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.

 

[Mathematech]

Maybe this student went on to develop IEEE standards :D

 

[mbd]

Speaking of intuition and instinct, QM depends critically on a point-particle view of matter. It is this view that has, as its consequence, indefiniteness of state, non-locality, and such.

Bell clearly shows that a point-particle viewpoint of matter leads to non-locality, and experiments do seem to confirm this.

If you execute a "loophole-free" EPR experiment against the loopholes that are motivated only by a particle viewpoint of matter, then the results will certainly seem to confirm an ontology of randomness and non-locality. In other words, the definitive experiment can at best claim to say (assuming success), that "If the world is made of particles, then the world is indefinite and non-local."

<Speculation>
However, if the "star stuff" are relationships, rather than particles, each end of which depends on the other at the speed of light, then there's no need for randomness or non-locality. A definitive experiment must rule this out. I call it the "aparticle" loophole.
</Speculation>

Here's a link to some recent work confirming the theoretical potential of an "aparticle" based theory at the astrophysics level. Note they still model the interaction over distance as a particle. I model it as a series of step waves through the relationship with observable events the consequence of a threshold having been reached.

http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.109.231301

 

[DrChinese]

... QM depends critically on a point-particle view of matter. It is this view that has, as its consequence, indefiniteness of state, non-locality, and such.

Bell clearly shows that a point-particle viewpoint of matter leads to non-locality, and experiments do seem to confirm this.

Actually, it is not QM that depends on that view. It is classical-type theories (that are ruled out by Bell) that depend on that "point-particle" view. There are plenty of folk who do NOT see quantum particles as point-like. If you accept the Heisenberg Uncertainty Principle as fundamental (or perhaps as a fundamental deduction of QM postulates), you probably will reject the point-like characterization of particles completely. Your conclusion will still be somewhat interpretation dependent. For example, Bohmian class theories typically view particles as point-like with a well-defined position. But in the general case, I see QM as silent on this point (sorry for unintended pun).

 

[mbd]

By point particle I mean in the Dirac delta sense, not in the absolute sense. Sorry for the imprecision.

Perhaps another way to look at it is as something separable from its context, or something that can exist in isolation.

In the Dirac delta sense, it is something for which there is a distance beyond which the upper bound of its influence on any other thing is on the order of 1/d^2.

 

[Darwin123]

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?

I suspect that if it is ghost written, then the ghost doesn't know much mathematics either. Please show me anyplace where the writer shows any "rigor".

Just out of curiosity, though:

Is "Joy Christian" his original name? The one that his parents gave him? Or did he pick this name as an adult?

 

[mbd]

I'm bothered by the personal attacks and speculation about mental health aimed at the subject of this thread. Can we please keep the criticism to the papers and the science?

 

[Mathematech]

If someone writes something like A(L) = 1 when L = 1 and A(L) = -1 when L = -1 and then denies that A(L) = L when L = +/-1 then you start worrying about some form of mental disorder.

 

[Tomahoc]

While you folks are discussing about Bell's Theorem. Are you aware of any Entanglement experiments which has disproven the theory that as entangled particles separate, they form a spacetime foliation with time synchronized to both of them from T-0 until collapse (this is assuming the wave function is not just in the equations but actually there in spacetime)? Is this possible or disproven already?

 

[Dadface]

I have been considering putting Bell's Theorem on my list of things to look at but I have been unable to get past the statement of his theorem:

"No physical theory of local hidden variables can ever reproduce all of the predictions of quantum theory"

If any theory cannot predict what is observed then that theory is flawed and should not be considered as a real theory at all.

Suppose that there can be such a thing as a real theory of local hidden variables.If so it
will reproduce all of the observable predictions of QM. The problem is that the details of such a theory are not known and nor are the details and subtleties of any detection methods known.

How then can Bell and his followers make generalised statements about all theories without a detailed knowledge of those theories?

 

[Mathematech]

I just finished reading James Weatheralls paper (see link posted by DrChinese), very good analysis. I think Christian was trying to do a model of the type discussed in the paper where measurement results are represented by rotation orientations - this is the sort of thing everyone tries to come up with when first encountering Bell. I did it myself as a kid after reading d'Espagnet's famous paper in Scientific American (http://www.sciam.com/media/pdf/197911_0158.pdf) - I even built some contraption with cardboard disks connected by a rod to picture what's going on. I didn't know about wedge products and bivectors but got by with good old ordinary 3 vectors and a lot of sines and cosines. If you do that sort of stuff (which is an explicitly realist model) you quickly discover that you simply cannot get by the counting arguments) Now at that young age I hadn't bought into the whole eigenstate ontology (or even known its mathematical details) so non-locality had to be the answer. But assuming relativity it was pretty clear also that some form of signaling or traveling influence couldn't be the answer - the conclusion was that there had to be something analogous to the rod between my cardboard disks in reality, but which truly behaved "rigidly" so that turning one disk turned the other and turned it instanteously not like in a real rod made up of molecules where the influence is pretty fast but not instantaneous. This I found deeply disturbing but became less disturbing over the years as I learned to appreciate that space and time is something that "emerges" from the fact that entities interact via electromagnetism and gravity, it isn't something that is just there in the first place.

 

[Mathematech]

Dadface, the notion of a "local hidden variable theory" has a very precise mathematical definition and this definition is general enough to include essentially any theory that excludes any faster than light (in particular instantaneous) connections between separated particles and assumes one can meaningfully count counterfactual values along with factual ones. The definition then allows us to calculate a numerical constraint that all such theories must obey. However QM doesn't obey that constraint and QM wins when checked experimentally.

 

[Nugatory]

How then can Bell and his followers make generalised statements about all theories without a detailed knowledge of those theories?

It's not a statement about "all theories", it's "all theories that depend on hidden variables with particular properties", and the proof proceeds from those properties.

 

[Greg-ulate]

If you accept the Heisenberg Uncertainty Principle as fundamental (or perhaps as a fundamental deduction of QM postulates), you probably will reject the point-like characterization of particles completely.

I learned to appreciate that space and time is something that "emerges" from the fact that entities interact via electromagnetism and gravity, it isn't something that is just there in the first place.

I finally like where this thread is going. I've literally been losing sleep over this for some time.

 

[DrChinese]

I have been considering putting Bell's Theorem on my list of things to look at but I have been unable to get past the statement of his theorem:

"No physical theory of local hidden variables can ever reproduce all of the predictions of quantum theory"

If any theory cannot predict what is observed then that theory is flawed and should not be considered as a real theory at all.

Suppose that there can be such a thing as a real theory of local hidden variables.If so it
will reproduce all of the observable predictions of QM. The problem is that the details of such a theory are not known and nor are the details and subtleties of any detection methods known.

How then can Bell and his followers make generalised statements about all theories without a detailed knowledge of those theories?

I think you have answered your own question! You should DEFINITELY look deeper at Bell's Theorem. I can't believe you have 1800 posts and we haven't been able to pull you in on this previously.

And while you are at it, ask yourself: what does it mean that there are hidden variables? It is only those theories which are ruled out by Bell (unless of course there are nonlocal interactions). You should go all the way back to the 1935 EPR paper to understand this point. They talk about "elements of reality" and define that specifically. Entangled particle pairs evidence EPR elements of reality, and those elements of reality imply hidden variables. Bell tackles that point head on. It turns out that it is not possible to have those elements of reality beyond what can actually be observed and expect a match to the QM predictions. Ergo there are no local hidden variables. We must live in an observer dependent universe.

 

[Dadface]

Thank you Mathematech and Nugatory and thank you DrChinese. DrChinese, your advice looks good. I just tried a google search to find the 1935 paper and your site on Bell came up.
I have visited your excellent site before but have just scanned it and not looked at it in enough detail to get,what I think, would be a thorough understanding. I will certainly look at the 1935 paper but I know I will have troubles with the maths.I haven't looked at that sort of maths for over fourty years.

 

[DrChinese]

Thank you Mathematech and Nugatory and thank you DrChinese. DrChinese, your advice looks good. I just tried a google search to find the 1935 paper and your site on Bell came up.
I have visited your excellent site before but have just scanned it and not looked at it in enough detail to get,what I think, would be a thorough understanding. I will certainly look at the 1935 paper but I know I will have troubles with the maths.I haven't looked at that sort of maths for over fourty years.

You can skip the math in EPR, just assume it is correct.

The real joy of the paper is that they define "element of reality" in a manner that it is difficult to refute. If you can predict a measurement outcome before it occurs, then there must be an element of reality somewhere associated with it. That is the case with an entangled particle pair, you can measure one to learn about the other.

Next: if you think of particle spin along different axes as being different observables (different elements of reality), then these must be predetermined if we are living in an observer independent reality. In such a reality, the Heisenberg Uncertainty Principle is NOT fundamentally true - because complementary elements of reality exist. That was what EPR sought to demonstrate, and they thought they had. Of course, Bohr and others rejected their conclusion as unwarranted. In fact, the two sides were at an impass.

Bell raised the bar by attempting to imagine hidden variables that would determine outcomes at many different angles. It turned out there was a major consistency conflict between the "elements of reality" criterion and the quantum predictions.

 

[Dadface]

Thank you DrChinese.
I will have a read up and give this some more thought. The Stanford Encyclopaedia of Philosophy seems to give a good account of EPR.

 

[Mathematech]

I read this book years ago

https://www.amazon.com/dp/0198242387/?tag=pfamazon01-20

A very good introduction to the subject. The math was at a very rigorous but nevertheless easy to understand level. As a mathematician there were some things I couild nitpick about but they were really only things a mathematician would nitpick about :)

The only things missing from this book were i) a detailed examination of how probabilities of counter-factual incompatible measurements differ from probabilities of compatible measurements (he seemed to be dismissive of Arthur Fine's work or he never really understood it) and ii) a detailed discussion of how a non-local mechanism would work although a lot of what is said these days hadn't been said yet when this book was written.

 

[mbd]

If one constructs a theory that is local, realistic, but not counterfactual definite, then the theory is not ruled out by Bell's Theorem. It is an open question whether one exists.

The interesting space is in the extremely subtle difference between realism and counterfactual definiteness. Here's a paper with a good explanation of the distinction:

http://arxiv.org/abs/0902.3827

An equivalent way to look at it is to consider the experimental constraints that the assumptions of Bell's Theorem require. A recent paper by Antonio Di Lorenzo explains, and defines quite clearly, the assumptions from a more experimental point of view.

http://pra.aps.org/pdf/PRA/v86/i4/e042119

 

[Nugatory]

The interesting space is in the extremely subtle difference between realism and counterfactual definiteness. Here's a paper with a good explanation of the distinction:

http://ajp.aapt.org/resource/1/ajpias/v78/i1/p111_s1?isAuthorized=no

Behind a paywall, unfortunately. Can you summarize the distinction as Blaylock sees it?