Joy Christian, Disproof of Bell's Theorem

[DrChinese]

I just read Gisin's paper "Non-realism: Deep Thought or a soft Option" (http://arxiv.org/pdf/0901.4255v2.pdf). He doesn't seem to be aware of the interpretation of "realism" as meaning counterfactual definiteness and doesn't even discuss it. He misses entirely the fact that the probability distributions in his equation 1 are not well defined in the face of non-counterfactual definiteness.

I have to admit that his argument seems more oriented towards reaching the desired conclusion than allowing for a fuller definition of "non-realism". For example: EPR defines realism as the simultaneous existence of (unlimited) elements of reality. So non-realism would be the denial of that. As you say, that makes things contextual; there are only a few simultaneous elements of reality for any system. What is "annoying" or "vague" about that (using his terms)?

 

[bohm2]

I just read Gisin's paper "Non-realism: Deep Thought or a soft Option" (http://arxiv.org/pdf/0901.4255v2.pdf). He doesn't seem to be aware of the interpretation of "realism" as meaning counterfactual definiteness and doesn't even discuss it. He misses entirely the fact that the probability distributions in his equation 1 are not well defined in the face of non-counterfactual definiteness.

You might want to look at the updated published version of that paper (see below). In the first footnote this is how Gisin defines "realism":

My personal definition of realism—that clearly has not been falsified—is another issue. For me realism means, very briefly, that physical systems possesses properties preexisting and independent of whether we measure the system or not; however these preexisting properties do not determine measurement outcomes, but only their propensities. Accordingly, there are realistic random events that reflect preexisting properties, as required by realism, simply the reflection is not deterministic.

http://www.gap-optique.unige.ch/wiki/_media/publications:bib:nonrealismfinal.pdf

I have trouble completely understanding what he means by this, to be honest.

 

[Mathematech]

I have trouble completely understanding what he means by this, to be honest.

Yeah I read that sentence and decided I needed another cup of coffee before attempting it again :D

I'm also half way through Joy Christians rebuttal http://arxiv.org/pdf/1301.1653.pdf and so far all I see is a lot of unconscious redefining of how probability works with lots of Clifford algebra thingies ("multivectors") sitting in equations that have the shape of actual statistical calculations but which otherwise have no justification because they aren't really statistical calculations.

We would need some reason for entangled particles to follow Clifford algebra based statistical mechanisms like this instead of normal statistics which is back to square one as this Clifford stuff is really just the usual tensor product Hibert space QM stats in a different notation. In the same way that the usual tensor product stuff appears to be implying some sort of non-local connection, so too is this mathematically equivalent Clifford algebra stuff.

 

[Mathematech]

Ok I read Gisin's definition again and it seems that he is also unaware of that the propensity approach he is advocating ends up producing the same statistics as a deterministic approach (one of Arthur Fine's results) - this is all discussed for example in Redhead's book https://www.amazon.com/dp/0198249373/?tag=pfamazon01-20

 

[Mathematech]

FYI: Arthur Fine's paper http://www.citeulike.org/user/egcavalcanti/article/6011736 where he shows that going for models that conform to what Gisin seems to be saying his personal definition of realism is, are in fact no more general than a local hidden variable theory.

 

[Mathematech]

Further subtle points about Fine's result http://www.jstor.org/stable/187655

 

[bohm2]

Yeah I read that sentence and decided I needed another cup of coffee before attempting it again

Gisin's definition of "realism" kind of reminds me of the epigenetic modifications of the genome by environment, except for the non-locality.

 

[Mathematech]

Actually after completing Joy Christians latest paper I'm not convinced the math is correct, its seemingly based on a Clifford Algebra model of what the tensor product Hilbert Space formalism is saying but also contains some dodgey limits. Either its just plain wrong or if fixable at most just copies what the standard formalism already tells us without adding any real explanantion - why should the stats conform to the Clifford algebra based pseudo-statistics based on a parallelized hypersphere ... if there isn't some non-local mechanism enforcing it?

 

[Avodyne]

I haven't gone through this whole thread, so this paper by Richard Gill may have already been cited: http://arxiv.org/abs/1203.1504

IMO, this paper is a completely convincing demonstration that Christian's claims about Bell are vacuous.

Christian has a reply paper, which IMO is as vacuous as his previous ones. Find it yourself if you care to.

 

[jtbell]

Yes, Gill's article has been discussed in this thread, beginning here:

https://www.physicsforums.com/showthread.php?p=3804759#post3804759

In fact, Gill himself chimed in:

https://www.physicsforums.com/showthread.php?p=3812865#post3812865

 

[Avodyne]

But it seems not everyone is convinced.

 

[bohm2]

Why should probability not ontologically exist? What kind of prejudice is that? I think quantum mechanics is telling us that it does exist, despite our intuition or instinct to the contrary. Our brains evolved and led us from success to success by hard-wiring in us a belief that nothing happens without a cause... this belief worked just fine, till we ran up against quantum mechanics.

Interesting comment since such a paper was recently published that kind of argues this:

We argue using simple models that all successful practical uses of probabilities originate in quantum fluctuations in the microscopic physical world around us, often propagated to macroscopic scales. Thus we claim there is no physically verified fully classical theory of probability. We comment on the general implications of this view, and specifically question the application of classical probability theory to cosmology in cases where key questions are known to have no quantum answer.

Origin of probabilities and their application to the multiverse
http://arxiv.org/pdf/1212.0953v1.pdf
Also discussed here:
Does Probability Come from Quantum Physics?
http://www.sciencedaily.com/releases/2013/02/130205151450.htm

 

[stevendaryl]

Why should probability not ontologically exist? What kind of prejudice is that? I think quantum mechanics is telling us that it does exist, despite our intuition or instinct to the contrary. Our brains evolved and led us from success to success by hard-wiring in us a belief that nothing happens without a cause... this belief worked just fine, till we ran up against quantum mechanics.

I think that there is a conflict, or at least a tension, between objective probabilities and relativity, even before you throw in quantum mechanics. Subjective probability of course is not affected by quantum mechanics or relativity, and the sort of "collapse" that happens when an observer gets new information is a process that goes on inside someone's head, not in the world. But a purely subjective notion of probability seems incomplete when talking about quantum mechanics, for two reasons: First, there's absolutely no reason to think that subjective probability should evolve via Schrödinger's equation, and second, having one person detecting a particle should have no effect on somebody else's subjective probability (until he finds out about it, anyway).

On the other hand, objective probability is hard to reconcile with relativity, unless it is of a very particular type. By "objective probability", I mean stochastic processes, in which the evolution of the state of the system is governed by a probabilistic transition matrix. However, when you consider relativity, there is no universal "time" to use for state evolution, there is only a local notion of time applicable within a small region. You could have a stochastic process based on local time, for instance, a particle's state could evolve nondeterministically as a function of the particle's proper time. However, that kind of stochastic evolution can't describe things like the probability of a particle being here or there, for the following reason:

Suppose that a particle has a 50/50 chance of being in one of two boxes, box A and box B, lightyears apart. Someone detects the particle in box A. A second later, (according to one reference frame), someone checks box B for the particle.

According to one reference frame, the particle has already been found, and so the second observer has zero chance of finding the particle. According to a second reference frame, the checking of the particle in B happens before the discovery of the particle in A. So in this frame, the particle has a nonzero chance of being found at B.​

This frame-dependence of probability causes no problems for subjective probability, but doesn't really make sense for objective probability.

This is a long-winded way of saying that in my opinion, the weirdness of the way probability works in quantum mechanics is sort of to be expected, because there is no good way for objective probability to work consistently with relativity.

On the other hand, if there secretly were a universal time, then you could have an ordinary stochastic evolution based on that universal time. I'm not sure how the Bohm theory generalizes to relativistic quantum mechanics. Does it use a preferred rest frame for the nonlocal quantum interactions?

 

[bohm2]

On the other hand, if there secretly were a universal time, then you could have an ordinary stochastic evolution based on that universal time. I'm not sure how the Bohm theory generalizes to relativistic quantum mechanics. Does it use a preferred rest frame for the nonlocal quantum interactions?

Generally, Bohmian models would seem to require a preferred rest frame for non-local correlations but Demystifier (Hrvoje Nikolic) our resident Bohmian expert on this forum has published a Bohmian model compatible with relativity. He does it by treating time on an equal footing with space and his model does not involve a preferred Lorenz frame. Some of his stuff can be found here:

Slide Presentation:
Making Bohmian Mechanics compatible with Relativity and Quantum Field Theory
http://www.tcm.phy.cam.ac.uk/~mdt26/tti_talks/deBB_10/nikolic_tti2010.pdf

Relativistic Quantum Mechanics and Quantum Field Theory
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/nikolic_2010d.pdf

Making nonlocal reality compatible with relativity
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/nikolic_2010a.pdf

Edit: There's also another Bohm approach that can be Lorentz invariant, with no need for a preferred reference frame at the hidden level but requires retrocausality:

A version of Bohm’s model incorporating retrocausality is presented, the aim being to explain the nonlocality of Bell’s theorem while maintaining Lorentz invariance in the underlying ontology. The strengths and weaknesses of this alternative model are compared with those of the standard Bohm model.

Causally Symmetric Bohm model
http://arxiv.org/ftp/quant-ph/papers/0601/0601095.pdf