure space; distance, area, or volume, we are measuring space. When we measure time, we are measuring a dynamic process, because duration, the quantity between the points of reference, is not external to the present moment, but is the state of the present between the dynamic occurrence of the reference events, so there is no actual vector of time. It emerges from the dynamic.

On the other hand, space is not emergent. C, the speed of light in a vacuum, is how fast light crosses empty space. How could it be a constant, without the assumption of a stable metric of space?

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Author Lawrence B Crowell replied on Oct. 8, 2012 @ 00:55 GMT
There are a lot of papers that failed to make that level. However, I would consider the scholarship in papers by Parikh, Gambini & Pullin, Fields, Anderberg, Rowlands, and Nieuwenhuizen which fell in the 4.2 to 3.8 range where I was at 4.0. Now compare that to some other papers further on up, such as Tamari, Blumschein, Klingman, Leshan, Merryman which either have factually wrong physics, advance silly propositions and in some cases clearly show a lack of basic understanding of physics. There are a range of essays that are post-modernist word salads up the line. The outcome here was unfortunate in my opinion, for there are complete nonsense papers all the way to the near top and some very good papers below, such as an interesting paper by A. Rej which is down in deep mud.

To be honest the rankings of these papers is in about half of the cases a dim reflection of their worth.

Cheers LC

Yuri Danoyan wrote on Oct. 8, 2012 @ 01:40 GMT
1.In the competition involved both professionals and amateurs.

If number of amateurs far exceeds the number of professionals, it can (I mean just the first round) to follow to question:

Is it possibly fair voting without "Throwing the Baby out with the Bath Water"?

2. Is the voting for FQXi members mandatory or voluntary in the first round?

If it is voluntary, how to save balance between numbers of professionals and amateurs?

3. Lot of essays does not correspond to the criteria of relevant.

Among leaders of contest I see philosophical essays absolutely not common with topic of contest.

4. Level of technical support is not high enough.

5.Contest participants who avoid discussions should be disqualified for passivity. I see such persons among a group of leaders.

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Jonathan J. Dickau wrote on Oct. 9, 2012 @ 01:56 GMT
Hello Lawrence,

You have my sympathies. I found it hard to believe when I saw my essay in 29th place at midnight on Friday, after spending most of the past week down in the 60s and 70s. I expected some large fluctuations at the end, with my final rank lower, and this is what happened. It was curious though that you ended up with a lower score, after I had seen your essay in the top tier and given you an 8, earlier on Friday. To calibrate that statement; I gave out no 10s, but used every other number at least once - and was still rating essays in the final hour.

My guess is that someone did attempt some technological jiggery pokery, and that the FQXi admins made an attempt to purge the erroneous entries, but may have voided some legitimate votes in the process. I am sorry that whatever happened affected you adversely, though I am elated at making the cut myself. You mentioned a possible joint effort in the future. I would be honored to co-author a paper with you, and if that works out, to submit a joint essay with you for some future contest.

I do not approach your knowledge level, but I have a knack for explaining highly technical subjects in a way laymen can understand, and apparently that is part of the requirement here. You mentioned the essay of Gambini and Pullin above, and I think they did an excellent job of reducing a subject I'd seen Jorge Pullin present in a highly technical fashion - a few years ago - to language any knowledgeable person could understand, without being a physicist.

That's tougher than it sounds. And perhaps it was my having learned about their work before, that made their paper easy to understand. But it's a shame some excellent essays, like theirs (and yours), did not end with a higher score.

All the Best,

Jonathan

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Author Lawrence B Crowell replied on Oct. 9, 2012 @ 14:23 GMT
Jonathan,

The whole kerfuffle this week started when I drew a comparison between the work of reasonable authors and those who wrote rubbish on Oct. 8, 2012 @ 00:55 GM just above, when somebody “anonymous” decided to link this to the authors of essays that I cited as sub-par. Klingman then rose to my challenge, where I indicated on his web site very clearly the problems with the...

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Jonathan J. Dickau replied on Oct. 10, 2012 @ 00:27 GMT
Thanks Lawrence,

Your thoughtful reply is appreciated. You will probably have more chances for papers in top journals than any of the less learned authors who finished above you in this contest. But I understand that this contest's ratings were gamed by some less than scrupulous authors, which made many scores including yours do flip flops.

They found out that some individuals figured out how to vote multiple times. It was pointed out that there were also one or two 'fake' entries and other brief papers that may have been written under a pseudonym, which would give an author of a legitimate essay of lesser quality the power to give top marks to their own essay, and two votes each to friends. This certainly yields a stacked deck.

I think perhaps a stricter initial acceptance policy is in order, to assure that nobody can submit multiple essays. And I have already been in touch with the webmaster with insights about how the tamperers could have done what they did, and how to stop them more effectively. I think they do have a handle on it, and I don't think the technical problems we saw this year will be a factor next time.

All the Best,

Jonathan

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Author Lawrence B Crowell replied on Oct. 10, 2012 @ 01:09 GMT
Because somebody wanted me to read their essay from the last contest I ended up looking at the rankings. I finished 26 out of 163, which is not bad. There were of course nonsense essays in the upper ranks. It did not appear that things were quite as skewed then as now.

If I do this again I will only write a very general or informal review. I am not going to write anything which is highly technical. Of course writing this will not be entirely easy, but at least I will not have to fuss with LaTeX and the rest.

Since authors rank each other's essays it does mean that cranky authors are judging your paper. I also suspect that cranks up-vote cranks. In part this contest is a bit of a popularity contest. One does have to schmooze a bit to get attention, and this can easily turn into what we used to call brown nosing.

Cheers LC

John Merryman wrote on Oct. 10, 2012 @ 02:16 GMT
Lawrence,

It is not that I don't understand frequency, but that I'm comparing it, as a vector of intervals, with time, as I am comparing amplitude to temperature. The frequencies of light from another star might cover the same spectrum as the sun, but the amplitude of those waves is less, thus cooler.

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Author Lawrence B Crowell replied on Oct. 10, 2012 @ 11:52 GMT
Temperature has no meaning for a single wave. Since you compare stars with the sun this refers to a statistical distribution of photons with a range of wavelengths. For a thermal distribution of photons there is a blackbody distribution rule due to Planck

I(ν, T) = (2hν^3/c^2) 1/(exp(hν/kT) - 1)

for h the Planck constant h = 2πħ and ν the frequency of photons. If you take the derivative of this function with respect to temperature, the maximum dI/dT = 0 occurs when there is a frequency

ν = σcT

for σ the Wein’s displacement constant. As a result the frequency of light at the peak of the black body curve scales with temperature. Usually this is expressed according to wavelength λ = c/ν. This is different from the amplitude.

A G-class star has the same blackbody temperature whether that star is the sun or a near copy of the sun 100 light years away. To compute the amount of power incident per unit area (watts/m^2 = irradiance) incident on a surface from the sun or a distant star one must integrate this with respect to frequency (remember frequency = 1/periodicity and power = d energy/d time) and integrate over the solid angle Ω of view to the sun and the star.

P = ∫I(ν,T)dν∫dΩ

The sun has a total solid angle of perspective Ω ~ 2πx(π/1000), while a star has an exceedingly small solid angle of perspective.

This is standard physics going back to the start of the 20th century. Temperature has nothing to do with wave amplitude, but is a statistical effect from a thermal distribution of photons.

Cheers LC

John Merryman replied on Oct. 10, 2012 @ 16:44 GMT
Lawrence,

Thank you for the informative reply, even though I'm not able to fully appreciate it. I suppose I'm applying sound waves to light, that increased amplitude=louder. Rather than test your patience with the various questions that come to mind, I'll stick to one:

You make the points; "Temperature has no meaning for a single wave." and "Temperature ... is a statistical effect from a thermal distribution of photons."

Would time have any meaning for a single event, or regular periodicity from a single interval? If it doesn't, than isn't time also an effect of change resulting from such thermodynamic activity?

One additional thought; If photons become entangled in transit, wouldn't "the frequency of light at the peak of the black body curve scales with temperature" mean this mass of small waves is really one big wave?

Thanks for the engagement. Promise I won't tell the guild.

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Author Lawrence B Crowell replied on Oct. 10, 2012 @ 17:23 GMT
In classical physics of particles moving in space one can talk about "a point in time." When you have wave mechanics there is an uncertainty relationship ΔωΔt = 1, where for the spread in the angular frequency Δω ~ ω this gives the uncertainty spread in time.

With blackbody radiation the photons are in a state of complete decoherence so there are no entanglements between them. This is probably a bit of an approximation, for entanglements may still exist but are so scrambled up that they are not discernable.

Cheers LC

Constantin Leshan wrote on Oct. 11, 2012 @ 09:14 GMT
Dear Lawrence B. Crowell,

In the past contest I have found flaws and errors in ~ 20 essays, including leading essays. However, in this contest'2012 I decided not to judge any essays because Brendan recommended avoiding the judgment atmosphere. Nevertheless, since Dr. Crowell estimates my essay, I also have the right to estimate his essay.

Some contestants invented a fast method that...

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Author Lawrence B Crowell wrote on Oct. 11, 2012 @ 13:50 GMT
Constantin,

I am not sure why you find it objectionable that I reference work by other physicists. For instance you bring umbrage to my referencing Cardenas’ work where he demonstrates the k = 1 FLRW model that is closed and recollapses violated the entropy bound of Bekenstein and Bousso. I do take these results and further work a consistent theory involving quantum forms of the Landau tri-critical point to demonstrate the onset of inflationary cosmology. This paper, referenced in my FQXi essay, received an accolade by GRF and was accepted for publication is Int. J. Theo. Phys. You similarly find it objectionable that I would use other references as well. Of course this is common practice.

In your paper you reject a range of physics, such as declaring quark or QCD wrong. Big bang is judged wrong by you, this in spite of a growing preponderance of evidence in its favor. You also have funny things, such as your figure 1 with photons moving at v = c + 75km/sec, which nobody who is well grounded in physics is going to take seriously.

Cheers LC

Constantin Leshan replied on Oct. 13, 2012 @ 16:03 GMT
Dr. Crowell,

I have found that your essay copy the generally known information, therefore it is a fraud! Imagine that I send such a story to contest. In this essay I tell first about Newton, then about Einstein and GR, string theory, Plank scale physics. It is a simple story about physics only that repeats the generally known information. Does such essay deserve any prize? I can produce...

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Author Lawrence B Crowell replied on Oct. 13, 2012 @ 22:46 GMT
The connection between Newton and quantum mechanics with quantum gravity is that a structure exists "under our noses." With variational mechanics there is an extension to the Feynman path integral. With BCFW recursion for QCD gluon calculations there is a correspondence with gravitons and M-theory. That was why I started out discussing Newton.

By declaring photons motion depending on the source you have really cut your throat. This simply is wrong.

LC

Constantin Leshan replied on Oct. 15, 2012 @ 10:35 GMT
Dr. Crowell wrote:"By declaring photons motion depending on the source you have really cut your throat. This simply is wrong".

Your statement shows that you don't read and don't understand my essay, therefore it is senseless to discuss it with you. Where you have found my declaration that "photons motion depend on the source"? Every scholar know that the photons speed do NOT depend on the source. In my example the photons move locally with the speed v = c. Now consider the contribution of cosmological expansion which increases the distance between these photons and the source. For this reasons, the distance between photons and the source grows in such a way as if photons move faster than light concerning the source. My example is absolutely correct physically, it is very strange that you don't understand such simple things.

Constantin

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