Hello Joy, Michael.

Joy - thanks so much for your note! It's good to hope that we're working on pieces of a puzzle that will ultimately fit together - as opposed to random scrap on the junkyard ... :)

Michael - your work on finding symmetries of the Standard Model from the parallelizable spheres reminds me of Geoffrey Dixon's. Are you familiar with his work? He's been advocating such a model over the past decades. You find points and references from his site: http://7stones.com/ with free material e.g. from http://7stones.com/Homepage/AlgebraSite/algebra0.html , "U(1)xSU(2)xSU(3): Original Derivation". If I remember correctly, Dixon proposes a 9+1 dimensional background geometry of nature (but I better stop here before writing something wrong). A newer approach to using such spheres comes from a somewhat different, algebraic angle: Cohl Furey's "Unified Theory of Ideals" ( http://arxiv.org/abs/1002.1497 ; recently accepted into PrD as I just found out!).

What keeps me from being a Platonist in the vein of Penrose, Godel and Rick Lockyer -- though I have the highest respect and admiration for all of them -- is exactly the dichotomy that Michael describes, between the language of nature and the facts of nature.

Joy, that's what compels me to accept Bell's theorem as a mathematical truth, while acknowledging that your topological framework is far superior for describing quantum correlations in a mathematically complete and physically falsifiable schema.

Mathematics always depends -- exactly as natural language depends -- on rules and assumptions. Take the Banach-Tarski paradox -- mathematicians know that the name is historical; it isn't actually a paradox though it is a highly counterintuitive construction. Dropping an assumption changes the game, however -- can one prove B-T without the axiom of choice? (I hope to someday, in fact.) Point is, that dropping assumptions -- paring a proposition to its bare essentials -- is the very definition of mathematical beauty. It's what attracted me to the Joy Christian framework like a moth to flame -- the idea that globally continuous measurement functions share identity with locally real results isn't something that one just wakes up believing in. It means suspending belief, in favor of a deductive argument and rational correspondence between the mathematical theory and physical result. Proving quantum correlations without assuming nonlocality is absolutely equivalent to proving the B-T construction without AC.

Don't speak to me of "disproof" -- speak to me of correspondence between language and experience.

Best to all,

Tom

Hi Tom,

Here is a statement of Bell's theorem by Abner Shimony (the S in the Bell-CHSH):

"No physical theory which is realistic as well as local [in the senses specified by EPR and Bell] can reproduce all of the statistical predictions of quantum mechanics."

And here is a Disproof of Bell's theorem.

Bell's so-called theorem was NOT a mathematical theorem. Its defenders would very much like to promote it as an ironclad mathematical theorem. But that is just selling tactic, not scientific truth.

Joy

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  • Post #104

Joy, no mathematical theorem is a scientific truth. It's a mathematical truth; that's what "theorem" actually means. Science and mathematics are not identical, even though we speak informally of the "mathematical sciences."

From the beginning and to this day, I have maintained that there is not a mathematician in the world who will agree with you that a theorem can be disproved. If that were the case, we wouldn't need mathematics to describe the natural world -- because we couldn't distinguish between events and numbers. That is, in fact, the very weakness of Bell's theorem that you spotted -- whether you are consciously aware of it or not -- and corrected.

Bell's theorem is perfectly sound as a theorem of arithmetic; on the interval {0,oo} there exist integers such that a bijection dependent on orientation of copies of N on the plane compels an inequality of the bijective sets. Easy to prove.

Problem is, the plane is not orientable. The existence theorem in arithmetic applied to Bell's experiment has the observer orienting the events by fiat, and ordering the numbers by the rules of arithmetic, and hence we get an observer created reality.

You are absolutely right, and I am your strongest defender -- a topology solution answers the challenge to have an objective, non-anthropocentric physics with a natural orientability that obviates nonlocality and preserves the observer's free will. I'm no voice in the wilderness, either -- I agree without qualification with what Boris Tsirelson told you on his Wikipedia talk page: "Evidently, your idea of Nature is substantially different from that of EPR, Bell and many others. Basically, Bell theorem says that Nature cannot be what is was assumed to be. Quantum theory proposes one new kind of Nature. You propose another new kind of Nature. So what? It will be exciting if your proposal will ultimately work better that quantum theory. But even that will not disprove Bell theorem. If the old kind of Nature is dead anyway, then Bell theorem is alive. So, here is your choice. Either you waive your author rights on the S^3/S^7 physics and kill Bell theorem, or you keep your author rights on the S^3/S^7 physics and withdraw your claim against Bell theorem. Wow! Your decision will tell us, whether you really hope that your S^3/S^7 physics will replace the quantum theory, or not. Surely you do not want to miss Nobel price and instead win a battle on Wikipedia! Boris Tsirelson (talk) 10:02, 4 June 2012 (UTC)

Trust, Joy that your physics *does* work better than quantum theory, and leave the theorem proving to the mathematicians. For surely, a purported disproof is identical to a proof which disproves itself. You'll never be able to escape that logical strait jacket. Don't let them put you in it!

As always, all my best,

Tom

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  • Post #105

Must have been logged out. The above is mine.

Tom,

You missed my point, as did Boris Tsirelson. Bell's so-called theorem was never a mathematical theorem. The word "theorem" in this context is simply a sells tactic, and you have fallen for it.

I have not disproved any mathematical theorem. That has never been my claim. This was a claim imposed on me by Philippe Grangier. Please read my reply to Grangier.

What I have disproved is the following statement of a so-called theorem:

"No physical theory which is realistic as well as local [in the senses specified by EPR and Bell] can reproduce all of the statistical predictions of quantum mechanics."

I categorically and strongly object to the mischaracterization of my framework by Boris Tsirelson (which you have quoted). Please read my reply to Boris on his page. In particular, I strongly object to his statement that "[my] idea of Nature is substantially different from that of EPR, Bell and many others." This statement is preposterous.

I stand by my use of the word "disproof." Neither Abner Shimony, nor any other well known foundationalists like Lucien Hardy, has ever objected to my use of the word "disproof" in this context. Only mathematicians have a problem with the word, and for all the wrong reasons. What has been disproved was never a theorem to begin with.

The issue is purely linguistic as far as I am concerned. It is not worth debating about.

All best,

Joy

On the idea that I may as well be hung for a sheep as for a lamb, let me add that Abner Shimony's statement ...

"No physical theory which is realistic as well as local [in the senses specified by EPR and Bell] can reproduce all of the statistical predictions of quantum mechanics."

... is also true.

The problem is, there's no way to prove it false. That is, if there is no physical domain that is both local and real, Shimony's tautology says that the probabilistic nature of quantum mechanics (nonlocal and real) is physical.

Just as Einstein held, though, if quantum mechanics were a complete physical theory it would necessarily describe the whole of reality in discrete quantum numbers. No statistical theory can do this.

What a classical, deterministic theory can do, however, is to specify the physical domain as a bounded continuum. That the bound of 4-dimension spacetime (Minkowski space) includes the 3-manifold as a local plane of measurement space -- a complete theory need only extend the bound to show that global distant events are also manifest on that local plane as a function of measurement continuous from an initial condition. Joy's topological framework meets that standard -- statistical inference on a bounded domain of globally continuous measurement functions means something quite different than that on an unbounded space of probability measurement.

Tom

Hi Joy,

Our replies crossed. I posted mine before I read yours.

We agree on everything except whether the issue of disproof is worth debating. You're absolutely right that only mathematicians are concerned about it; not as a debate, but as a principle of mathematical logic.

I've always said I agree with Grangier and Tsirelson on this relatively narrow yet important point.

Thing is, there may be methods of formal language that will preempt conventional mathematics in the future -- Lev Goldfarb's ETS formalism, Gregory Chaitin's experimental mathematics, and Steven Wolfram's prgram are possible examples -- yet any of these systems have to remain internally self-consistent, or else there's no need to even have a formal language to describe natural phenomena.

Yes of course I read and comprehended your reply to Boris "... A possibility is that we will find exactly where the boundary lies. More plausible to me is that we will find that there is no boundary. ... It is this possibility, of a homogeneous account of the world, which is for me the chief motivation of the study of the so-called 'hidden variable' possibility.'" I even agree with your reply. That doesn't change my mind that Boris is correct that the mathematics of Bell's theorem is true -- it's an easy sell, if that's the way you think of it. There's plenty of trivial mathematics in the canon.

All best,

Tom

I wanted to deal with this separately:

"I strongly object to (Boris Tsirelson's) statement that '[my] idea of Nature is substantially different from that of EPR, Bell and many others.' This statement is preposterous."

Preposterous to you, Joy, because you know intimately the topology by which you support your conclusions. Put yourself in the position of those who are not living in that framework. My own first reaction to your claim that Bell based his theorem on the wrong topology was, "So what? He wasn't doing topology." And that's true. Neither EPR, nor Bell, were aware of any topological implications of a complete local realistic theory -- and most still aren't.

Being right and being believed aren't always congruent. We can only strive to stand on the side of truth, even against belief.

Tom

Tom,

Boris should have known better. He is a very competent mathematician (unlike some we have encountered in the recent past). His mischaracterisation of my work stems, not from his lack of understanding of any mathematical concept such as topology, but from his total disregard for the original arguments by EPR and Bell. Here is what he says about Bell's own paper: "And frankly I never read carefully the original Bell's argument... Why? Just because I do not care much about the history of physics etc..."

After making such a startling confession, how can he go on to claim that "[my] idea of Nature is substantially different from that of EPR, Bell and many others"? What does he know about Bell's idea of Nature, let alone that of EPR? He has not even read Bell's original paper, let alone read that of EPR and the later crucial elaborations on their paper by Bell, Clauser, Shimony, and others which I have closely followed in my analysis. So, I am afraid, I am not impressed by Boris's wrongful assertions about my work.

Best,

Joy

Hi Joy and Tom,

I agree that the issue of "disproof" is a linguistic one, but I would argue that it is an important one as the underlying issue is the choice between maths or physics. The use of the word "theorem" in the Bell context is a choice of maths meaning that is "simply a sells tactic" in the physics context, and until I read Joy's work I too fell for it.

I would question continuing to group EPR and Bell together as if they were dealing with the same physics context, as Joy's work shows that Bell's context is not the correct physics context for EPR - Joy's starting point is a statement of observational physics, for which one feels rather silly for not having noticed before. The real point in physics is that Bell's "theorem" is not the barrier to QT not being fundamental that the usage of the word "theorem" implies. Usage of "theorem" has been a very effective sales tactic that has effectively prevented searches for alternative explanations for QT for decades. In the physics context of what "Bell's theorem" has been claimed to mean, "disproof" seems appropriate to me.

I think that we probably agree that "no mathematical theorem is a scientific truth", the problem is that a great many physicists believe that Maths=Nature, which entails the belief that "a mathematical theorem is a scientific truth". It seems to me that some of the opposition that Joy is encountering is due this belief (the character of some of the responses seem to indicate that it is not a rational belief).

Michael

Yes Michael, I tend to agree with what you have summarized.

We know, at least since Wigner, that interplay between maths and physics is a subtle one, and one has to be careful not to get carried away by maths as if it were physics. But maths is a siren too tempting for some, including myself.

Joy

Hi Jens and Tom,

There is a definite connection with Geoffrey Dixon and Cohl Furey - the difference is the discrete part of countable particles (by * I mean otimes):

Dixon considers the algebra: T=C*Q*O

Furey considers the algebra: R*C*H*O

I consider a physical manifold: S0*S1*S3*S7

The difference is between the space of an algebra and considering the physical manifold for a cyclical (S1), closed universe (S3) with compactified particle dimensions (S7) in 11D GR without *any* additional fields. The previous issue with such pure geometric theories such as Kalzua-Klein theories has been: no particles, the discrete part - S0 for particle/anti-particle - has been missing. The existence of a non-trivial map (electroweak vacuum) from the S7 to the S3 is *critical* here, because it breaks the sphere S7 into S3 fibre and S4 base-space which further separates into S3 and S1. This transition from S7 to a space locally of the form (S3*(S3*S1)) gives the condition for topological monopoles/anti-monopoles and the required S0 to give the full picture with discrete particles - the correct spectrum of 12 fermionic topological defects. The same algebraic structure which gives the correct eigenvalues in the algebraic case of Dixon and Furey gives the same eigenvalues for the topological defects - despite a colour difference.

It is on this point of deriving the discrete part S0 of particles/anti-particles that my physical manifold framework differs with the others, and the pure octonion view. In those views the discrete part of particles has to be explicitly added *on top of* the algebraic view. Adding a continuous real number valued field, i.e. R, to the algebra of C*H*O (i.e. Furey) then has to add a means of getting the discrete part S0 from R for particles/anti-particles. This is natural for QT being fundamental - but it isn't! (see Joy's book or mine, or the papers).

The comparison of my results with those of Dixon and Furey reveals the critical difference and what may turn out to be the deciding factor:

1) If QT were fundamental then R*C*H*O would be the right (algebraic) choice and the colour group SU(3), but matter fields, electroweak vacuum and QT would have to be added by hand

2) If QT is not fundamental then the continuous physical manifold S1*S3*S7 with a twist in it (electroweak vacuum) gives discrete particles S0 and QT is *derived* as a change in mathematical representation, but the colour group would be locally SO(3) (not globally SO(3) because the colour space is S3 fibre of S7) by identifying physical spaces with group spaces. This identification gives the correct coupling constants for SU(2) and U(1) (and Weinberg angle) as geometric scale factors between the physical sub-spaces of the broken S7 and the unit spheres of the group spaces.

QT is proven *not* to be fundamental by 2 different routes (mine and Joy's). How to get QT and the discrete S0 of particle/anti-particle is the critical element - which is why it is the topic of my essay. What is the fundamental assumption standing in the way of physics? Answer: assuming QT is fundamental.

Michael

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  • Post #114

Hi Michael & Joy,

Good discussion.

Allow me to reference the title of Michael's essay. I think we all agree that the answer is "no." I think we can all agree that the continuum cannot be deduced from the assumption of discrete elements in a multiply connected space.

If I capitulate to agreement that Bell's theorem should never have been called a theorem, however, I am compelled to say that the arithmetic arguments of Gill, Moldoveanu, Aaronson, et al are wrong. Except they aren't. According to all mathematical logic as we know and accept it, Bell's theorem and the inequality argument derived from it, is a logically closed judgment of how numbers behave -- as simple an an Excel program, as Gill describes it. As simple as a 2-player game with four outcomes and no equilibrium point, as Aaronson describes it. Anything we program as a continuous iteration of discrete values in a nonorientable measure space is going to give us those results, because the space is not simply connected. The outcome probabilities are true.

Michael, I am not convinced that most physicists think maths = nature. I think that they just don't care about the role of mathematical language in physics, and really why should they in any operational sense? One can roll the dice, input data to an Excel program, or feed random bits to Alice and Bob, and see what happens.

To convince someone that E(a,b) = - a.b requires the same level of physical demonstration as E = mc^2 because we cannot see a full 4pi rotation in a simply connected space that Joy's result implies, any more than we can see the atomic binding energy that supports Einstein's result, until after experimental data are compiled. So it is at least as clear to me -- as I think it is to Boris Tsirelson -- that there *is* a profound difference between conventional interpretations of quantum theory via Bell's theorem -- and Joy's framework, which is not another QM interpretation but an entirely different framework for predicting quantum correlations.

I don't want to be put in the position of debating the meaning of "theorem" with mathematicians, because I know I am going to lose if I allow a theorem to be the subject of disproof. When I talk to a mathematician, I want only to be clear that we are working in the same domain and range. Sure I agree with you both that Bell's theorem does not apply to the physical domain -- I said so in my essay. Only after we establish domain and range, can we speak of proof. So one can say that Bell's theorem is not proved in this domain of continuous measurement functions, not that it is disproved in some domain of probability measure.

All best,

Tom

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  • Post #115

Don't understand why I keep losing my log in. The above is mone.

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  • Post #116

" What is the fundamental assumption standing in the way of physics? Answer: assuming QT is fundamental."

Nailhead, meet hammer.

Tom,

"...Bell's theorem is not proved in [the] domain of continuous measurement functions, not that it is disproved in some domain of probability measure."

Fair enough.

What interests me and Michael, though, is that Bell's theorem is disproved in the *physical* domain. Who cares if it is proved in some mathematical domain that is irrelevant to physics?

Joy

"What interests me and Michael, though, is that Bell's theorem is disproved in the *physical* domain. Who cares if it is proved in some mathematical domain that is irrelevant to physics?"

We don't know what mathematical domain (if any) is irrelevant to physics. We do know, however, that the physical domain can be defined as the complete space of continuous measurement functions. Your framework captures it. Bell's doesn't.

Tom

"We don't know what mathematical domain (if any) is irrelevant to physics."

True.

But we *do* know---and precisely so---what physical and mathematical domains are relevant in the context of the EPR-Bohm experiment, which is the context of the Bell's so-called theorem. Bell and his followers were mistaken to think that his theorem is applicable in these domains. It is not, as I have shown.

Joy

Hi Tom,

I said many - not most - physicists seem to believe Maths=Nature; some can be found in this essay contest. Being lax about the role of mathematical language in physics can lead to explicit or implicit assertions of the form Maths=Nature slipping into physics unchallenged by those who don't share this belief; the claim that Bell's theorem applies to EPR seems to be one of them. The standard interpretation of QT doesn't depend on Bell; only the false "proof" of don't bother looking past QT depends on Bell and this gives the physics sense for Joy's "disproof". Joy's initial correction about the analysis of EPR (1 to 2):

1) A(n,l): R3*L -> S0

2) A(n,l): R3*L -> S2 sub S3

is basically just a piece of observational physics that is framework independent. An alternative description for Bell's Theorem would be that it is irrelevant to physics, but this fails to take into account the impact that the "proof" has had on physics. The phrasing of a "disproof" that the maths doesn't apply to EPR conflicts with maths usage and is consequently contentious, but on the other hand it parallels the inappropriate use of "proof" in the first place - which is really the point of Joy's work.

Joy's framework does have a non-trivial topological condition that differs from the flat empty space normally taken to be the background for QT. It is a condition I am happy with because the EPR scenario doesn't involve flat empty space, but the space around two particles and Joy's correlation results reproduce QT for this space not being the same as empty space far away from particles. In my case, particles are topological defects in spatial structure and so the space about 2 particles is non-trivial. For the conditions of EPR, space would be flat because the spatial curvature is within the hidden domain, but charges in dimensionally reduced theories give torsion in space - the same basic topological conditions on space as required for the correlation.

Einstein's hoped for elimination of probabilities from predicted measurement results doesn't really work out with a hidden domain because it is ... well ... hidden. So all measurement results involve an average over the hidden domain - such as Joy's correlation results. The difference is that this is just a normal classical physics average and not a "weird" quantum physics one - whether this would have quite hit the spot for Einstein is debatable.

Michael