Joy Christian, Disproof of Bell's Theorem

[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)\bulletB(t-|X₁-X₂|)=-1 and B(t)\bulletA(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.

 

[gill1109]

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.

 

[Mathematech]

Its even got infinitisimals (in a sense) Double.Epsilon :)

 

[Mathematech]

Theory of Hidden Authors ... just a thought, is it possible that Joy Christian really doesn't know much math at all and all the math is being ghost written for him by someone else who is trying to rigorize some hand waving from Christian and stuff is getting lost in translation somewhere?

 

[Nugatory]

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

Digression: That's not a C# thing, it's a property of the IEEE 754/854 floating point arithmetic standard, which is honored by just about all modern programming languages and processor architectures. The IEEE "Infinity"values have a number of useful arithmetic properties for dealing with corner cases in numerical computations, but they are not infinity in any mathematical sense, and thinking about them that way almost guarantees a program that will deliver bogus results under some conditions.

 

[mbd]

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.

It is an open question, and, in my opinion, the biggest and most interesting open question. Certainly, though, the evidence points very strongly toward an ontology of randomness. I do in fact think God plays dice with the Universe. But, he rolls spherical dice and the result depends on when you ask the question.