Dr. Kadin

I apologize for not having yet commented on your essay, I am woefully behind!

I agree with you that seriously reconsidering quantum theory is drawing much less attention in this FQXi contest than it should be - it is as if it is the assumption that still cannot be questioned, even when all other assumptions are up for grabs! My essay makes a rather more serious challenge to the assumptions of quantum theory than is perhaps initially apparent, and proceeds to show that QT isn't fundamental as its mathematical form can be derived by a change in mathematical representation.

It is not just us essay contestants who are encountering problems challenging the assumption of quantum theory. Joy Christian's work shows that Bell's theorem doesn't prove that QT has no replacement - which effectively seems to me to amount to a proof that QT isn't fundamental - and has been getting serious stick, as opposed to being ignored. My essay outlines a totally independent proof of the same thing. In strict physics terms this opens the door to seriously questioning the status of QT, and hopefully this may happen before the end of the contest.

I think your closing lines nicely capture what's gone wrong with physics:

"Generations of physicists have been educated to ignore physical intuition about the paradoxes, while focusing on mathematics divorced from physical pictures. In response, the field of theoretical physics became more mathematically abstract, straying far from its origins explaining the behavior of real objects moving in real space."

Incidentally, the same is also true of general relativity, which has become something of a mathematical map detached from its physical territory - a trend which looks as though it is set to get a lot worse with notions of emergent dimensions.

Michael

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  • Post #73

always a poor team still of strategists full of hate, still a poor band of frustrated, probably that your young life at school was difficult, probably that you makes a kind of revenge in making the bad. Jonathan , I have pity my friend and for your frustrated friends also. You are not foundamental, nor universal, nor relevant and still less an imrpover. Let me laugh in seeing your poor strategy and your hate increasing. I love USA and I am christian.

What is your poor probelm ? the vanity. I don't know me, buy a bibble and makes a redemption.I don't know, you are not relevant in fact even in your strategy.

Become a murder, it is better you know. And we shall see how shall be your humility in front of our god. You are a comic.Ok he said, ok.

Hi Joy,

I am currently reading your book, and it is the highlight of my year! - unless I am completely missunderstanding it ;-)

Your disproof of Bell's theorem seems to me to be effectively amount to a proof that QT is not fundamental, as your model demonstrates that a local classical physics theory *can* exist, would I be correct? If so, then my proof is a totally independent proof that QT is not fundamental. Now that I am coming to understand your work better I think that my work is related - I have come from the physics side, whereas you have come from the maths side.

It seems to me that the usage of the word 'local' is causing problems, because it can have several meanings. This is the point I was trying to make with my diagram in the attachment below. Your usage of the word 'local' seems to correspond to the physics intuition of a continuous path of subluminal causation, whereas there is also 'local' space-time separation in relativistic dynamics and the two won't be the same if the background metric changes. The illustration seems to provide the only way I can think of squaring physics intuition 'local' with apparent non-local space-time separations. Since your analysis is for R3, is it possible that such a relativistic change in metric signature is being captured in the global structure of the S3 function space?

Chapter 7 gives the general case as being a local function of the form

A(x,l): X*L -> Y sub Z

Where x is some orientation in the space X, and Z is constrained to be either S3 or S7. For the common case of spin orientation - which is an internal particle property - x is a 3-vector and X=R3. It seems to me that the same argument would apply to the gauge orientation x of the internal particle property space of gauge symmetries. As the isospin group space is S3 and electromagnetism is S1, the option of Z=S3 is too smal ... which *only* leaves S7. Is this correct?

I register that this S7 could also be flat as well. I don't yet know how this would square with my S10 unified field theory as I am currently on chapter 7.

MichaelAttachment #1: 2_Local_to_nonlocal.pdf

Hi Michael,

Thank you for your kind words. I think we are on the same page as far as the understanding my central message is concerned, but we may have different views about some of the details.

In particular, you are correct to read my disproof as a proof that QT is not fundamental. The credit for this observation, however, must go first to Einstein, and then to Bell, before my work is even considered. Einstein argued most of his life that QT is not a fundamental theory, and Bell's work (which is based on the earlier work on hidden variables by von Neumann) clarified and quantified Einstein's position tremendously. My work is entirely in the tradition of Einstein, von Neumann, and Bell, but of course these giants do not consider going beyond the algebra of the real line, whereas both you and I consider the most general division algebra possible, namely the octonionic algebra, associated with S7. I too feel that our work is related, but I must admit that I haven't had time to digest some of your arguments (these days I am preoccupied in clarifying the relationship between SU(2) and SO(3) even further to understand the issue of "flatness" you alluded to above).

You have rightly raised the question about my usage of the word "local." I have used a very precise definition of "local" provided by Bell. This definition is theory-independent. In particular, it is independent of relativistic considerations. On the other hand, it may not remain valid if the space-time metric itself changes its signature during the course of dynamics, say, of an EPR pair. I am not sure whether a relativistic change in metric signature of the kind you have considered is captured in the global structure of the S3 function space. My feeling is that if such a change in signature is allowed then strong quantum correlations would be wiped out. That is not such a bad thing, however, for we do observe both quantum as well as classical correlations. In fact, more often than not we observe classical correlations rather than quantum correlations.

I think you are right to think that the same argument would apply to the gauge orientation x of the internal particle property space of gauge symmetries, with S7 substituted for S3. But the details here are beyond my field of expertise, so I am unable to be all that confident about this.

The octonionic S7 is indeed flat, and it is this discipline of "flatness" of S7 that is responsible for the strong quantum correlations. That is my claim in any case.

Thanks again for your kind words about my book. It is good to be appreciated.

Best,

Joy

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  • Post #76

Michael

"Concerns can also be raised about the gravitational "constant" G and the "constant" speed of light c, asking...

Your concerns is valid.See my essay

http://fqxi.org/community/forum/topic/1413

Dear Michael

Your paper is very interesting.See my essay

http://fqxi.org/community/forum/topic/1468

I believe QM is not As Fundamental As It Seems

If we want to reconcile quantum, we should give up one implicit assumption we tend to forget: the differentiability. What would be the benefits of these changes? It has many surprising consequences. We show that the weird uncertainty principle and non-commutativity become straightforward in the circumstances of non-differentiable functions. It's just the result of the divergence of usual definition of \emph{velocity}. All weirdness of quantum mechanics are due to we are trying to making sense of nonsense.

Thanks,

Xiong

Hello again Michael (and Joy),

It gives a whole new meaning to the term 'fabric of space' when you are talking in literal terms about fibers in the bundle from the Hopf fibration of S3, which constitute that fabric. I'm continuing here where my comments will be visible.

My understanding is that it's the parallelism within that fibration which produces both correlations and flatness. The fact that S3 and S7 are parallelizable is what guarantees - in effect - that this is what will happen when we examine how the fiber bundle is disposed in these spaces.

I too am reading Joy's book, but I have not gotten too far yet. Ergo; given some familiarity with the topic of debate, most of what I have read so far is familiar and easy to follow.

It would appear that both your work Michael, and Joy Christian's, point to a road by which Quantum Mechanics may be derived emergently. Curiously, it also ties in with some theoretical ideas I've been working on for a couple of decades, or at least it appears that it may.

More later,

Jonathan

    Hi Jonathan,

    I will let Michael respond to your comments in his own way, but let me just endorse two of your observations:

    "My understanding is that it's the parallelism within that fibration which produces both correlations and flatness."

    This is essentially correct as far as parallelism is concerned, but one need not consider fibrations of S3 or S7 at all to parallelize them. Since both of these spheres are simply-connected spaces, their parallelization amounts to vanishing of their Riemann curvature tensors. This ensures that torsions within them would be non-vanishing, because otherwise they would reduce to flat Euclidean spaces. Fibrations thus simply provide nice visualizations of these features. Full details on this can be found in Chapter 7 of my book. In addition, I am currently working on a new paper that may clarify the issue of parallelization further, at least in the case of the 3-sphere.

    "It would appear that both your work Michael, and Joy Christian's, point to a road by which Quantum Mechanics may be derived emergently."

    This is correct. In fact I have already derived ALL possible quantum correlations within my local-realistic framework, thus reproducing the kinematical part of quantum mechanics in toto. Moreover, my latest FQXi grant is for investigating how the dynamics of quantum theory would emerge from my framework. So far no progress has been made in this front, but, as they say: watch this space.

    Joy

    Hi Jonathan,

    Taking the "fabric of space" as literally being a physical surface is the first assumption of my STUF-Theory, the second is that this physical surface realises *all* of the spheres S0, S1, S3, S7. This comes from the relevance of the normed division algebras to metric spaces, and the Relativity meta-principle of make no preference - so all of them. The map condition from S7 -> S3 could be added as a pre-condition, but I think that will come unstuck on the cyclicality S1 of the closed S3 universe. So the unification principle - S3 and S7 unified in S10 - perhaps doesn't really have the status of an assumption. I then apply GR to this assumed physical surface in the extended number of dimensions. Despite appearances, I make NO further assumptions beyond the unification being undone S10 -> S3 * S7 and the non-trivial map S7->S3.

    The Kaluza-Klein style of theory results from a compactification-inflation see-saw powered by the transfer of radiation from S7 to S3. This gives the compactified dimensions of a KK style theory, but this is NOT an assumption. It follows from a *correction* to GR to make it into a physical theory of a physical 'fabric of space' - global conditions applying to a closed space require the cosmological term to vary with radius (see attachment). Not having such a dependence is a simplistic error that is neither mathematically nor physically correct. Like Joy's correction to Bell's assumed S0 space, it is a naïve mistake that is quite astonishing we have gone along with - revealing the power and dangers of group-think euphemistically labelled 'scientific consensus'.

    With a quantum field theory background I haven't fully switched my thinking to all the repercussions of a physical 'fabric of space' and what it physically means for a closed universe to be the fibre-bundle S3. I hadn't registered that it meant there could exist non-standard connections between gravity and particle decays until your Sept 4 comment.

    MichaelAttachment #1: Balloon_world.pdf

    FQXi'ers - On the connection of my work to Joy Christian's (in parts because it's long)

    Joy expressed Bell's analysis about whether there could exist a 'complete' 'local' theory that could replace Quantum Theory, as Bell considering functions of the form

    A(n,l): R3 * L -> S0 (see eqn 1.1)

    R3 is a co-ordinate based denotation of the flat Euclidean space E3 in which the 3-vector orientation n resides, the space L is a space of 'hidden' variables which gives 'complete' states and S0 is the function co-domain for the observable A. Joy identified that the function co-domain S0 is rather trivially wrong, it should be S2 sub S3 (see eqn 2) as the possible orientations of the 3-vector n define a 2-sphere. Quantum correlations follow from the topology of the spaces.

    My work effectively addresses what is meant by 'hidden' variable and 'complete' states in physics, neither of which were sufficiently well-defined by Bell. There are effectively 2 different underlying meanings for 'complete'

    1) mathematical completeness - every theorem in a formal system can be derived

    2) scientific completeness - every observation can be predicted

    Bell fails to specify which he means. This shortcoming can be viewed as originating with the original EPR paper which gives the meaning of 'complete' as: "every element of the physical reality must have a counterpart in the physical theory". But this isn't physics! It fails to specify how you would verify that this was true - namely by experiment. This is why I use 'physically-real' to specify a term in a theory that *directly* corresponds to an observable feature in reality (I took this term from a QT textbook discussion of Bell's theorem). Any mathematical term which does not have this 1-to-1 correspondence is a 'non-physically-real' term, eg. the wave-function denotes strictly countable numbers of electrons by the real-numbers, and since 0.5 of an electron is never measured in an experiment, the wave-function is a non-physically-real term.

    There are also 2 possible meanings for 'hidden' and Bell fails to specify which

    1) hidden from the subset A, B of observables considered in a correlation experiment - in which case the hidden variable could be found in the future by a new experiment

    2) hidden from all possible observables - in which case it is a non-physically-real term!

    Option 2 is what is implicitly meant by Bell, but how such a conspiracy of Nature could arise is not considered. The missing element is dynamics, which is because the physical space of the EPR scenario isn't just Euclidean space E3, but a Euclidian sub-space of Minkowski space-time M4. There are an infinite number of ways of picking out E3 from M4, parameterised by the velocity v of the reference frame, i.e. E3(v) sub M4. Joy didn't make this correction either, but it doesn't change his correlation results because they depend upon integrating over the space of the 'hidden' variable to get expectation values. This may suggest that the parameterisation E3(v) could just be dismissed. However, this would effectively amount to setting v=0 for all the reference frames of the scenario, but without any relative motion there is no dynamics and so nothing happens - thus setting v=0 is unphysical!

      In the archetypal EPR scenario, the interaction point is stationary and the two objects move in opposite directions:

      A(n, l): (E3(v>0) sub M4) * L -> S2 sub S3

      B(n, l): (E3(-v) sub M4) * L -> S2 sub S3

      The condition E3(v>0) sub M4 adds the minimum dynamics condition to Joy's analysis - and adds Relativity - where constraints on the expectation value integral (eqn 3.2 in Joy's book) or normalisation of the 'hidden' variable should make it possible to turn Bell's 'locality' condition of factorisation (eqn 4) into the space-time separation condition v<c (v parameterises E3 and c is in M4). My work predicts that this should be the case, because I identify a scenario with a suitable conspiracy of Nature that gives a hidden domain L.

      Any observable (A, B) is ultimately based upon some particle reaction which will take some minimum time t_min to occur, so if the local causation of the domain L occurs on times scales t<t_min then it will be hidden from all possible observation. This will be the case for a particle with a physical scale of the Planck length and internal dynamics that occur on a time-scale set by the Planck time - which is the case in my model where particles are Planck holes with radius of the Planck length. Furthermore, as every observation takes so long that very many cycles of the local dynamics on the time-scale of the hidden domain L occur within the measurement time-scale, the calculation of all observables *must* take an average over the domain L (such as eqns 5 and 6).

      However, for the hidden domain being that of a black hole particle on the Planck scale, the rotation causes a maximal ergo-region where the metric signature of Minkowski space-time M4 is reversed, ie. (-,+,+,+) -> (+,+,+,+). This means that there will be one more +1 or -1 issue in Joy's analysis, where the prediction of my work is that averaging over this metric reversal in the hidden domain L is the *source* of the illusion of non-locality in QT. I would expect that extending Joy's work by applying it to the correct physical space E3(v) sub M4 would explicitly show this - and in so doing snooker Joy's critics (even if they all don't register it). Being brutally accurate about the applicability of Bell's analysis to the spaces of physics would score him as 0 for 3.

      Joy's flatness condition on the topological spaces S3 and S7 is actually in agreement with my results - despite appearances given by previous discussion. The issue is that the flatness condition doesn't technically apply to empty space, as that would mean there were no particles in the EPR scenario - so nothing happened! EPR requires 2 particles to dynamically interact, and so the flatness condition applies to the space in the vicinity of the 2 particles - this is *not* the same thing as empty space. The particles of my work are topological defects in the structure of space, which necessarily will give a torsion in the space around them - torsions in space is how the particle forces arise in a Kaluza-Klein style theory. In my work, I show that the formalism of QT is an *approximation* that is required to get a scientifically complete theory because the physically-real classical physics theory is mathematically incomplete, and that the approximation *only* holds in the limit of point-like particles and flat space-time. This approximation limit effectively integrates over the region of space of the ergo-region and gravitational curvature, and this gives the origin of the hidden domain L.

      My flatness condition is a local condition - as in only applies in the local vicinity of particles - and not a global condition on all of space ie. the universe isn't required to be flat. Joy's flatness condition is also such a local condition that doesn't necessarily imply that the whole universe is flat - if it did that would imply teleparallel gravity. But as a local condition, it just implies that the particle forces are associated with torsions in space - which is the case in my work - and gravity is left being due to curvature of space. This distinction would naturally explain the difference between the forces of gravity (curvature) and particles (torsion).

      Hi Michael,

      You're talking my language now (or rather, the language of Nature) ...

      " ... the hidden domain being that of a black hole particle on the Planck scale, the rotation causes a maximal ergo-region where the metric signature of Minkowski space-time M4 is reversed, ie. (-,+,+,+) -> (+,+,+,+). This means that there will be one more +1 or -1 issue in Joy's analysis, where the prediction of my work is that averaging over this metric reversal in the hidden domain L is the *source* of the illusion of non-locality in QT."

      That's exactly what I mean by the source of all information from the point at infinity. I think this is well supported by Lamport's result (Buridan's principle) for all continuous measurement functions. No quantum entanglement, just the illusion, as Joy allows -- with orientability playing the key role. The point at infinity in Minkowski space is everywhere close to the observer, while the physical measurement is nondegenerate near the singularity.

      "I would expect that extending Joy's work by applying it to the correct physical space E3(v) sub M4 would explicitly show this - and in so doing snooker Joy's critics (even if they all don't register it)."

      I don't know. I think we're back into this question of measure space vs. physical space. My sentiment is still toward S^7 as a complete physical space, just as Joy has it. No compactification, octonionic degrees of freedom.

      " ... the universe isn't required to be flat. Joy's flatness condition is also such a local condition that doesn't necessarily imply that the whole universe is flat - if it did that would imply teleparallel gravity."

      Actually, I think that is what he means to imply. Flatness and curvature have to be relative for a fully relativistic theory consistent with your definitions of completeness (which are nice). As in ordinary geometry the straight line is a special case for the curve, topology renders the continuum in curved space.

      All best,

      Tom

      Hi Tom,

      The question of measure space vs. physical space is *precisely* the point to address, especially in the context of the distinction between local - as in the local vicinity of particles - and global structure. Both Joy's and my results regarding QT are local (vicinity) results about the description of measurements, i.e. conditions on measurement space which imply conditions on physical space, namely that it must be locally (vinicity) flat.

      Extending this result to the global structure of space and teleparallel gravity does seem to be Joy's intent (is stated in his book as such). My point is that this is not technically a *necessary* implication. Joy's results are fully compatible with a locally flat spatial structure and gravity being due to the curvature of space. It must be noted that the flatness condition coming from the condition of scientific completeness of the measurement space is restricted to the local vicinity of the particle interaction. Extending the result beyond this domain is technically an invalid induction.

      I was concentrating on Joy's work and missed your discussion where you mentioned compactification and Kaluza-Klein theories. Mine is only a KK-style theory as it explicitly does *not* assume a fixed size compactified dimension as in standard KK - which you quite rightly in my opinion object to as that was the problem I had with KK. I refer you my reply to Jonathan about the cosmological 'constant' being a naive error that is not correct in GR! My extended GR includes the correction for a *physical* GR theory and consequently contains a compactification-inflation see-saw - I *derive* both inflation and dimensional compactification as consequences of assuming that the 'fabric of space' is a real physical surface.

      A further consequence of the compactified S7 is that all scales are measured relative to them, and measuring the scale of S7 relative to itself gives the constant of 1. So the constant scale of the compactified dimensions is a total illusion, NOT an artificial assumption. This gives a non-trivial example of the sort of point Jonathan makes about measuring rods in his essay.

      Michael

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      • Post #85

      My be contradiction "global vs local" is wrong assumption?

      Greetings folks,

      I must say that reading the comments above brings the feeling of coming home, or finding myself unexpectedly in a familiar place. Reading your essay, Michael, brings with it a sense of being told things I already knew or believed, with the sense that an expert is telling you why it's finally OK to believe those things. The correct application of Gödel's theorem as opening up possibilities and choices, rather than closing things down, is most welcome.

      But a lot of what I read in your STUFT paper and the material discussed in Joy Christian's book put me in a geometrical playground of unlimited proportions, and let me have my favorite toys in the sandbox with me. I learn a lot through visualization. I take Alain Connes' recommendation to budding mathematicians seriously, by taking time to recline and reflect periodically when absorbing new concepts, and I find it serves me greatly.

      The thing is; it keeps me on track, because it is harder to visualize things - including abstract formulations in higher Math - that lead to impossibilities. This is why I find the work you and Joy are doing so exciting, because it jibes well with what my visualizations tell me, and it appears to lead to physically realistic possibilities. Of course, that doesn't mean that it IS what is real, but it could be.

      Regards,

      Jonathan

        Hi Jonathan,

        What you are saying is music to my ears. And I suspect it is music to Michael's ears too.

        However, while you, Rick, Michael, Tom, Fred, and others are trying to take these ideas further, I am engaged in addressing your very prudent caution: "...that doesn't mean that it IS what is real..."

        I want to make sure that it IS real before proceeding further. And in physics we do that by testing our hypotheses experimentally. Despite opposition, scepticism, detraction, and even scorn and derision, I am completely convinced by my theoretical analysis. What I am not sure about, however, is whether Nature prefers to side with me and Michael or with the quantum mystics. Only she can answer this question correctly, and I intend to get her answer.

        Joy

        My faith in rationalism agrees with Joy -- scientific results cannot be objective without a clear correspondence between the abstract description and the physical measurement.

        If this framework isn't true, then I have to agree with Einstein: "I would feel sorry for the dear Lord ..." There is no rule that says the world has to be rational; if it isn't, though, we've been doing science all wrong for 300 years. I can't imagine the alternative.

        Tom

        Hi Joy,

        Does my description of the connection of my work to yours seem correct to you?

        On the topic of experimental tests, would I be correct in thinking that the correlation inequalities for observables arising through gravitational interactions, i.e. astronomical observations, could provide a test for teleparallel gravity? As your work implies that this would be required for gravity to be quantied, is there a test here for whether gravity is quantised or not?

        Obviously I don't think it is - as QT is not fundamental and so Nature is under no obligation to comply with the prior beliefs of physicists and have quantised gravity - but an experimental test would nice.

        Michael

        Hi Michael,

        I look at it this way: Bell's theorem proves explicitly that quantum configuration space cannot be mapped onto physical space without a nonlocal model. To believers, this amounts to saying that there is no analytical explanation of locally real quantum correlations. One cannot logically extrapolate to that conclusion, however:

        Quantum configuration space requires us to assume a bounded set of perfect information (such is the source of quantum mysticism inherent in a probabilistic measure). The orientable topology, as Joy has it, requires only that Nature have a choice of output in every measurement function continuous from the initial condition. This necessarily eliminates support for nonlocal realism from all proofs based on the law of the excluded middle, which of course is all the nonconstructive proofs of Bell's theorem.

        Bell's theorem is then reduced to an existence proof for the inequality between local measure results and simultaneous results of nonlocal experiments not performed. Trivial -- because relativity already denies simultaneity of events.

        Best,

        Tom

        Hi Michael,

        I think your criticism of either Bell or EPR about their ideas of completeness and hidden variables is not justified. EPR, for example, were very cautious in stating that their condition of completeness is only a necessary condition (for their intended purposes), not a sufficient condition. Your understanding of what Bell meant by "hidden variables" is also incorrect. What Bell had in mind was what you write as option 1, not what you write as option 2. The issue of dynamics is also irrelevant for the analysis of both EPR and Bell. Given their premises, the argument of EPR is logically impeccable. Given the premises of Bell---which are based on the premises of EPR and the views of Einstein---his theorem too is both logically and mathematically impeccable. It does contain a massive blunder, however, in the very first equation of his famous paper, as I bring out in my work. Whether to call this a mathematical error or merely a wrong assumption is a matter of taste.

        Having said this, we are of course not required to adhere to either EPR's logic or Bell's mathematics beyond what is demanded by physics. So, in that respect, in the spirit of exploration and investigation, I fully endorse your efforts. In particular, the issue of dynamics should indeed be considered as you are considering, and you have some very insightful remarks in this regard. I myself have very different ideas about how to investigate the issue of dynamics, since my primary concern is basic quantum mechanics, not relativistic or gravitational physics.

        I also like your thoughts about the flatness condition and whether or not it should be extended to the universe as a whole. I largely agree with what you have written about this. But again I would not discount any options at this stage because neither of us have anything near a full theory of physics (in fact mine is not even a theory---I prefer to call it a mere "framework").

        As for the experimental test of my framework I do not have anything as exotic as teleparallel gravity or quantum gravity in mind. At the moment I am simply trying to test whether the topology of our physical space respects SU(2) symmetry in the macroscopic domain as I claim, or SO(3) symmetry. This may seem disappointing, but my entire framework depends on this distinction. If this test is successful, then I have some further ideas about how to test the S7 hypothesis.

        Finally, since I agree with the view that QT is not a fundamental theory, the question of quantizing gravity does not even arise. QT and GR are simply two epiphenomenal sides of a yet to be discovered perfect, one-sided coin.

        Best,

        Joy