Is Quantum Theory As Fundamental As It Seems? by Michael James Goodband

Hi Jonathan,

You raise a very interesting point that I hadn't registered. I was just adopting the standard closed universe picture of GR and not registering it implied that S3 space-time must be a fibre-bundle, which as you suggest could result in unexpected effects. Further non-standard effects could arise in my model because the electroweak vacuum is of the form of a twist in the compactified dimensions in going all the way around the universe. So the sort of ripples you suggest might also involve changes in the electroweak vacuum, which could result in changes to the decay rates of particles. Such results could well be relevant, and perhaps provide a test for the topological structure of space-time. The problem I would have is that the particle masses and particle family mixing angles are not calculable in my model, which is a bit of problem for calculating changes to particle decay rates.

With particles being topological defects in my model, simple heuristic arguments say that neutrinos must have a non-zero mass, which is suggested in the link as being a possible factor. The topological defect particles take the form of compactified rotating black holes, which means particles would have rotational frame-dragging that should give non-standard spin interactions - but with a cross-section that would be too small to be of relevance for particle decay effects.

Another non-standard thought that occurred to me reading Joy Christian's book is that S3 can occur as a flat sphere with zero curvature - so could the universe be closed and flat at the same time?

I did enjoy, thanks!

Michael

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

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 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 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