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FQXi Essay Contest - Spring, 2017
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Bell's Theory of Beables and the Concept of `Universe' by Ian Durham
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Author Ian Durham wrote on Jan. 30, 2018 @ 22:35 GMT
Essay AbstractFrom its earliest days nearly a century ago, quantum mechanics has proven itself to be a tremendously accurate yet intellectually unsatisfying theory to many. Not the least of its problems is that it is a theory about the results of measurements. As John Bell once said in introducing the concept of `beables', it should be possible to say what _is_ rather than merely what _is_observed_. In this essay I consider the question of whether a universe can be a beable and what that implies about the fundamental nature of that universe. I conclude that a universe that is a beable within the framework of some theory, cannot be fundamental.
Author BioIan Durham spends his days as a quantum physicist and reluctant department chair. That's also how he spends his nights. Occasionally he goes fishing.
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austin fearnley wrote on Jan. 31, 2018 @ 09:20 GMT
An interesting paper.
Having a universe as a/the fundamental entity occurs in quite a few contest essays here (including mine).
In my paper there are four fundamental sets of 'universes' based on the idea that the three colour dimensions and spin are each 4D block of spacetime. Using these four 4D blocks as building blocks I used a preon model to build (non-mathematically, alas) all SM particles with the correct eigenvalues and decay paths. Whether or not these universes are fundamental is unknown. The higgs messes it up by there being weak isospin in particles/fields and in the higgs environment so I had to include weak isospin as if it were a fundamental property of particles when really it isn't, for me, as I derives it from the colour dimensions. Normal spacetime I have as emergent, or at least the metric is, and it is unclear to me if our spacetime is just the spin 4D block dressed with an emergent metric and having an unknown topology. Since I have spacetime as emergent it is possible that all my four 'universes' are emergent by an unknown origin. The three colour universes have a group structure and I suspect that the group structure is built from three precursor colourless universes with no group structure.
With respect to your comments on the neutrino, in my preon model all SM particles are built from preons and the neutrino is simply a different combination of preons, and hence with different properties, than say are the electrons. So, to me, neutrinos are special but not quite as special as usually taken.
Best wishes
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Luca Valeri wrote on Jan. 31, 2018 @ 09:38 GMT
Dear Ian,
What a nice idea to use Bell's theory of beables to discuss, what is fundamental. Bell's view of beables - I belief - is how most of us think about how the universe looks like.
You nicely show, that a universe that is a beable cannot be fundamental. It consists of all that exists. And certainly the universe itself exists independently of any observation. But are the things the universe consists of itself beables in your opinion? If no, how can the universe itself be a beable an being constructed of non-beables?
I always liked Bohr. However Bell and Einstein are the ones that are nearer to our thinking on what is real. So when I try to defend Bohr, I always have in mind Bell and Einstein, to explain how Bohr could have been right.
In my essay "The quantum sheep - In defence of a positivist view on physic" (not online yet), I gave a precise physical/mathematical meaning of Bohr's reply on EPR about "[the] influence of the very conditions which define the possible types of predictions regarding the future behaviour of the system." As a consequence I show, that the condition under which our fundamental concepts can be defined depends on the state of the universe as a whole. Hence also the description of the universe as consisting of these fundamental concepts depends on the the state of the universe. Can it then still be a beable?
Thanks for your nicely written essay and I hope you find time to read my essay.
Luca
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Luca Valeri replied on Jan. 31, 2018 @ 09:48 GMT
By the way, in my essay I put a black or a white sheep in a box and give it different coloured flowers to eat. I ask how the laws must look like, in order to be able to know the colour of the sheep.
Luca
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Author Ian Durham replied on Feb. 5, 2018 @ 17:42 GMT
Thank you for the nice comments!
Flavio Del Santo wrote on Jan. 31, 2018 @ 10:15 GMT
Dear Ian Durham,
a clearly written and interesting essay, thank you for sharing. However it seems that you are using induction not in the usual way it is used by Comte and the following philosophers of science. By 'induction' you merely mean a methodology that allows to relate theory and observations. But this is improper, since induction is only one (and quite surpassed) way of doing this. Induction tries to justify a universal law from a finite number of observed instances. After Comte and the post-Popper era, almost no one in science claims to use inductive inferences. So, your sentence "At the heart of the problem of inference, more properly
known as the problem of induction [24], is what John Bell referred to as the ‘subject-object distinction’" doesn't seems to me anyhow correct. The subject-object ditinction, that is the actual core of your essay, is one of the most profound open problems in quantum mechanics, and possibly in physics in general, but definitely is not the same as the problem of induction.
Besides this, nice essay. I wish you success.
Flavio
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Author Ian Durham replied on Feb. 5, 2018 @ 17:44 GMT
Hmm. Thanks for pointing that out. I think I see your point though I'm not necessarily saying that the subject-object distinction is all there is to induction and inference. I'm simply saying that it is one facet of it.
Wilhelmus de Wilde de Wilde wrote on Jan. 31, 2018 @ 19:21 GMT
Dear Ian,
“Universal beables may not be knowable, but local ones, as in those bounded within a particular region of space-time, might.” I wonder if the particular regions you mention are those that agents can think of ? Because then these regions can be infinite. I agree that “universal” beables are not knowable when universal means beyond konowable.
“At the very least, it...
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Dear Ian,
“Universal beables may not be knowable, but local ones, as in those bounded within a particular region of space-time, might.” I wonder if the particular regions you mention are those that agents can think of ? Because then these regions can be infinite. I agree that “universal” beables are not knowable when universal means beyond konowable.
“At the very least, it suggests that Maxwell’s electromagnetic theory is incomplete”. Isn’t EVERY Theory incomplete ? Human intelligence is only a very short time trying to find the HOW and WHY of our existence, let’s hope for the future developments (if any)....
“I may awake tomorrow to find that I am actually a Buddhist monk living in a monastery in the Himalaya and that my life as a physicist was nothing but a dream.” Indeed in the here and (until) now you are a physicist. This is the reality Loop you are conscious of right (until) now. In another Loop the probability of being the Buddhist monk is available andthe monk dreams being a physicist.(what is better ?)
I think Fields are experienced through technical addings to our senses, they are transformed to comprehensible information, so they are “interpretations”..of emergent agents (for humanity with 5 senses) in an emergent reality.
‘universe of our experience’ the world around us reaches us as on the surface of Subjective Simultaneity Spheres around us , the result of these experiences are the models to explain our experiences.
“Everett-De Witt multiverse, for example, includes an infinite number of universes. This definition is simply too vague to qualify as a beable for any realistic theory.” I can fully agree with that so I devellopped another perception that could also explain the problems as are solved by MWI. Therefore I would be grateful if you could read
my essay “Foundational Quantum Reality Loops and leave a comment and/or rating on it.
“But the wavefunction in the Wheeler-DeWitt equation suffers from no such defect since it is said to be ‘timeless’, i.e. it simply ‘is’.”. The simply “IS” is more difficult as we think (I think). Timeless can also mean “eternal” or not present in the time restriction so outside of our “reality” (is that the same as “non-existing”) a “notable”...
It was a pleasure reading your contribution, it was helpful for my own quest.
Best regards
Wilhelmus de Wilde
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Author Ian Durham replied on Feb. 5, 2018 @ 17:47 GMT
Thanks Wilhelmus! Some very interesting thoughts indeed. Yes, every theory is incomplete. Absolutely, though there is some debate about whether we may eventually find one that is not. This would be the "theory of everything" if it actually exists. I'm not convinced such a thing is even attainable.
Marcel-Marie LeBel wrote on Jan. 31, 2018 @ 19:49 GMT
Ian,`
Excellent essay on what is really fundamental. Your essay a keeper – downloaded!
“we could attempt to deduce them from first principles, i.e. axiomatize them”.
This is what I attempt to do in my essay. I replace axioms by necessary requirement from the basic logic of the rule of non-contradiction.
A beable is pious word meant to replace the infamous “substance” conjured up by Metaphysics. I don’t use the “M” word anymore, but I do work with “substance” and “cause” ...
Check it out!
All the bests,
Marcel,
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Robert H McEachern wrote on Jan. 31, 2018 @ 21:52 GMT
From page 4: "One approach to the problem of induction is to build theories from the ground up. That is, rather than construct theories based on our observations of the world, we could attempt to deduce them from first principles, i.e. axiomatize them." Four hundred years ago, Bacon proclaimed that reliance upon that very approach was directly responsible for delaying scientific progress for 2000 years. In other words, it is a dead-end as far as understanding "reality" is concerned. Rejecting that approach, in favor of induction, subsequently formed the basis of what came to be called THE "scientific method". The axiomatic approach is the method of choice for mathematics. But Physics is not Mathematics. Whatever the problems with induction, deduction, based upon dubious premises (the only kind that exist, pertaining to "reality") is even more problematic.
From page 7: "The universe’s existence is independent of our observation of it." But one truly fundamental fact remains: Our observations are not independent of the universe's existence, even if that universe is no more that some vat in which our brains sit. The universe, whatever its structure may be, is fundamental to our existence.
Rob McEachern
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Author Ian Durham replied on Feb. 5, 2018 @ 17:50 GMT
I actually agree with both your statements. In my essay, I am only saying that the universe is not fundamental in the types of theories in which it can properly serve as a beable in the sense implied by Bell. Likewise, in no way am I saying that deduction will get around the problem of induction. Indeed, a good chunk of my PhD thesis was on precisely that.
Robert H McEachern replied on Feb. 5, 2018 @ 19:21 GMT
"I am only saying that the universe is not fundamental in the types of theories..." I agree. My point is, that says more about the nature of mathematical theories, than about the nature of the universe. Theories are virtually devoid of information. The universe is not. Hence, the map fails to provide anything more than a very meager description of the territory. Reality is determined by the vast information content of the initial conditions, not the exceedingly sparse information content of sets of equations; change the initial conditions, and you change the resulting reality, even if the equations remain the same.
Rob McEachern
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Georgina Woodward wrote on Feb. 1, 2018 @ 03:21 GMT
Hi Ian, I like your essay very much. I agree that consideration of beables is very important. As you discuss before the end there is lack of clarity about what is meant by 'the universe' or even 'the totality of all that exists'. I think there needs to be separate terms for different versions of the universe or notions of the universe. Clearly the beable universe is not the same as the visible universe. At least as I see it, the beable universe is what exists -Now and the visible universe is what can be generated from receivable, EM signals.You wrote " The universe’s existence is independent of our observation of it. We don’t simply observe that it exists, it does exist."I.D. But what we observe is not what exists. We observe products of our senses or measurements which are relational, tying back in with the one side of a cow. The beables are the sources of all observations of them.
The beable cow has no difficulty being in a black /brown 'superposition' of states. In one man's view of the universe it is brown and in another's it is black. So the seen universes are not identical to the beable universe. Each man's observation gives a singular, limited, fixed state that is an impoverished version of what exists. If he was to make more observations and the cow was to turn around it might seem that the blackness or brownness of cows is random! (I don't mean that literally but as an illustration of the relational aspect of what something is deemed to be.
Kind regards Georgina
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Author Ian Durham replied on Feb. 5, 2018 @ 17:56 GMT
Hmm. I guess the question of existence is a sticky one. Personally, as I suggested in the essay, there are certain things that simply aren't provable. But the essence of science is that there
are objectively knowable things. So while knowledge in quantum mechanics may be probabilistic, it is still knowledge and it is still predictable in the aggregate, i.e. the probabilistic sense. For instance, while I may not be able to predict if a single cow is brown or black, presumably many such measurements will tell me, on average, what many such cows will be and it is that average (mean or expectation value) that is ultimately highly predictable. After all, quantum electrodynamics, which is built on quantum mechanics, is arguably the most predictively accurate theory ever constructed in terms of how well theoretical predictions match experimental outcomes.
Joe Fisher wrote on Feb. 1, 2018 @ 16:54 GMT
Dear Ian Durham,
FQXi.org is clearly seeking to confirm whether Nature is fundamental.
Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.
All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.
Only the truth can set you free.
Joe Fisher, Realist
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Dizhechko Boris Semyonovich wrote on Feb. 1, 2018 @ 17:41 GMT
Dear Ian Durham, I agree that the universe can not be fundamental, but the space is the foundation for building the fundamental theories about it, because it is matter according to Descartes identity. New Cartesian physics, in which this principle of the identity of space and matter builds the universe from scratch and pretends to be the theory of everything. . Look at my essay [https://fqxi.org/]New Cartesian Physics[/community/forum/topic/2999] in which I showed how radically the physics can change if it follows this principle. Rate and leave your comment there.
Sincerely, Dizhechko Boris Semyonovich.
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Francesco D'Isa wrote on Feb. 1, 2018 @ 21:10 GMT
Dear Ian,
thank you for your good essay, I found some interesting points in commons with mine about absolute relativism, but we follow different paths. I think that you could be interested in the book "Why the World Does Not Exist" by Markus Gabriel. It's a divulgative text, but the core idea has something in common with yours.
Bests,
Francesco
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Author Ian Durham replied on Feb. 5, 2018 @ 17:57 GMT
Thanks for the name of that book. I have never heard of it.
Francesco D'Isa replied on Feb. 5, 2018 @ 19:09 GMT
John C Hodge wrote on Feb. 2, 2018 @ 15:12 GMT
Ian:
Wonderful, instructive essay.
I note each of us has experience of the universe that is slightly different than others. These experiences form the basis of our descriptions as you note with the cow. So our experiences form the basis of our descriptions. Thus, the science need to repeat the observations and to interpret the observations to benefit ourselves.
Hodge
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Cristinel Stoica wrote on Feb. 3, 2018 @ 19:19 GMT
Dear Ian,
I enjoyed reading your essay. It contains very interesting discussions of Bell's beables and the relation with what is fundamental, and you explain in a very engaging way. The conclusion is surprising and intriguing. Happy birthday, and success with the contest!
Best wishes,
Cristi
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Author Ian Durham replied on Feb. 5, 2018 @ 17:58 GMT
Thanks Cristi! And thanks for the birthday wishes! Hoping to get to reading your essay soon.
Anonymous wrote on Feb. 4, 2018 @ 23:04 GMT
Hello Ian,
Surprised to see you claim existence of a neutrino magnetic moment. Quick google search gives reasonably recent reference
https://www.sciencedirect.com/science/article/pii/S
0370269315009545
where they claim an upper bound only of a few 10^-11 Bohr magnetons. Hope this is not central to your point.
Trying to get some sense of what a beable is. What is...
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Hello Ian,
Surprised to see you claim existence of a neutrino magnetic moment. Quick google search gives reasonably recent reference
https://www.sciencedirect.com/science/article/pii/S
0370269315009545
where they claim an upper bound only of a few 10^-11 Bohr magnetons. Hope this is not central to your point.
Trying to get some sense of what a beable is. What is relation between beable and the enigmatic unobservable wavefunction? Beables are observables? If so, then a beable would be the incoherent lump of energy we get when we collapse a wavefunction, beable = single measurement observable? If, why not just call it that? If not, how is it different?
Now I'm confused, see the statement that vector potential is not observable. What about Aharonov-Bohm effect? The quantum phase associate with a potential can be measured, just isn't a single measurement observable. Phase is relative, requires two measurements.
and beyond that the statement that E and H fields are beables. They are not single measurement observables. What we measure in collapsing a photon wave function is dependent on how we collapse it - do we use a loop antenna or a whip antenna?
finally googled for beable and got this - anything that could possibly be. So it becomes a task of figuring out what is impossible? Such fun. Thank you bery much.
section 2 opens right on point with this - "can a universe be a beable?"
answer is yes.
local and nonlocal keep popping up in the text. Distinction is straightforward, and not confined to what we usually regard as a quantum-only phenomenon.
Unlike the 1/r hidden variable quantum potential of deBroglie-Bohm, it is the
1/r^2 potential operative in nonlocality. inverse square potentials are those who forces are orthogonal to the resulting direction of motion. They can do no work, cannot communication energy/information, only quantum phase, not a single measurement observable.
Inverse square potentials include scale invariant quantum Hall of the vector Lorentz force (this is Aharonov-Bohm effect), centrifugal, Coriolis, chiral, three body,... all scale invariant. They cannot be shielded. Brings gravity to mind.
Darn. Wish I had more to offer here, but just don't get the hidden variable pilot wave stuff and all that has been associated with it. Perhaps I'm tying beables too tightly to dBB? In any case I'm more confused that when I started. To my mind it is just wavefunctions and their interactions, and all the rest is windowdressing we fuss with when we can't see out the window - dark, snow to the rooftops, ice a quarter inch thick on the inside of the glass,... This is what the picture you paint looks to me. Entertaining at times but no fire in the fireplace, and too many empty rooms.
Don't feel like i know enough at this point to rate this essay. Just confused.
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Author Ian Durham replied on Feb. 5, 2018 @ 18:04 GMT
Actually Bell was a dBB proponent. And you are not the only one who finds beables a bit vague. If you read Bell's original papers, they are not all consistent. What they do seem to represent is an evolution of his thinking on the concept. But the short answer is that, in modern terms, most people accept that a beable, whatever it is, sets the ontology for a theory.
As for the neutrino magnetic moment, it is worth pointing out that the current constraints are all experimental and have only been able to show that, if it exists, it has an upper bound that is extremely small but, crucially, non-zero. As such, there are some alternative theories in which the neutrino is not a fundamental particle but rather consists of something like a W+ boson and something else (the exact other particle escapes me at the moment).
Anyway, it is certainly not crucial to my argument.
Member Ken Wharton wrote on Feb. 5, 2018 @ 21:15 GMT
Hi Ian,
Yay, beables! :-)
One important point about Bell's use of "local beables" that I think it's important to stress, is that every beable is *somewhere* and *somewhen*. In other words, they're parameters that are functions on spacetime. (To take Bell's example that you quote, the field values in classical E+M are clearly spacetime-localized beables.) In fact, if you take this spacetime-localization as the proper reading of his "belonging to objects" quote, the problems you note in section 1 pretty much vanish, I think.
Then, when you get to nonlocal beables like wavefunctions, it also becomes clearer that you're talking about something very different. Concepts that apply to local beables don't necessarily apply to nonlocal beables. (In my way of thinking, the latter shouldn't even be called "beables" at all -- I prefer "ontology" here, to keep beables connected to spacetime, with wavefunctions and functionals of field configurations in some broader category.)
But then I certainly come around to agreeing with your conclusion: if the universe is the sum total of all the beables, then the *universe* isn't fundamental -- the *beables* are! But would you be okay with adding the laws and boundary conditions that constrain those beables to the set of things that are "fundamental"?
Thanks for the essay! -Ken
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Author Ian Durham replied on Feb. 7, 2018 @ 03:20 GMT
Thanks Ken. Yes, I absolutely think that the laws and boundary conditions that constrain the beables *must* be fundamental, at least within a given theory. So if the given theory is about the universe as a whole, then they would be *the* fundamental entities.
As far as Bell goes, perhaps not surprisingly I have a slightly different reading of what he means by "beable" in the sense that I don't think he is as consistent and clear across his papers as everyone seems to think he is. So I'm not sure I entirely agree with your first two points, though I will have to think more about them.
But, yay beables! Never thought I would write this kind of essay (or reach that conclusion, for that matter) and yet here I am...
Steven Andresen wrote on Feb. 6, 2018 @ 05:23 GMT
Dear Ian Durham
Just letting you know that I am making a start on reading of your essay, and hope that you might also take a glance over mine please? I look forward to the sharing of thoughtful opinion. Congratulations on your essay rating as it stands, and best of luck for the contest conclusion.
My essay is titled
“Darwinian Universal Fundamental Origin”. It stands as a novel test for whether a natural organisational principle can serve a rationale, for emergence of complex systems of physics and cosmology. I will be interested to have my effort judged on both the basis of prospect and of novelty.
Thank you & kind regards
Steven Andresen
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Satyavarapu Naga Parameswara Gupta wrote on Feb. 10, 2018 @ 02:08 GMT
Respected Prof Ian Durham
Wonderful conclusion..... " a universe that is a beable within the framework of some theory, cannot be fundamental." by the way....
Here in my essay energy to mass conversion is proposed...……..….. yours is very nice essay best wishes …. I highly appreciate hope your essay and hope for reciprocity ….You may please spend some of the valuable time on...
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Respected Prof Ian Durham
Wonderful conclusion..... " a universe that is a beable within the framework of some theory, cannot be fundamental." by the way....
Here in my essay energy to mass conversion is proposed...……..….. yours is very nice essay best wishes …. I highly appreciate hope your essay and hope for reciprocity ….You may please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance
Some of the Main foundational points of Dynamic Universe Model :-No Isotropy
-No Homogeneity
-No Space-time continuum
-Non-uniform density of matter, universe is lumpy
-No singularities
-No collisions between bodies
-No blackholes
-No warm holes
-No Bigbang
-No repulsion between distant Galaxies
-Non-empty Universe
-No imaginary or negative time axis
-No imaginary X, Y, Z axes
-No differential and Integral Equations mathematically
-No General Relativity and Model does not reduce to GR on any condition
-No Creation of matter like Bigbang or steady-state models
-No many mini Bigbangs
-No Missing Mass / Dark matter
-No Dark energy
-No Bigbang generated CMB detected
-No Multi-verses
Here:
-Accelerating Expanding universe with 33% Blue shifted Galaxies
-Newton’s Gravitation law works everywhere in the same way
-All bodies dynamically moving
-All bodies move in dynamic Equilibrium
-Closed universe model no light or bodies will go away from universe
-Single Universe no baby universes
-Time is linear as observed on earth, moving forward only
-Independent x,y,z coordinate axes and Time axis no interdependencies between axes..
-UGF (Universal Gravitational Force) calculated on every point-mass
-Tensors (Linear) used for giving UNIQUE solutions for each time step
-Uses everyday physics as achievable by engineering
-21000 linear equations are used in an Excel sheet
-Computerized calculations uses 16 decimal digit accuracy
-Data mining and data warehousing techniques are used for data extraction from large amounts of data.
- Many predictions of Dynamic Universe Model came true….Have a look at
http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.h
tml
I request you to please have a look at my essay also, and give some of your esteemed criticism for your information……..
Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.
In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from “http://vaksdynamicuniversemodel.blogspot.in/ ”
I request you to please post your reply in my essay also, so that I can get an intimation that you repliedBest
=snp
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Thomas Howard Ray wrote on Feb. 13, 2018 @ 21:20 GMT
Hi Ian,
I'm left a little confused. Are you a Bellist or are you not?
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Author Ian Durham replied on Feb. 13, 2018 @ 21:34 GMT
I'm not an "anything"-ist. Bell clearly had some really good ideas but I certainly don't agree with him on everything. What interests me are the implications of his theory of beables. I haven't decided whether I like it as a theory or not, but that's because I don't think it's been vetted enough yet. This effort was a small one on my part to further vet his theory.
Thomas Howard Ray replied on Feb. 14, 2018 @ 00:13 GMT
Ok, I get it now.
The reason I asked is that your conclusion from the abstract: " ... that a universe that is a beable within the framework of some theory, cannot be fundamental" is absolute.
Since general relativity is a mathematically complete theory -- not a framework -- in which beables exist and dynamically interact, universe included, Bell's theorem cannot be fundamental by your criteria.
Another reason one might consider Bell falsified, is that all proofs for the theorem (that I have seen) are based on double negation.
There are other reasons, too.
Enjoyed the essay.
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Author Ian Durham replied on Feb. 26, 2018 @ 20:44 GMT
It's not really possible to "falsify" Bell's theorem. It's worth taking a look at some of the alternative derivations out there as they make it more clear what is going on. Two examples that spring to mind include Wigner's version (which is the one derived in Sakurai) and the one David Harrison derives as a pedagogical tool (it was floating around online somewhere).
Edwin Eugene Klingman wrote on Feb. 14, 2018 @ 01:09 GMT
Dear Ian Durham,
You begin with a logician [or a general semanticist] pointing out limits on how much we can reasonably infer from a given observation. Thanks! Don't see much of that these days. You then say "quantum mechanics is ostensibly a [statistical] theory about the results of measurements."
Bell, based on dBB, investigated "objective properties –...
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Dear Ian Durham,
You begin with a logician [
or a general semanticist] pointing out limits on how much we can reasonably infer from a given observation. Thanks! Don't see much of that these days. You then say "
quantum mechanics is ostensibly a [statistical]
theory about the results of measurements."
Bell, based on dBB, investigated "
objective properties – beables – assigned to objects", in the way that physically real fields
E and
H are beables and Maxwell's theory. My current essay reviews Hertz's extension of Maxwell's equations that Einstein based his 1905 paper on. I hope you will read it and comment on it.
If one considers an ultimately dense vortex in a self-interacting field, it might seem to shrink to a point (like a skater pulling in her arms). Before that happens it may reach a limiting point [not describable in a brief comment] where electric charge comes into being. Does all of the 'vortex' go into the charged particle, or does a remnant survive (as a neutrino)? In a comment above you refer to a neutrino as potentially not a fundamental particle, but something like a W+ boson and something else. If a boson is a vortex in an ultradense 'perfect fluid' such as created at LHC, a neutrino may be a Z boson remnant (and nothing else) which yields a left-handed Majorana 'particle'.
I'm in full agreement with Bell about real scalar fields but 'unreal' scalar electric potential. As one is the gradient or integral of the other, why should both be real? You ask "
are fundamental beables knowable, and, if so how can we know them?" I suggest that if we can model them well enough to predict their mass (which SM cannot do) this might count for 'knowledge'. And yes, it
is better to understand the universe we
live in! Also glad you do not believe wave functions necessarily pose a problem for beables. A moving boat will induce a wave and moving mass can also. Rather than discuss your 'universe as beable', may I point out relevant aspects of Bell [copied from my response to another author]:
Referring to Bell's "momentous no-go theorem", if you look at his first paper, his very first equation determines the outcome:
A = +/-1, B = +/-1, where A and B are measurements on Stern-Gerlach. This is based on the assumption of quantum qubits. But QM provides only probabilistic predictions. Many-body experiments on spin
do yield qubit outcomes, as should be expected. Stern-Gerlach
does not yield qubit outcomes, but smeared results that match 3D spin dynamics in an inhomogeneous field. However Pauli's mathematical projection of qubit mechanics:
O|+> = +|+>, O|-> = -|-> is Bell's assumption of reality. In other words Bell claims to look for a classical (local variable) description of Stern-Gerlach, but then
constrains the problem to quantum results based on the mathematical projection of Pauli, not on the empirical results of Stern-Gerlach.
Feynman later put
the final nail in this coffin by assuming that his favorite two-slit photon experiment could be carried over directly to a two-slit spin analog (the SG experiment). Of course
the same equations apply, because he's making
the same mathematical projection, but the actual physics of the photon in two-slits is vastly different from the physics of atoms in an inhomogeneous magnetic field, and Feynman's extended SG gedanken model has
never been tested. Despite that, several QM textbooks base QM on his model.
Since Feynman and Bell's math and logic have been accepted as gospel, local realism has been excluded from physics. A no-go theorem based on atoms in a magnetic field, constrained to never-tested single-qubit spin results, is then "proved" by photon-based experiments which actually do produce two-state results: on/off detections.
I repeat - the entire entanglement industry is based on the erroneous assumption that the results of the Stern-Gerlach atomic experiments are +1 and -1 deflections, "tested" by photonic experiments that use +1 and 0 detections. The atomic data produced by Stern-Gerlach clearly conflicts with Bell's initial assumption, but instead of trying sophisticated tests of Stern-Gerlach using modern technology the whole entanglement industry is based on 1922 experiments that clearly do not yield +1 and -1 results. The confusion of 1920s quantum mechanics is locked in, compounded by 1960's theoretical claims.
My suggestion is to look for the basic assumptions that violate intuition and that lead to nonsense. My current essay provides a possible example of such.
Thank you for surprising yourself with an essay on beables!
My very best regards and best wishes,
Edwin Eugene Klingman
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Member Kevin H Knuth wrote on Feb. 15, 2018 @ 04:39 GMT
Thank you, Ian for yet another insightful and thought-provoking essay.
I remember that late night (for me) when I, in South Africa, and you, in Maine, were scrambling to get our essays into shape. I am very glad that you succeeded.
I enjoyed the parable about the economist, mathematician, and logician. Clearly, the logician was not a Bayesian and could not incorporate his prior information about the coloring of cows. Surprisingly, the mathematician seems to have been a Bayesian; and the economist a very poor one with ridiculous priors about the nature of cows in a region.
Your discussion of Bell's beables is interesting, and after reading a few pages in I feel that I could write an essay in response to this. The idea of assigning things, beables, properties is something I have given a lot of thought to. At this point, this idea that objects have positions in space and time, or have speeds or energy and momentum is clearly not right. Each of these 'properties' is observer-dependent, which means that they are not properties possessed by the objects in question, but instead represent a relationship between the object and the observer. This makes me feel more strongly that this is one of the problems of physics. These quantities represent relationships, not properties. It is possibly this fact that has led physics astray.
You now have me thinking about how one can conceive of my influence theory, which results in an emergent space-time, in terms of beables.
Thank you for an interesting, stimulating, and thoughtful essay!
Kevin Knuth
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Author Ian Durham replied on Feb. 18, 2018 @ 21:00 GMT
Thanks Kevin! Hoping to get to your essay in the next week or two.
Anyway, I would be curious to know what you come up with in regard to beables within influence theory. I find beables attractive since I firmly believe in an objective reality, but I'm also not entirely married to the concept either. Really I've just begun to explore it in a bit more depth.
Peter Jackson wrote on Feb. 17, 2018 @ 19:18 GMT
Ian,
If both 'tentative' Maxwell's and Quantum Theory appear incomplete, which would you suggest is most lacking in it's correspondence with nature? or perhaps 'misunderstood'?
And I have a problem with Beables I hope you can help with. I liked Bell and maybe-ables, but checking for answers to the above question I added Maxwell's 4-momenta states including 'curl' into Bohr's (no) starting assumptions for pair particles led to interaction momentum transfer issues. Everything turned into damn beables! I mean the whole ontological construction, like 3 great chains of beehives with clouds of fermions everywhere! I can rotate them any way I like (x,y,z) but they never go away. You can imagine the implications (honey pouring from every crevice!)
I'm still a bit shocked and amazed. I can't seem get away from them but I hope you can show me how. I tried the detection loophole but, to make it worse, Declan Traill's short essay gives a matching computer code and violation plot with CHSH>2 and steering violation >1. I checked Bells predictions and it did seem to match, including the 'amaze' bit, so it looks right. But you're the expert. Help needed!
I enjoyed the rest of your essay too and agree on universes, though did find a consistent shape and cyclic mechanism in a published paper. Would that qualify morphologically? I'll dig it out if you're interested.
Look forward to your advice about all those might justbe-ables.
Very best
Peter
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Author Ian Durham replied on Feb. 18, 2018 @ 21:08 GMT
Hmm. I'm not sure how something can "turn into" a beable. It seems to me that, in the sense meant by Bell, a beable is a feature of a theory. It's the ontology of that theory. Whether something is ontological or not within a given theory doesn't seem to have anything to do with what you can "do" with it in that theory. So whether something "goes away" or not depending on what you do with it doesn't determine whether it's a beable.
Peter Jackson replied on Feb. 21, 2018 @ 21:11 GMT
Ian,
I read Bells Be-ables a little more literally, as 'something that 'IS'. My point then is that if we substitute 'guesses' about particles and interactions for actual test states and mechanisms, which then
provides the ontology.
I've just been pointed to the Poincare Sphere,with the 4 orthogonal conjugate vectors I identify in my experiment. THAT is one of the string of Beables' which reproduces QM's predictions.
Of course that's impossible you say. Well Bell didn't think so, and it seems he was right. I hope as the expert you'll have a careful check through and see if you can find a flaw. It may be quite important!
Very best
Peter
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Peter Jackson replied on Feb. 24, 2018 @ 13:39 GMT
Ian,
....Fact is I describe an ontological sequence with a different starting assumption (as now found in OAM, not 'singlet,' 'supposed' or 'no assumed' states), which, like it or not, fully reproduces QM predictions. No silly assumptions are used and no silly outcome found.
If anyone can find a flaw wouldn't it be you? I'd be very grateful for your analysis.
I've just posted the below in my posts as it's impossible to reconstruct the ontological mechanism on a quick scan.
AS MOST STRUGGLE WITH THE CLASSICAL SEQUENCE (TO MUCH TO HOLD IN MIND ALL AT ONCE) A QUICK OUTLINE INTRO IS HERE;
1. Start with Poincare sphere OAM; with 2 orthogonal momenta pairs NOT 'singlets'.
2. Pairs have antiparalell axis (random shared y,z). (photon wavefront sim.)
3. Interact with identical (polariser electron) spheres rotatable by A,B.
4. Momentum exchange as actually proved, by Cos latitude at tan intersection.
5. Result; 'SAME' or 'OPP' vector Re-emit polarised with amplitude phase dependent.
6. Photomultiplier electrons give 2nd Cos distribution & 90o phase values.
7. The non detects are all below a threshold amplitude at either channel angle.
8. Statisticians then analyse using CORRECT assumptions about what's 'measured!
The numbers match CHSH>2 and steering inequality >1 As the matching computer code & plot in Declan Traill's short essay. All is Bell compliant as he didn't falsify the trick with reversible green/red socks (the TWO pairs of states).
After deriving it in last years figs I only discovered the Poincare sphere already existed thanks to Ulla M during this contest. I hope that helps introduce the ontology.
Peter
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Steve Dufourny wrote on Feb. 20, 2018 @ 11:38 GMT
Hello Ian,
I enjoyed your essay, it was a real pleasure to read.I liked also how you see the works of Wheeler and its geometrodynamics considering the wavesfunctions, it was a relevant Reading, I learn in the same time.
All the best in this contest
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Author Ian Durham replied on Feb. 26, 2018 @ 20:45 GMT
Vladimir Nikolaevich Fedorov wrote on Feb. 22, 2018 @ 06:36 GMT
Dear Ian,
I highly estimate you essay exelent.
It is so close to me. «From its earliest days nearly a century ago, quantum mechanics has proven itself to be a tremendously accurate yet intellectually unsatisfying theory to many». «A universe without structure, without elements is meaningless». «The universe’s existence is independent of our observation of it».
I hope that my modest achievements can be information for reflection for you.
Vladimir Fedorov
https://fqxi.org/community/forum/topic/3080
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Steven Andresen wrote on Feb. 22, 2018 @ 07:09 GMT
Dear Ian
If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don’t rate them at all. Infact I haven’t issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to...
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Dear Ian
If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don’t rate them at all. Infact I haven’t issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to gain.
Beyond my essay’s introduction, I place a microscope on the subjects of universal complexity and natural forces. I do so within context that clock operation is driven by Quantum Mechanical forces (atomic and photonic), while clocks also serve measure of General Relativity’s effects (spacetime, time dilation). In this respect clocks can be said to possess a split personality, giving them the distinction that they are simultaneously a study in QM, while GR is a study of clocks. The situation stands whereby we have two fundamental theories of the world, but just one world. And we have a singular device which serves study of both those fundamental theories. Two fundamental theories, but one device? Please join me and my essay in questioning this circumstance?
My essay goes on to identify natural forces in their universal roles, how they motivate the building of and maintaining complex universal structures and processes. When we look at how star fusion processes sit within a “narrow range of sensitivity” that stars are neither led to explode nor collapse under gravity. We think how lucky we are that the universe is just so. We can also count our lucky stars that the fusion process that marks the birth of a star, also leads to an eruption of photons from its surface. And again, how lucky we are! for if they didn’t then gas accumulation wouldn’t be halted and the star would again be led to collapse.
Could a natural organisation principle have been responsible for fine tuning universal systems? Faced with how lucky we appear to have been, shouldn’t we consider this possibility?
For our luck surely didnt run out there, for these photons stream down on earth, liquifying oceans which drive geochemical processes that we “life” are reliant upon. The Earth is made up of elements that possess the chemical potentials that life is entirely dependent upon. Those chemical potentials are not expressed in the absence of water solvency. So again, how amazingly fortunate we are that these chemical potentials exist in the first instance, and additionally within an environment of abundant water solvency such as Earth, able to express these potentials.
My essay is attempt of something audacious. It questions the fundamental nature of the interaction between space and matter Guv = Tuv, and hypothesizes the equality between space curvature and atomic forces is due to common process. Space gives up a potential in exchange for atomic forces in a conversion process, which drives atomic activity. And furthermore, that Baryons only exist because this energy potential of space exists and is available for exploitation. Baryon characteristics and behaviours, complexity of structure and process might then be explained in terms of being evolved and optimised for this purpose and existence. Removing need for so many layers of extraordinary luck to eventuate our own existence. It attempts an interpretation of the above mentioned stellar processes within these terms, but also extends much further. It shines a light on molecular structure that binds matter together, as potentially being an evolved agency that enhances rigidity and therefor persistence of universal system. We then turn a questioning mind towards Earths unlikely geochemical processes, (for which we living things owe so much) and look at its central theme and propensity for molecular rock forming processes. The existence of chemical potentials and their diverse range of molecular bond formation activities? The abundance of water solvent on Earth, for which many geochemical rock forming processes could not be expressed without? The question of a watery Earth? is then implicated as being part of an evolved system that arose for purpose and reason, alongside the same reason and purpose that molecular bonds and chemistry processes arose.
By identifying atomic forces as having their origin in space, we have identified how they perpetually act, and deliver work products. Forces drive clocks and clock activity is shown by GR to dilate. My essay details the principle of force dilation and applies it to a universal mystery. My essay raises the possibility, that nature in possession of a natural energy potential, will spontaneously generate a circumstance of Darwinian emergence. It did so on Earth, and perhaps it did so within a wider scope. We learnt how biology generates intricate structure and complexity, and now we learn how it might explain for intricate structure and complexity within universal physical systems.
To steal a phrase from my essay “A world product of evolved optimization”.
Best of luck for the conclusion of the contest
Kind regards
Steven Andresen
Darwinian Universal Fundamental Origin
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Gordon Watson wrote on Feb. 24, 2018 @ 11:16 GMT
Dear Ian,
Bell's work takes centre-stage in my research, so your essay (already much annotated) is excellent for me. To keep it simple for now, here's how I parse your Abstract:
"From its earliest days nearly a century ago, quantum mechanics has proven itself to be a tremendously accurate yet intellectually unsatisfying theory to many." This issue is the focus of my research. Please...
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Dear Ian,
Bell's work takes centre-stage in my research, so your essay (already much annotated) is excellent for me. To keep it simple for now, here's how I parse your Abstract:
"From its earliest days nearly a century ago, quantum mechanics has proven itself to be a tremendously accurate yet intellectually unsatisfying theory to many." This issue is the focus of my research. Please see Fröhner, hyperlinked at Reference [12] in my essay; or via direct link to the PDF (which may be slow)
Missing link between probability theory and quantum mechanics: the Riesz-Fejér theorem. "Not the least of its problems is that it is a theory about the results of measurements." Yes, I prefer to speak of tests (which are secondary to the initial beables).
"As John Bell once said in introducing the concept of ‘beables’, it should be possible to say what
is rather than merely what
is observed." Yes, to say also: what
is inferable and not observable; what
is interactively sensitive and what is not.
"In this essay I consider the question of whether a universe can be a beable and what that implies about the fundamental nature of that universe." Spacetime is a beable in my theorising.
"I conclude that a universe that is a beable within the framework of some theory, cannot be fundamental." I conclude that spacetime is fundamental; it provides the framework for my theory.
Since your comments on my theory will be welcome at any time, here is some background from my essay thread:
Background to Wholistic Mechanics (WM)Whereas QM emerged from the UV-catastrophe ca1905, WM emerges from the locality-catastrophe typified by John Bell's dilemma ca1965: ie, seriously ambivalent about AAD, Bell adamantly rejected locality. He later surmised that maybe he and his followers were being rather silly -- correctly; as we show -- for WM is the local theory that resolves Bell's dilemma [there is no AAD] and proves the Bellian silliness.
So WM begins by bringing just one change to modern physics: rejecting naive-realism,
true realism insists that some beables change interactively, after Bohr's disturbance-dictum. Thus recognising the minimum-action associated with Planck's constant, WM then recognises the maximum speed associated with light: for
true locality insists that no influence propagates superluminally, after Einstein.
The union of these two classical principles -- the foundation of WM -- is
true local realism (TLR). Under TLR, EPR's naive criterion for "an element of physical reality" is corrected, then the Laws of Malus and Bayes are validated in the quantum world. Then, via the R-F theorem ca1915, Born's Law is seen to derive from elementary Fourier theory. This in turn allows us to understand the physical significance of Dirac's notation; etc. Thus, beginning with these elementary natural principles, WM's universe-of-discourse focuses on beables in spacetime: with mathematics taken to be our best logic.
NB: Formulated in 1989 in response to a challenging article by David Mermin (1988), many leading Bellian physicists and philosophers have committed to review the foundations of WM and its early results. Since no such review has ever been delivered, I am not yet aware of any defect in the theory. Further, WM provides many ways to refute Bell's theorem (BT): one such is provided on p.8 of my essay.
PS: To those who dismiss my essay due to an alleged typo in the heading, I follow C. S. Peirce (absent his severity): "It is entirely contrary to good English usage to spell premiss, 'premise,' and this spelling ... simply betrays ignorance of the history of logic.” [End of background story]
Ian, warmly appreciating your essay; assuring you that critical comments on my own ideas are welcome at any time;
and with best regards,
Gordon Watson
More realistic fundamentals: quantum theory from one premiss.
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Dizhechko Boris Semyonovich wrote on Feb. 25, 2018 @ 12:08 GMT
Dear Ian Durham, In the basis of the New Cartesian Physics is “true local realism”. For a long time believed that the Foundation for fundamental theories is matter, an attribute which had mass. Once there was a formula of mass – energy equivalence, and mass lost the status of a value characterizing the amount of matter, about it rarely began to remember and physics has lost the Foundation. Any theory of everything is created in such circumstances would not be fundamental. The principle of identity of space and matter Descartes, according to which physical space is matter and matter is space that moves, gives us the Foundation for fundamental theories.
The principle of identity of physical space and matter allows us to use physics to study living matter. For this we need to pay attention to the fact that matter within the body is the same as outside the body. Our brain creates an image of the outside world not within themselves and the space around them. This way the outside world has an active nature, as it controls the body.
New Cartesian Physics needs your support to develop further. Visit my page and give your assessment there.
I hope on highly appreciate her ideas.
FQXi Fundamental in New Cartesian Physics by Dizhechko Boris SemyonovichI wish you success! Sincerely, Boris Dizhechko
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richard kingsley nixey wrote on Feb. 26, 2018 @ 20:16 GMT
Ian,
I won't comment or question as you seem to have disengaged and left many good ones above unanswered so it seems pointless.
Shame.
Richard.
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Author Ian Durham replied on Feb. 26, 2018 @ 20:47 GMT
But you just commented...
Which of the "good" ones did I leave unanswered?
Peter Jackson wrote on Feb. 28, 2018 @ 10:48 GMT
Hi Ian,
I'd hoped you'd answer mine, and the only other one seems to be Gordon Watson's. Richard was one of the few who made the effort to follow and check out the classical QM derivation and agreed it. Declan Traill's plot shows the correlations are correct with loophole closed, so the mechanism explains the low intensity geometry inadequate to trigger 'clicks' in terms of the minor axis of highly elliptical 'polarity'.
But Richard's not a full time professional in the field like yourself so your own unencumbered analysis would be greatly appreciated.
How familiar are you with the spin stats theorem SST? You'll probably know what I learned; that in the SST the SO(1,3) group can be decomposed into the direct product of two different SU(2) subgroups. The Lie algebras of the two different groups can be exchanged by hermitean conjugation. This implies that one SU(2) group is left handed and the other is right-handed. Also the Dirac spinor we're so fond of is actually a left-handed spinor stacked on top of a right-handed spinor (a 4-component spinor). The stacked spinors can be exchanged by hermitian conjugation.
One of the spinor representations (let's say the left-handed one) corresponds to a matter particle. The other (conjugate) representation corresponds to an antimatter particle. The Dirac equation is nothing more than a projection operator which projects out either the upper spinor or the lower one.
None of that is needed for the derivation ontology & mechanism and it's incomplete anyway, but can you see how it all corresponds?
All shocking I know, but now you've had a couple of weeks to get used to the new way of looking. Heisenberg 'position' was only a guess as 'momentum' seemed to have been 'taken', but that really means more 'orbital' position, which is the the 2nd orthogonal momentum. I can't recall; Did you see the non integer spin derivation & video?
Very Best
Peter
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Author Ian Durham replied on Mar. 1, 2018 @ 20:23 GMT
Hi Peter,
Well, to be perfectly honest, I'm really not entirely sure what you're trying to say. So when you ask if I see how it all corresponds, my response is how all *what* corresponds?
Ian
Peter Jackson replied on Mar. 2, 2018 @ 10:40 GMT
Ian,
My Feb 24 post outlines the classical mechanism in the essay.
I'm saying that if we start with the Maxwell/(Poincare Sphere) 4 momenta state for electrons and the pairs (rather than 'no' assumption or superposed 'singlet' states) then with a simple momentum transfer ('measurement') mechanism, the entire tranche of QM predictions and findings can be reproduced with classical mechanics & modern photonics.
As a good scientist I'm sure you won't let shock or cognitive dissonance make you dismiss the concept or run and hide. The computer plot confirms the result, so the question is, as an expert, can you identify where the mechanism may be 'wrong' or what it 'misses'?
The key to EPR resolution is that A,B polariser field directions are reversible, and the 'measurement' on interaction is either 'SAME' or 'OPPOSITE' vector (then an amplitude pair subject to y,z axis ellipticity on orthogonal axes).
So if we have A,B +,-, either can reverse setting angle to get A,B +,+ or -,-. Cos distributions are implicit in the Poincare sphere (as I show), applied a 2nd time at the photomultiplier. In between +1,-1 are then Bayesian distributions, so 'undecidable' at 90o.
So beyond a local interference range NO 'action at a distance' is required to explain the outcomes!!
This is such a leap of understanding it needs an acknowledged expert to either falsify or confirm it. Not that difficult a task!
Very best
Peter
PS Do contact me direct, on;
pj.ukc.edu@physics.org
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Author Ian Durham replied on Mar. 4, 2018 @ 03:45 GMT
Peter,
Let's start with your first sentence:
"I'm saying that if we start with the Maxwell/(Poincare Sphere) 4 momenta state for electrons and the pairs (rather than 'no' assumption or superposed 'singlet' states) then with a simple momentum transfer ('measurement') mechanism, the entire tranche of QM predictions and findings can be reproduced with classical mechanics & modern photonics."
My first question is, I assume that you're talking about the Poincaré sphere from optics? What does that have to do with 4-momentum states? And I don't understand what you mean by "and the pairs".
Ian
Juan Ramón González Álvarez wrote on Mar. 1, 2018 @ 19:59 GMT
Finally it was an ox, and the mathematician, the economist, and
the logician were all wrong.... ;-)
Quantum mechanics is a theory about quantum motion. Measurements would be explained by the theory.
Bells' beables aren't really needed or useful, and several of his definitions only add confusion to a topic which already has a good amount of it.
Indeed the universe is colloquially "the totality of everything that
exists". There is no problem with the idea of multiple 'universes'; they would be simply regions of the real universe. The problem here is on Everettians that want to change the meaning of universe to pretend that there are many.
The operational definition confounds the universe with the observable universe.
Defining the universe based in a based on a wavefunction is wrong. First because wavefunction is a definition of a state of an object not the object. Second, because wavefunctions only can describe some quantum states. And using wavefunctions associated to the WdW equation even adds more problems, because the equation is wrong, as even one of his authors admitted.
"IS THE UNIVERSE FUNDAMENTAL?" No. The universe is a collection of particles.
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Gordon Watson wrote on Mar. 15, 2018 @ 07:04 GMT
Dear Ian; further to my earlier comments, please: Since
we cannot both be right, would you mind commenting on my half-page refutation of Bell's theorem?
See ¶13 in
More realistic fundamentals: quantum theory from one premiss.
NB: I clarify Bell's 1964-(1) functions by allowing that, pairwise, the HV (λ) heading toward Alice need no be the same as that (μ) heading toward Bob; ie, it is sufficient that they are highly correlated via the pairwise conservation of total angular momentum. Thus, consistent with Bell's 1964-(12) normalization condition:
Further, in my analysis: after leaving the source, each pristine particle remains pristine until its interaction with a polarizer. Then, in that I allow for perturbative interactions, my use of delta-functions represents the perturbative impact of each such interaction.
My equation (26) then represents the distribution of perturbed particles proceeding to Alice's analyzer. Thus (with b and μ similarly for Bob):
PS: Bridging the continuous and the discrete -- and thus Bell's related indifference -- integrals are used here by me for generality. Then, since the arguments of Bell's 1964-(1) functions include a continuous variable λ, ρ(λ) in Bell 1964-(2) must include delta-functions. Thus, under Bell's terms, my refutation is both mathematically and physically significant.
PLEASE: When you reply -- or if you will not -- please drop a note on my essay-thread so that I receive an alert. Many thanks; Gordon
Current FQXi essay
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Author Ian Durham replied on Mar. 16, 2018 @ 17:23 GMT
Hi Gordon,
I will have to read your essay, but I will say that you can't really "refute" Bell's theorem. It's just a theorem. What you seem to be presenting is an alternate view, i.e. that Bell's derivation of his inequalities used a certain set of conditions that you think does not capture all of reality. There's nothing necessarily wrong with that, but that doesn't mean Bell was necessarily wrong either.
Anyway, I will try to get to reading your essay soon.
Ian
Gordon Watson replied on May. 29, 2018 @ 02:22 GMT
Dear Ian,
Congratulations of your success in the essay contest!
Is it too much for me to now hope that this success has bought you some time to defend your view re Bell against my own: so that my essay-writing might improve?
For, in the context of EPRB, Bell believed: "In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant.” Subsequently, by his own admission, he lived with the unresolved dilemma of AAD: yes or no.
In my Lorentz-invariant theory -- and in the context of EPRB -- I bring local (non-contextual) hidden-variables to quantum mechanics to determine the results of individual measurements without changing the statistical predictions. So it seems to me that AAD and well-known Bellian inequalities and claims are thereby refuted.
With my best regards, please let me know if you'll not be critiquing my view; Gordon
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