Joy Christian, Disproof of Bell's Theorem

[harrylin]

I copied my comment + reference over there, which has the effect of including the above.

Looking at the time stamp, we had the same idea at the same time.

 

[StevieTNZ]

Oh-ho, here we go again. No, Joy, measurement outcomes are not bivectors from unit sphere, they are numbers { -1; 1 }. That's how they are defined in Bell's paper and that is also the way how they come out of experiments. And their mean is 0 and their standard deviation is 1. Not bivectors, just numbers 0 and 1.

I can't be bothered anymore, but if you substitute I and \textbf{a} from definitions elsewhere in his paper, you will get \sigma(\textbf{a})=\sum a_{j}\beta_{j} where a_{j} are coefficients of unit vector \textbf{a} and \beta_{j} are "basis bivectors". Brain ruptures at this point...

So that pretty much destroys Joy's response to the argument against his original paper?

 

[billschnieder]

Joy Christian has now responded to Richard Gill's purported refutation:

http://arxiv.org/abs/1203.2529

I identify a number of errors in Richard Gill’s purported refutation of my disproof of Bell’s theorem.
In particular, I point out that his central argument is based, not only on a rather trivial misreading
of my counterexample to Bell’s theorem, but also on a simple oversight of a freedom of choice in
the orientation of a Clifford algebra. What is innovative and original in my counterexample is thus
mistaken for an error, at the expense of the professed universality and generality of Bell’s theorem.

 

[gill1109]

Thanks, Bill Schnieder. Joy has changed his postulates to patch the error. The new postulates are mutually contradictory. So first there was a model and a mistake, now there's no mistake but no model either. Vanished in a puff of smoke.

 

[bohm2]

I posted that paper in this thread above but I gave up trying to understand the debate. A very long one and not too friendly one that can be followed more fully here in this FQXi Blog:

Disproofs of disproofs of disproofs of disproofs...
http://www.fqxi.org/community/forum/topic/1247

 

[yoda jedi]

Just curious. Doesn't the new PBR theorem reach the same conclusion as Bell's making Joy Christian's refutation of Bell's theorem (even if it was conceivable) a mute point, at least with respect to arguing for a local realistic model:

Thus, prior to Bell’s theorem, the only open possibility for a local hidden variable theory was a psi-epistemic theory. Of course, Bell’s theorem rules out all local hidden variable theories, regardless of the status of the quantum state within them. Nevertheless, the PBR result now gives an arguably simpler route to the same conclusion by ruling out psi-epistemic theories, allowing us to infer nonlocality directly from EPR.

Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/

The quantum state cannot be interpreted statistically
http://lanl.arxiv.org/pdf/1111.3328v1.pdf

PBR place strong constraints on epistemic interpretations rather than rule out.

 

[bohm2]

PBR place a strong constraints on psi-epistemic interpretations rather than rule out.

My question really wasn't about this point. Joy Christian's preservation of local realism relies on refutation of Bell's. Even if that could be done, my question was whether non-locality can be inferred directly via PBR without Bell's theorem. Matt Leifer in his blog answered in a post:

Question by poster:

Hi Matt, Do you still believe that PBR directly implies non-locality, without Bell’s as I think you argued in a section of Quantum Times article?
“It (PBR) provides a simple proof of many other known theorems, and it supercharges the EPR argument, converting it into a rigorous proof of nonlocality that has the same status as Bell’s theorem. ”

Matt's reply:

Yes, but this requires the factorization assumption used by PBR. At the time of writing, I was hopeful that we could prove the PBR theorem without factorization, but now I know that this is not possible. Therefore, the standard Bell-inequality arguments are still preferable as they involve one less assumption.

Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/q...-the-pbr-theorem/comment-page-1/#comment-2877

 

[yoda jedi]

my question was whether non-locality can be inferred directly via PBR without Bell's theorem. Matt Leifer in his blog answered in a post:


Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/q...-the-pbr-theorem/comment-page-1/#comment-2877

i understand, like your question of "Loophole-free demonstration of nonlocality"




.

 

[bohm2]

i understand, in the same manner, like your question of "Loophole-free demonstration of nonlocality".

Exactly.

 

[Mathematech]

my 2-form's worth on the subject: Its been well known since the work of Philippe Eberhard and Arthur Fine in 70s and 80s that a model produces Bell's Inequalities if and only if it is equivalent to a "local hidden variable theory". The term "local hidden variable theory" has a precise mathematical definition it doesn't simply mean any model that has quantities unknown to the observer that determine all outcomes, the quantities have to have sufficient structure to allow probabilities to be calculated via the mechanisms of formal probability theory (sigma algebras etc etc). Some of the people who have commented in this topic seem to have a vague grasp of this when they describe Joy Christian's example as "unrealistic" etc etc but they are missing the point, Fine and Eberhard showed that any such example is "unrealistic" in this sense, but what Christian and others show is that such "unrealistic" behaviour is not really unrealistic and it manifests in some fairly simple models of EPR experiments, like the one Christian manages to present in a single page.

 

[gill1109]

Unfortunately Christian's single page contains a glaring error in the algebra, as well as being conceptually completely misguided, see http://arxiv.org/abs/1203.1504

On the other hand, no technically advanced parts of formal probability theory are needed to derive Bell inequalities from a local hidden variables model. No sigma algebras or whatever. They follow from absolutely elementary logical reasoning, elementary arithmetic, elementary (counting) probability, see for instance http://arxiv.org/abs/1207.5103

 

[Mathematech]

I'll take a look at the links you provide. The derivation of Bell's Inequality doesn't need any knowledge of sigma algebras etc, but standard probability structure is implicit when one takes various averages to produce the inequality and assumes them to be meaningful. If you look at Fine's work in the 80s the key to what's going on is that local hidden variable theories always have well defined joint probability distributions for pairs of variables which really don't according to QM. Taking Eberhard's work into consideration, local hidden variable theories have this problem because they implicitly assume counterfactual definiteness.

Although a lot of people have an issue with denying counterfactual definiteness, they shouldn't its something that fails even in mundane examples such as asking what's in your fist when your palm is flat or what's on your lap when you are standing. ("Fist contents" and "flat palm orienation" are incompatible observables and do not have well defined joint probabilities) In layman's terms what's going wrong in hidden variable theories is that they are insisting that you can talk about having something in your fist at the same time as your palm is flat and as a result they can never produce correct correlations.

Now maybe Joy Christian's example is erroneous (I will check the refutation) but there have been many others who have come up with correct similar examples - and all they are really doing is constructing something which loosely speaking amounts the "fist-palm" example using some sort of non-distributive lattice or tensor algebra of some kind. The reason why such examples are valuable is that they show people that they have to be careful in jumping to conclusions about non-locality or denial of philosohical realism simply because a standard hidden variable theory cannot produce QM correlations. They also show that there are mundane cases where you can't treat a pair of variables as having a well defined joint probability distribution (or without going into such detail, where you can't just average stuff and assume the average makes sense).

The main problem with Joy Christians work is his attitude - the very title "Disproof of Bell's Theorem" is troublesome/cranky because it isn't disproving Bell or finding an error is Bell's reasoning, its merely trying to come up with an example of something we've known about since the 70s basically.

 

[mbd]

At the heart of the debate over Bell, local realism, and such, is an implicit assumption that events originate with emission and end with measurment. More specifically, the applicability of Bell's Theorem to nature and certain conclusions about CHSH experiments depend critically on the veracity of the assumption that entanglement involves the coincident emission of two particles that can then be identified, and thus have their entanglement tested, by a coincident detection. This assumption may not be correct.

I've shown that direct particle-to-particle interactions, or relationships, that share information at the speed of light for a non-zero duration are adequate to generate "quantum" results in CHSH experiments.

https://docs.google.com/open?id=0BxBGJRkQXyjweXR2R3ExTlEyNm8

 

[Mathematech]

Busy getting into Gill's refutation right now, regretting that I didn't pay more attention at the workshop on Clifford algebras I attended almost 20 yrs ago! I found this http://www.mrao.cam.ac.uk/~clifford/publications/ps/imag_numbs.ps.gz online, looks like a good intro and refresher.

 

[Mathematech]

Ok, I read and thoroughly enjoyed Gill's refutation paper but have still to read Christian's rebuttal. I have to say at this point I don't actually understand Christian's calculations my initial understanding of the notation which seemed to confirm his result appears to be wrong. (Another regret I'm having, back in the day I remember thinking "quaternions? I'll never need this, I can always look them up one day if I do ... well the day finally came :D )

Regarding the concluding discussion in Gill's paper, "There is no limitation in Bell's theorem on the space in which the hidden variables live." Well yes true as long as we recognize the subsequent bit about realism and locality, in particular realism. Gills says: "Realism", however it is defined, comes down, effectively, to the mathematical existence of the outcomes of unperformed experiments, alongside of those which were actually performed." Well local models that do violate Bell's Inequality work precisely by encoding the lack of a well defined outcomes of unperformed experiments thus preventing the type of averaging or counting that is needed in the derivation of Bell's Theorem. I initially assumed that Christian was trying the same sort of thing but the algebra was over my head.

What for me is an important point is that such models are not really "non-realist" in the true philosophical sense. Although Bell's "realism" seems sensible on the surface it isn't sensible at all because it amounts to saying that we can talk sensibly about a particle being in a position eigenstate which we didn't measure and don't know at the same time that we did measure and do know that it is in a particular momentum eigenstate - and that is just plain nonsense. That it is nonsense is just a consequence of how Fourier transforms work (or more gnerally how change of eigenbases works) and there is nothing philisophically non-realist about it - so it its very unfortunate that Bell and others dubbed this "realism". The failue of this kind of realism is no worse than failing to have a lap when standing up, I'm not a spooky subjective entity because my lap disappeared when I stood up, but the fact that Bell and others seem to imply that it is (or alternatively try to imply that faster than light signalling exists) is a bit of crankiness on their part and its precisely what sets of off the anti-Bell cranks.

 

[Mathematech]

BTW the sort of stuff I'm talking about when I speak of local models that violate Bell's Theorem, I mean the sort of things that Rovelli, Omnes, Hartle etc have come up with. They all reject non-local communication but have models consistent with ordinary QM correlations not with Bell's Theorem and they manage this by failing to be "realist" in Bell's narrow sense but are nevertheless still "realist" in a philosophical sense.

 

[mbd]

BTW the sort of stuff I'm talking about when I speak of local models that violate Bell's Theorem, I mean the sort of things that Rovelli, Omnes, Hartle etc have come up with. They all reject non-local communication but have models consistent with ordinary QM correlations not with Bell's Theorem and they manage this by failing to be "realist" in Bell's narrow sense but are nevertheless still "realist" in a philosophical sense.

Thanks for this! Is there a good source for a precise definition of Bell's meaning of realism, as well as "consensus" definitions?

 

[Mathematech]

Off hand I can't think of any good sources although I have read many confusing ones. When it comes to Bell's Theorem, "realism" means counterfactual definiteness. Counterfactual definiteness is typically poorly explained in texts often with some statement along the lines that if a different experiment had been performed (e.g. position measured instead of momentum) then it would have produced a definite result. Now that isn't quite what counterfactual definiteness is about as all interpretations of QM agree that if you do an experiment you get a definite result, even raw Copenhagen says that. What counterfactual definiteness really says is that such a counterfactual outcome is still statistically meaningful for a time where I have performed a different experiment that is quantum mechanically incompatible.

To give a real world non-QM analogy, assuming counterfactual definiteness in a QM situtaion amounts to counting how many times your fist contained some unspecified item according to a guess without having checked it but instead having seen to the contrary that your palm was open and that your hand wasn't even clenched in a fist all - such counts are obviously meaningless nonsense. Similarly refinements of Copenhagen QM avoid Bell's Theorem without the need for non-locality by similarly considering the calculations in the derivation of Bell's Theorem to be meaningless sums.

 

[gill1109]

The point is that counterfactual definiteness was never a problem in physics till QM came along. Secondly, the perfect anticorrelations predicted by the singlet state make it a very natural assumption (when you measure the two particles in the same way you get equal and opposite results - hard to imagine except by supposing the different measurement outcomes for different settings are already "fixed" for the two particles at the source). (cf EPR argument for "elements of reality").

Finally, the fact remains that it is impossible to generate violations of Bell inequalities in a rigorously regulated experiment by non-quantum means. (Rigorously regulated means: no post-selection, no non-detections; random settings; proper space-time separation so that Alice's measurement is finished before Bob's setting could become available and vice -versa). When the definitive experiment is done in a year or two (several experimental groups are getting very close) we'll know for sure that nature - quantum reality - is non classical. Nature is not deterministic but irreducibly stochastic.

 

[Hurkyl]

Although a lot of people have an issue with denying counterfactual definiteness, they shouldn't its something that fails even in mundane examples such as asking what's in your fist when your palm is flat or what's on your lap when you are standing. ("Fist contents" and "flat palm orienation" are incompatible observables and do not have well defined joint probabilities)

Joint probabilities are irrelevant: "fist contents", as you've defined it, is ill defined all on its own.

 

[Mathematech]

The thing is we are dealing with superpositions of correlated pairs of states and counting outcomes of measurements on these which cannot all simultaneously be factual due to incompatibilities of the observables involved, does not produce the correct statistics. The so called "non-realist" approaches feel that this is sufficiently explained by the fact that there is no reason such calculations should produce meaningful values or match the results obtained by the standard Hilbert space formalism.

This to some extent relates to the logical analysis of loaded statements like "Do you still beat your wife? Write +1 if you do and -1 if you don't." What's the answer? Well if you never beat your wife in the first place or don't even have a wife, the answer cannot be said to be either +1 or -1. From the point of view of so called non-realists, the derivation of Bell's Theorem is representing the answer as an unspecified but nevertheless definite amount x and then concluding something like even if we don't know the value of x we do know we must have |x| = 1.

 

[gill1109]

"Realism" in this context should be called "idealism". Because it asserts the equal realness of the outcome of the measurement with the setting which you did not use, alongside of the outcome of the same measurement with the setting which you did actually use. OK so you can scoff at this. The point is, in all of classical physics this would not have been problematic. The mathematical model of physics allow you to replace an actual setting with a different (counterfactual) setting and still read off an outcome. Bell shows us that quantum reality cannot be modeled in a classical way.

Most Bell-deniers deny this.

"Non-realist" interpretations of quantum mechanics don't resolve these issues. They simply refuse to discuss them. The fact that QM is intrinsically different from any physics which went before us swept under a carpet of verbiage. The fact that QM predicts real world phenomena which are impossible under any classical-like physics, is likewise hidden from view. In other words, such interpretations are merely a comfort-blanket.

 

[Hurkyl]

This to some extent relates to the logical analysis of loaded statements like "Do you still beat your wife? Write +1 if you do and -1 if you don't." What's the answer?

The analogy can be used, but not the way you are setting it up.

I can set a spin-about-Z-measuring-device up in front of any particle. I can't set up a spousal-abuse-measuring-device in front of an unmarried man. The relationship between spin-about-Z and spin-about-X is of a fundamentally different type than the relationship between having a spouse and whether you abuse her.

The analogy can be used, though, in regards to "What spin about Z did you measure?" versus "Did you use a spin-about-Z-measuring device?"

 

[Mathematech]

Indeed QM cannot be modeled in a classical way, but we need to be sure we understand what we mean when we say "classical way".

I don't think the "non-realist" approaches can be dismissed as "refusing to discuss". When your particle is in an x-axis spin eigenstate, it mathematically is not in a y-axis eigenstate, this is straightforward mathematics. Recognizing that it is meaningless to speak of the y-axis eigenstate of a particle you know to be in an x-eigenstate is not a refusal to discuss, its being sensible. Similarly recognizing that you don't have a fist when your palm is open is not a refusal to discuss fists. Indeed insisting that one can talk of simultaneous x and y-axis eigenstates is what is cranky, but ultimately this is what so-called "realist" interpretations are doing.

 

[Hurkyl]

When your particle is in an x-axis spin eigenstate, it mathematically is not in a y-axis eigenstate, this is straightforward mathematics. Recognizing that it is meaningless to speak of the y-axis eigenstate of a particle you know to be in an x-eigenstate is not a refusal to discuss, its being sensible.

I can feed such a through a spin-about-y-measuring-device, and it will give me an answer.

The realist philosophy (as used in this context) is that the measuring device is measuring some quality the particle actually has, and so there is some aspect of the "true" physical state of the particle that would determine the result of measurement -- or if we accept non-determinism, would determine a probability distribution on the outcomes.

The description of the particle as being in an x-axis eigenstate is actually sufficient for this task, as it tells us of the 50-50 distribution on the outcomes of the y measurement.

 

[Mathematech]

Another point I'd like to make, although my last few posts have been defending the "non-realist" explanations of why QM produces different results to a local hidden variable theory, if one delves into the philosophy there are views which to do not see non-counterfactual definiteness and non-locality as two different explanations but which consider the possibility that the notions are intimately related and that QM escapes Bell by virtue of both counterfactual definiteness and certain notions of locality failing - that an x spin measurement of particle A results in a non-local influence on particle B which puts it in a superposition of Y spin states making it meaningless to speak of its Y spin if that isn't measured.

 

[Mathematech]

One could argue in fact that the very tensor product Hilbert space formalism used for two entangled particles itself implies failures of both counterfactual definiteness and locality - the Hilbert space formalism alone implying failure of the former and the tensor product implying failure of the latter ... but this is a subject for volumes of books not something that be explained in a forum :)

 

[Mathematech]

Back to Joy Christian's paper - I'm reading the rebuttal to Gill, but I am at a complete loss to understand what he is on about in his "A fallacy of misplaced concreteness" section when he goes on about statistical vs algebraic variables.

 

[Nugatory]

Back to Joy Christian's paper - I'm reading the rebuttal to Gill, but I am at a complete loss to understand what he is on about in his "A fallacy of misplaced concreteness" section when he goes on about statistical vs algebraic variables.

Join the club...

 

[gill1109]

Realism does not insist on simultaneous x and y-axis eigenstates. Realism asks the sensible question: is the statistical nature of quantum mechanical predictions merely the reflection of statistical variation in presently unknown variables at a deeper level of physical description?

Answer: no! The statistical nature of QM is intrinsic, it's for real. In fact there's a nice theorem that violation of Bell inequalities together with locality implies that nature must be non-deterministic. It's because of intrinsic indeterminism that QM allows observable phenomena to exist which would be impossible in a classical, deterministic, locality obeying, universe.