Bell’s Theorem Refuted: Bell’s 1964:(15) is False

[gill1109]

The Bell experiment deals with whole particles but the spin states of pairs of particles are entangled by QM. Each particle pair has to be treated as a single unit wrt spin state. So, wrt spin, if Alice had a constant angle for the whole experiment, that would correspond to the untreated slit 1 of Susskind's experiment. Bob's magnet would carry out the role corresponding to the treatment at slit 2. Susskind is treating different halves of an electron differently while Bell's experiment is treating different halves of a 'single entity wrt spin state' differently. 4pi periodicity should apply in both cases.

In a Bell experiment on particles in the singlet state, the orientation of one of the magnets would be repeatedly and randomly set to be 0 or 90 degrees; the orientation of the other is repeatedly and randomly set to be 45 or 135 degrees. They are each rotated back and forth through 90 degrees in random fashion (by the toss of a coin, two new coin tosses for each new particle pair).

Please distinguish how one might describe the states of the particles in quantum mechanics, and operations which you do on the lab on macroscopic objects. The word "quantum mechanics" is not part of the description of the experimental protocol. You instruct your lab assistants to switch switches and turn knobs and count clicks.

[Joy Christian]

4pi periodicity should apply in both cases.

4pi periodicity does apply in both cases. It cannot not apply, because 4pi periodicity is a necessary consequence of the topological properties of the physical space itself, which is S^3, not R^3. 4pi periodicity thus applies in both classical and quantum domain, necessitating the strong EPRB correlations we observe in Nature.

[Ben6993]

Hi Joy, I was arguing that Dirac's belt analogy worked well for the two-slit Susskind experiment and the Bell experiment assuming that single entities were operated on differently at each of their ends (ie at each slit of a two-slit experiment/or/ at A and B in a Bell experiment) and, for the Bell experiment, under the assumption that QM entanglement holds true. (That is despite {us both} not believing in entangled spin states.)

[Joy Christian]

Hi Joy, I was arguing that Dirac's belt analogy worked well for the two-slit Susskind experiment and the Bell experiment assuming that single entities were operated on differently at each of their ends (ie at each slit of a two-slit experiment/or/ at A and B in a Bell experiment) and, for the Bell experiment, under the assumption that QM entanglement holds true. (That is despite {us both} not believing in entangled spin states.)

Hi Ben,

Yes, I understand your argument and I agree with it. But in addition (consistent with what we both believe) I am saying that the Dirac's belt analogy also works (and it must work) for even a classical, macroscopic EPRB-type experiment, such as the one I have proposed. So we are in full agreement here.

[gill1109]

The Bell experiment does not assume QM entanglement. The Bell experiment does not require the notion of "particle", even.

You might suspect that there is something specially peculiar about spin- particles. In fact there are many other ways of creating the troublesome correlations. So the following argument makes no reference to spin-particles, or any other particular particles.
Finally you might suspect that the very notion of particle, and particle orbit, freely used above in introducing the problem, has somehow led us astray. Indeed did not Einstein think that fields rather than particles are at the bottom of everything? So the following argument will not mention particles, nor indeed fields, nor any other particular picture of what goes on at the microscopic level. Nor will it involve any use of the words ‘quantum mechanical system’, which can have an unfortunate effect on the discussion. The difficulty is not created by any such picture or any such terminology. It is created by the predictions about the correlations in the visible outputs of certain conceivable experimental set-ups.

[Joy Christian]

The Bell experiment does not assume QM entanglement. The Bell experiment does not require the notion of "particle", even.

Correct.

You might suspect that there is something specially peculiar about spin- particles. In fact there are many other ways of creating the troublesome correlations. So the following argument makes no reference to spin-particles, or any other particular particles.
Finally you might suspect that the very notion of particle, and particle orbit, freely used above in introducing the problem, has somehow led us astray. Indeed did not Einstein think that fields rather than particles are at the bottom of everything? So the following argument will not mention particles, nor indeed fields, nor any other particular picture of what goes on at the microscopic level. Nor will it involve any use of the words ‘quantum mechanical system’, which can have an unfortunate effect on the discussion. The difficulty is not created by any such picture or any such terminology. It is created by the predictions about the correlations in the visible outputs of certain conceivable experimental set-ups.

What has led Bell and his followers astray is the implicit assumption of a naïve topology of the physical space we live in. Once the correct topology is restored there is no difficulty in reproducing All quantum correlations purely local-realistically: http://libertesphilosophica.info/blog/d ... orem-book/. Ben understands this very well.

[gill1109]

Sorry, "spin-" should have been "spin-1/2", twice, in my quote from Bell's "Bertlman's socks...". Copy-paste issue.

But notice that topology is a non-issue here. There is no topology issue in the experimental protocol. You can put whatever topology you like in the underlying physics but it doesn't change the experiment.

[FrediFizzx]

But notice that topology is a non-issue here. There is no topology issue in the experimental protocol. You can put whatever topology you like in the underlying physics but it doesn't change the experiment.

LOL! I guess you didn't watch the Susskind lecture that Ben provided a link for.

[Joy Christian]

But notice that topology is a non-issue here. There is no topology issue in the experimental protocol. You can put whatever topology you like in the underlying physics but it doesn't change the experiment.

These statements provide a nice example of the usual naïveté of the followers of Bell.

Anyone with a basic training in the physics of space-time and the mathematics of topology and analysis should be able to understand the difference between the experimental (or operational) protocol on the one hand and the topology of the physical space in which the measurement events are occurring on the other hand:

.

Evidently this prescription is operationally identical to the one proposed by Bell apart from the use of the correct codomain of the measurement functions. Once the meaning of this prescription is understood and the correlations are calculated accordingly (using the standard procedure), the strong correlations follow inevitably.

The only remaining mystery is why some people are going through such an extraordinary length to not understand this derivation: http://arxiv.org/abs/1405.2355.

[gill1109]

But notice that topology is a non-issue here. There is no topology issue in the experimental protocol. You can put whatever topology you like in the underlying physics but it doesn't change the experiment.

LOL! I guess you didn't watch the Susskind lecture that Ben provided a link for.

No, because it is irrelevant to the description in macroscopic terms of the experimental arrangement and data analysis. In Bell-CHSH experiments, measurement outcomes are clicks in one or the other detector. They are counted and the data registered in ordinary computers. What kind of fancy mathematics is used to try to explain the underlying physics is totally irrelevant. In any particular time window there is either an event of some particular kind or there isn't.

You can give outcomes values "-1" and "+1" if you like and think of those values as points in whatever fancy topological space you like, if that helps you understand the "correlations" which you observe. If you come up with a local hidden variables theory those local hidden variables can be represented by whatever exotic mathematical objects you like. None of this makes any difference to Bell's analysis.

Anyway, this is off-topic. Gordon Watson's analysis is not about fancy topology, it is about elementary maths and logic, and it takes Bell's set-up for granted.

[FrediFizzx]

Watch the lecture.

[Joy Christian]

None of this makes any difference to Bell's analysis

Indeed. Neither does it make any difference to the Cinderella story.

Gordon Watson's analysis is not about fancy topology...

There is nothing fancy about topology. But one does have to know what the word means.

[gill1109]

Watch the lecture.

Yes I'll do that. Should be interesting.

[Q-reeus]

...The only remaining mystery is why some people are going through such an extraordinary length to not understand this derivation: http://arxiv.org/abs/1405.2355.

Joy - I'm a QM layman in the category of, as Mulder's wall-poster read in the X-files: "I want to believe". However one slices and dices it, the standard QM view of entanglement/non-locality implies magic as literally at the heart of 'reality' - to the extent one's QM interpretation even allows an objective 'reality'.

On the other hand, it's very hard to see how your proposed 'exploding balls' classical experiment would do other than reproduce classical stats. And apart from being not so easy to actualize satisfactorally, one might suspect only elementary particle/particle pairs would really 'feel' the difference between S^3 and R^3 re Bell inequality. Can you point to some feature of S^3 spacetime (or spacetime slice) that admits a fully deterministic, no randomness involved, macroscopic classical physical experiment - mechanical, optical, electrical or whatever, that clearly is contrary to that predicted for normally assumed R^3 spacetime/spacetime slice? If so that should unequivocally settle things.

[Joy Christian]

On the other hand, it's very hard to see how your proposed 'exploding balls' classical experiment would do other than reproduce classical stats. And apart from being not so easy to actualize satisfactorally, one might suspect only elementary particle/particle pairs would really 'feel' the difference between S^3 and R^3 re Bell inequality. Can you point to some feature of S^3 spacetime (or spacetime slice) that admits a fully deterministic, no randomness involved, macroscopic classical physical experiment - mechanical, optical, electrical or whatever, that clearly is contrary to that predicted for normally assumed R^3 spacetime/spacetime slice? If so that should unequivocally settle things.

S^3, by definition, is a set of all unit quaternions. Thus your question can be answered by the phenomenon of gimbal lock. This phenomenon cannot be described without using quaternions (it cannot be described by using vectors, for example). That is why aviation engineers are more familiar with quaternions than physicists. Without using quaternions in describing, understanding, and eliminating the gimbal lock issue the fatality rate in aviation accidents would be extremely high.

As for my proposed experiment, it's predictions based on the S^3 model have been successfully simulated, thereby defeating a pseudo challenge by Richard Gill.

[Q-reeus]

S^3, by definition, is a set of all unit quaternions. Thus your question can be answered by the phenomenon of gimbal lock. This phenomenon cannot be described without using quaternions (it cannot be described by using vectors, for example). That is why aviation engineers are more familiar with quaternions than physicists. Without using quaternions in describing, understanding, and eliminating the gimbal lock issue the fatality rate in aviation accidents would be extremely high.

As for my proposed experiment, it's predictions based on the S^3 model have been successfully simulated, thereby defeating a pseudo challenge by Richard Gill.

Reading the Wikipedia article https://en.wikipedia.org/wiki/Gimbal_lock, I get the impression issue of gimbal lock is one of mathematical limitation using Euler angles, with no implication a gyro physically lives in anything more exotic than regular 3D space. So that phenomenon don't seem to qualify as experimental evidence we do live in a more exotic space.

[Joy Christian]

S^3, by definition, is a set of all unit quaternions. Thus your question can be answered by the phenomenon of gimbal lock. This phenomenon cannot be described without using quaternions (it cannot be described by using vectors, for example). That is why aviation engineers are more familiar with quaternions than physicists. Without using quaternions in describing, understanding, and eliminating the gimbal lock issue the fatality rate in aviation accidents would be extremely high.

As for my proposed experiment, it's predictions based on the S^3 model have been successfully simulated, thereby defeating a pseudo challenge by Richard Gill.

Reading the Wikipedia article https://en.wikipedia.org/wiki/Gimbal_lock, I get the impression issue of gimbal lock is one of mathematical limitation using Euler angles, with no implication a gyro physically lives in anything more exotic than regular 3D space. So that phenomenon don't seem to qualify as experimental evidence we do live in a more exotic space.

S^3 is a 3D space, just as R^3 is a 3D space. It is a spatial slice of one of the solutions of Einstein's field equations.

Let us take this one step at a time: Would you say that the planet we live on is describable as a flatland R^2, or do we sometimes have to describe it as a surface S^2?

In other words, can we get away with describing the planet we live on as a flat surface R^2 in every conceivable physical scenario, or sometimes we simply cannot?

Similarly, our usual assumption that we live in a flat 3D space R^3 is an illusion. One only needs to look at a gimbal lock or Dirac's belt trick to recognize this fact.

Just as R^2 is a tangent space at every point of S^2, our illusory flat 3D space R^3 is a tangent space at every point of the round 3D space S^3. We live in S^3, not R^3.

[Q-reeus]

S^3 is a 3D space, just as R^3 is a 3D space. It is a spatial slice of one of the solutions of Einstein's field equations.

Let us take this one step at a time: Would you say that the planet we live on is describable as a flatland R^2, or do we sometimes have to describe it as a surface S^2?

In other words, can we get away with describing the planet we live on as a flat surface R^2 in every conceivable physical scenario, or sometimes we simply cannot?

Sure, as you below write flatness is local not global re earth's surface.

Similarly, our usual assumption that we live in a flat 3D space R^3 is an illusion. One only needs to look at a gimbal lock or Dirac's belt trick to recognize this fact.

Just as R^2 is a tangent space at every point of S^2, our illusory flat 3D space R^3 is a tangent space at every point of the round 3D space S^3. We live in S^3, not R^3.

The Dirac belt trick is interesting but simply an illustration of belt topology performed in ordinary 3D space. One problem I'm having with above line of thought is that if some normally unnoticed spacial curvature is explanation, it should:

1: Lead to physical effects that depart from 'flatland' predictions as a linear or perhaps quadratic function of spatial separation. EPRB type scenarios afaik don't seem to have that kind of dependence. I'm still trying to imagine a macroscopic deterministic classical effect that clearly distinguishes S^3 from R^3. Something involving light beams and mirrors or whatever have you.

2: Have a well defined source. You mentioned solution of EFE's. But significant curvature there is a function of an enormous energy-momentum distribution. What else is there that would provide curvature in near enough to Minkowski flat spacetime that nevertheless accounts for Bell inequality etc.? Maybe I'm just not getting the basics here.

[Joy Christian]

The Dirac belt trick is interesting but simply an illustration of belt topology performed in ordinary 3D space. One problem I'm having with above line of thought is that if some normally unnoticed spacial curvature is explanation, it should:

1: Lead to physical effects that depart from 'flatland' predictions as a linear or perhaps quadratic function of spatial separation. EPRB type scenarios afaik don't seem to have that kind of dependence. I'm still trying to imagine a macroscopic deterministic classical effect that clearly distinguishes S^3 from R^3. Something involving light beams and mirrors or whatever have you.

2: Have a well defined source. You mentioned solution of EFE's. But significant curvature there is a function of an enormous energy-momentum distribution. What else is there that would provide curvature in near enough to Minkowski flat spacetime that nevertheless accounts for Bell inequality etc.? Maybe I'm just not getting the basics here.

At this point we must depart from the intuitive picture of what is going on. If what I am saying was intuitively so simple to understand, then people would have understood it long time ago. But unfortunately things are not so simple and we must get into technicalities. First such technicality is to understand the difference between the extrinsic curvature (like what we see in the surface of the earth) and intrinsic curvature relevant in Einstein's theory. But even that is not enough. One must also understand the difference between the Riemann curvature versus by the torsion tensor. S^3 is best described by zero Riemann curvature but non-zero torsion. Thus in this description S^3 is as flat as a sheet of paper as far as its curvature is concerned but "non-flat" in terms of its intrinsic torsion. As you can see, we are now getting into some serious technicalities. Unfortunately these technicalities are unavoidable to understand what is going on in the EPRB-type experiments.

It is the torsion within S^3 that is responsible for the strong EPRB correlations we observe, and this torsion has nothing to do with any spatial separation or source.

[Q-reeus]

At this point we must depart from the intuitive picture of what is going on. If what I am saying was intuitively so simple to understand, then people would have understood it long time ago. But unfortunately things are not so simple and we must get into technicalities. First such technicality is to understand the difference between the extrinsic curvature (like what we see in the surface of the earth) and intrinsic curvature relevant in Einstein's theory.

Not to quibble but earth's surface does have nonzero Gaussian curvature.

But even that is not enough. One must also understand the difference between the Riemann curvature versus by the torsion tensor. S^3 is best described by zero Riemann curvature but non-zero torsion. Thus in this description S^3 is as flat as a sheet of paper as far as its curvature is concerned but "non-flat" in terms of its intrinsic torsion. As you can see, we are now getting into some serious technicalities. Unfortunately these technicalities are unavoidable to understand what is going on in the EPRB-type experiments.

It is the torsion within S^3 that is responsible for the strong EPRB correlations we observe, and this torsion has nothing to do with any spatial separation or source.
OK so in flatland we have zero curvature but this nonzero torsion. Am aware that GR can be reformulated as Telleparallel gravity which treats spacetime as spatially flat background but having torsion. In that formulation torsion is still generated by stress-energy-momentum source similar to how curvature is in GR, right? And thus is generally quite nonuniform and negligible in absence of large mass source. So getting back to nominally source-free flatland, what is the source of significant torsion in your picture? Seems to me one has to posit some kind of uniform value that is somehow source-free and an intrinsic property of spacetime. Is that correct? Hard to sensibly imagine this (my limitation no doubt) as the picture I have is; fapp source-free implies uniformity/isotropy thus an all-pervading uniform scalar field with no directionality possible.