Joy Christian, Disproof of Bell's Theorem

[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.

 

[Mathematech]

Realism doesn't insist on simultaneous eigenstates if one assumes values of observables to be something other than the eigenvalues of the eigenstates into which we force the system when measuring it (say if we assume them to really be values of functions on hidden variables). But in that case we get Bell's inequalities which disagree with QM and QM wins experimentally ... so we end up having to accept that values of observables really are the eigenvalues etc etc and once we accept that, one sees that where "realism" is going wrong is that it essentially is demanding something which amounts to simultaneous eigenstates - but one has to buy into the eigenstate "ontology" to say this. Hope I'm making sense.

Another thought, everyone goes on about Bell, but let's not forget the Kochen-Specker paradox, here the question of locality vs non-locality doesn't enter, and we have that assuming counterfactual definiteness for pairs of incompatible observables gives the wrong stats. Kochen-Specker shows that "realism" doesn't work and QM is "non-realist" regardless of the question of locality vs non-locality.

Regarding which explanation is the best explanation for why QM doesn't satisfy Bell's inequalities/hidden variable stats, I think the "non-realists" are correct in saying failure of counterfactual definiteness is enough to explain why QM doesn't produce the same stats but I suspect that it doesn't explain why QM does get the particular stats that it does produce instead. To escape Bell, failure of counterfactual definiteness is sufficient but for a complete reproduction of the exact same stats as QM I suspect a notion of non-locality is still needed.

 

[DrChinese]

Realism doesn't insist on simultaneous eigenstates if one assumes values of observables to be something other than the eigenvalues of the eigenstates into which we force the system when measuring it (say if we assume them to really be values of functions on hidden variables). But in that case we get Bell's inequalities which disagree with QM and QM wins experimentally ... so we end up having to accept that values of observables really are the eigenvalues etc etc and once we accept that, one sees that where "realism" is going wrong is that it essentially is demanding something which amounts to simultaneous eigenstates - but one has to buy into the eigenstate "ontology" to say this. Hope I'm making sense.

Another thought, everyone goes on about Bell, but let's not forget the Kochen-Specker paradox, here the question of locality vs non-locality doesn't enter, and we have that assuming counterfactual definiteness for pairs of incompatible observables gives the wrong stats. Kochen-Specker shows that "realism" doesn't work and QM is "non-realist" regardless of the question of locality vs non-locality.

Regarding which explanation is the best explanation for why QM doesn't satisfy Bell's inequalities/hidden variable stats, I think the "non-realists" are correct in saying failure of counterfactual definiteness is enough to explain why QM doesn't produce the same stats but I suspect that it doesn't explain why QM does get the particular stats that it does produce instead. To escape Bell, failure of counterfactual definiteness is sufficient but for a complete reproduction of the exact same stats as QM I suspect a notion of non-locality is still needed.

Nice comments. I have recently noticed more writers saying that nature is both nonlocal and nonrealistic.

 

[bohm2]

Nice comments. I have recently noticed more writers saying that nature is both nonlocal and nonrealistic.

I don't understand this at all. I mean, what is the difference between:

1. "local non-realism" versus
2. "non-local non-realism"?

I mean, if one assumes that nature is non-local at some level, doesn't all the rest follow?

 

[Maui]

I don't understand this at all. I mean, what is the difference between:

1. "local non-realism" versus
2. "non-local non-realism"?

I mean, if one assumes that nature is non-local at some level, doesn't all the rest follow?

Non-realism is enough to get you off the hook, figuratively speaking. You can do(or pretend to do) local physics without spooky action at a distance. That's my impression.

 

[bohm2]

Non-realism is enough to get you off the hook, figuratively speaking. You can do(or pretend to do) local physics without spooky action at a distance. That's my impression.

I agree but then it seems the choice is between non-realism versus non-locality. Why both?

 

[Mathematech]

Hmm well the consistent histories approaches are "non-real" but local in the sense that they don't posit any non-local mechanism. Depending on how one formalizes something like the transactional interpretation, you can get a theory that is both "non-real" and non-local. Bohmian mechanics is real and non-local.

 

[Maui]

I agree but then it seems the choice is between non-realism versus non-locality. Why both?

For the loopholes. You have to eliminate all conspiracy theories(that involves all HVT) to have a solid foundation for such profound shifts in perspective.

 

[Mathematech]

Not sure if there is anything yet that proves it but I suspect that non-locality is the only thing that can explain why the tensor product formalism for composite states actually works and gives the results that it does, whereas non-realsim merely explains why it doesn't give the same results as a hidden variable theory.

 

[bohm2]

Not sure if there is anything yet that proves it but I suspect that non-locality is the only thing that can explain why the tensor product formalism for composite states actually works and gives the results that it does, whereas non-realsim merely explains why it doesn't give the same results as a hidden variable theory.

But a non-local realistic theory like Bohmian mechanics does give the same results. So, again, I don't understand why one needs both non-locality and non-realism.

 

[Mathematech]

My gut feel on the non-locality behind entangled particles is not that there is some form of signal that is tranmitted rather that the concept of being separated in space actually breaks down for certain quantum phenomena for the question of where the particles are detected and measured "distance in space" is meaningful, for the question of what composite spin state the system is in, the concept of "distance in space" may not be applicable ... ok getting wishy washy philisophical here.

 

[Maui]

But a non-local realistic theory like Bohmian mechanics does give the same results. So, again, I don't understand why one needs both non-locality and non-realism.

To weed off the unnatural assumptions. Do you like having 100 different interpretations giving the same results?

 

[bohm2]

My gut feel on the non-locality behind entangled particles is not that there is some form of signal that is tranmitted rather that the concept of being separated in space actually breaks down for certain quantum phenomena for the question of where the particles are detected and measured "distance in space" is meaningful, for the question of what composite spin state the system is in, the concept of "distance in space" may not be applicable ... ok getting wishy washy philisophical here.

I agree with you and that is the argument made by Gisin here:

To put the tension in other words: no story in space-time can tell us how nonlocal correlations happen, hence nonlocal quantum correlations seem to emerge, somehow, from outside space-time.

Quantum nonlocality: How does Nature perform the trick?
http://lanl.arxiv.org/pdf/0912.1475.pdf

This is summarized nicely here also:

If so, whatever causes entanglement does not travel from one place to the other; the category of “place” simply isn't meaningful to it. It might be said to lie *beyond* spacetime. Two particles that are half a world apart are, in some deeper sense, right on top of each other. If some level of reality underlies quantum mechanics, that level must be non-spatial.

How Quantum Entanglement Transcends Space and Time
http://www.fqxi.org/community/forum/topic/994?search=1
Looking Beyond Space and Time to Cope With Quantum Theory
http://www.sciencedaily.com/releases/2012/10/121028142217.htm

But all of this is compatible with models that are non-local yet realistic.

 

[Mathematech]

Hmm how does Bohmian mechanics deal with Kochen-Specker?

 

[bohm2]

Hmm how does Bohmian mechanics deal with Kochen-Specker?

Bohmian mechanics is non-local and contextual so it has no problem with Kochen-Specker.

 

[Mathematech]

Aah right coming back to me, non-locality allows plausible contextuality.

 

[mbd]

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.

What are the additional experimental conditions in the upcoming potentially definitive experiments?

In a photon experiment with space-like separation, I have shown that unless the optical pathways are blocked for a very significant portion of presumed particle flight, then a speed-of-light interaction acting for a non-zero time interval can explain the correlations. A traditional way to look at it would be to consider an extended wave packet with more information than just a frequency, duration, and envelope.

Synchronized rapidly rotating disks, with a slit in each, like the "chopper" described in Hans De Raedt's paper on Neutron interferometry, (http://arxiv.org/abs/1208.2367) but placed as close to the measuring apparatus as possible. The size of the slit should be as small as possible without reaching the scale where a significant portion of photons interact with the slit but still reach the detector. In this experiment, the coincident detection counts diminish but their correlation should not.

There may be an equivalent experimental condition, which is why I'm curious as to what measures are being taken with future experiments. If it is just closing all of the recognized loopholes in one experiment, then I believe that would not be definitive.

Another compelling theoretical case for doing an experiment with the "chopper" condition is John Cramer's transactional interpretation of QM (http://www.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html ). The experiment then might at least tell us where the superluminal effects go: E->A and E->B or A<->B

Of course, this would only lead to a conclusive result if the mechanism of "teleportation" travels only through the same pathways as the particles themselves.

 

[bohm2]

Aah right coming back to me, non-locality allows plausible contextuality.

Yes, as outlined here:

One of the basic ideas of Bohmian Mechanics is that position is the only basic observable to which all other observables of orthodox QM can be reduced. So, Bohmian Mechanics will qualify VD (value definiteness) as follows: “Not all observables defined in orthodox QM for a physical system are defined in Bohmian Mechanics, but those that are (i.e. only position) do have definite values at all times.” Both this modification of VD (value definiteness) and the rejection of NC (noncontextuality) immediately immunize Bohmian Mechanics against any no HV argument from the Kochen Specker Theorem.

The Kochen-Specker Theorem
http://plato.stanford.edu/entries/kochen-specker/index.html

So, while the KS theorem establishes a contradiction between VD + NC and QM, the qualification above immunizes Bohmian mechanics from contradiction.

 

[mbd]

repost to follow because of edit issue ...

 

[mbd]

Regarding Bell and KS, I'm trying to get clarity on the definitions in order to determine applicability to a hypothetical system. Consider a system of two vectors, A and B, at two points in space X₁,X₂, with c=1. Let the two be in a bi-direcitonal relationship that maintains the rule A(t)$\bullet$B(t-|X₁-X₂|)=-1 and B(t)$\bullet$A(t-|X₁-X₂|)=-1.

This system seems to me to be both realistic and deterministic?

It seems to me to be value definite too, in that the result of an observation is the negative of the observed?

It seems to be contextual, in that an observer affects the observed. Although, an observer in a directed relationship could observe noncontextually.

But, there is the question of -what- is being observed. Is it the observed in the past, or is it the "messenger"? There are solutions to the equation involving a chain of vectors, so there's the question of "which" is being observed too!

 

[gill1109]

mbd asked "What are the additional experimental conditions in the upcoming potentially definitive experiments?"

It's not a question of "additional". Bell's papers make perfectly clear how a Bell-CHSH experiment needs to be performed, in order that the experimental findings would disprove local realism. Alice's measurement setting needs to be generated at Alice's location while the particles are "in flight" and her measurement needs to be completed before any information concerning Bob's setting could have reached her apparatus; and vice versa. Implicit in this is that every pair of particles do both get measured.

In real world experiments to date, though the space-time constraints have been satisfied, it has not been possible to detect and measure every particle. The outcome at each measurement station is not +/-1 but +/-1 or "no show". For a situation with ternary outcomes one needs a different, appropriate, Bell inequality. If one focusses on the correlations between outcomes conditional on both particles being measured, the appropriate inequality looks just like CHSH but with the bound "2" replaced by 2 plus a positive term depending on the overall experimental efficiency, defined as the minimum over settings and parties of the probability of an outcome in one party's wing of the experiment given an outcome in the other. When the efficiency is above 70% then the relevant bound is smaller than 2 sqrt 2.

So a good experiment has to have efficiency above 70% and close to perfect reproduction of the singlet correlations. And detectors far apart, setting generation fast and unpredictable, duration of measurement fast.

It has still not been done, though I believe several experimental groups are getting close, at last, 30 years on from Aspect's experiment.

 

[Mathematech]

I'm still having no joy trying to understand Joy Christian's rebuttal. If A(a,\lambda) = +1 when \lambda = +1 and A(a,\lambda) = -1 when \lambda = -1, in what sense doesn't A(a,\lambda) = \lambda? or is the +/-1 that A(a\lambda) is set to something other than normal +/-1 which don't multiply together as we expect? Surely someone with his credentials hasn't completely lost the plot?

 

[gill1109]

"Surely someone with his credentials hasn't completely lost the plot?"

What credentials? A PhD in the foundations of physics means you are good with words and ideas and imagery, and are well-read. It doesn't mean that you can do mathematics.

In earlier versions of Christian's model, the sign error was much more deeply hidden. Florin Moldoveanu carefully studied all versions and found the same error in about four different guises.

 

[Mathematech]

I think there is a whole range of unrecognized "cognitive disorders" out there that aren't being diagnosed or treated by psychologists.

The other day I found a paper by someone who thought that they had proven that the standard definition of natural numbers implied the existence of a greatest natural number if the natural numbers are not treated as a proper class. The author was clearly intelligent, had a PhD, but was completely failing to grasp the very basics of the theory of ordinals - and was unaware that he was failing to grasp it.

Worse, there was the case of a fairly capable student, who picked up the basics of Pascal programming within a day ... and went on to write a program which in his words was for testing if infinity existed ...by writing an unending loop that incremented a counter and printed the result. oO

 

[DrChinese]

Here is a new paper with another take:

http://arxiv.org/abs/1212.4854

Abstract: "I present a local, deterministic model of the EPR-Bohm experiment, inspired by recent work by Joy Christian, that appears at first blush to be in tension with Bell-type theorems. I argue that the model ultimately fails to do what a hidden variable theory needs to do, but that it is interesting nonetheless because the way it fails helps clarify the scope and generality of Bell-type theorems. I formulate and prove a minor proposition that makes explicit how Bell-type theorems rule out models of the sort I describe here. "

(Of course Christian disagrees...)

 

[mbd]

Worse, there was the case of a fairly capable student, who picked up the basics of Pascal programming within a day ... and went on to write a program which in his words was for testing if infinity existed ...by writing an unending loop that incremented a counter and printed the result. oO

Ontologically speaking, infinity does not exist, nor does probability.

In C#, though, both negative infinity and positive infinity exist:
Double.PositiveInfinity and Double.NegativeInfinity.