This follows on from my post last week, “To Be or Not To Be (a Local Realist),” which discusses Joy Christian’s “Disproof of Bell’s Theorem.” Joy’s response to my post is here.

As I was stating at the end of part one, I am grateful to Joy Christian for give such a detailed answer in “Quantum Music from a Classical Sphere.” I was puzzled by his arguments and I was preparing several short replies to various points, when I realized this was getting out of hand and it was better to have a single coherent reply in a new post.

Let me start by saying that the topics we are presenting here are hard and there is no absolute agreement even between experts on the very definitions of what one means by locality, realism or contextuality, or a no-go theorem for hidden variable theories.  Some people consider quantum mechanics as local and non-realistic, while others insist on non-locality. Contextual hidden variable theories encompass a wide and ill-defined domain that is probably best defined by their opposition to the much sharper-defined non-contextual hidden variable theories. Some people think that non-contextual hidden variable theories were rejected by the theorems of Gleason and Kochen- Specker and Bell’s theorem is important only to reject some additional contextual hidden variable theories. Other people point out that the Kochen- Specker theorem cannot be put to any experimental test, and the importance of Bell’s theorem is to reject non-contextual hidden variable theories. Finally, some people think contextual hidden variable theories are unphysical, while others think they are the future of physics.

To cut through this confusing mess, the best approach is to rely on accurate historical narratives. This would provide a stable setting for the meanings of the terms used, which would allow a common discussion ground where we can compare apples to apples. Also it is best to seek experimental results to settle disputes instead of debates, however interesting. Last, speculation about future results is best not to be discussed at all. If those tenets are followed, charges of “alarming confusions” and a fruitless dialogue can be avoided.

With this preparation, let me attempt to explain what contextuality for hidden variable is, why Joy’s result is contextual, and what it all means.

First some preliminaries. Earlier I discussed the EPR paper and then I jumped to Bell’s contribution. However, historically Bohr also made an early critical observation in his attempt to refute EPR’s argument. Bohr was using the good old fashioned complementarity principle: in some experiments the particles behaves like waves, while in others like point particles. However, one cannot see them both in the same experiment. Therefore this invalidates EPR’s argument where on one arm of the experiment one behavior is measured, while in the other arm the complementary behavior is measured. To justify this experimentally, Bohr noted that observations depend not only on the state of the system but also on the disposition of the apparatus. And indeed, no physicist is ever going to deny this. Joy mentioned general relativity, and I can also point out for example electrostatics, and any other theories requiring boundary value problems. Joy considers this “contextuality,” but I would argue that this is clearly an overreaching usage of the term, which in hidden variable theories has a very different meaning which I will define later in its historical context. For the sake of the clarity, let’s call this “Bohr’s contextuality”.

As a supporting argument for his position, Joy mentioned Bell’s classical paper “On the problem of hidden variables in quantum mechanics.” However, Bell’s paper has a slightly different intention than Joy presented. Bell did not have an abstract for this paper and please allow me to explain how I understand this famous paper.

Einstein once said: “God does not play dice” and Bohr replied: “Do not tell God what to do.”  In a similar vein, I would say Bell’s main idea of the paper is: “Do not tell me how to construct my hidden variable theories.” Requirements which are obeyed by quantum mechanics are not necessarily obeyed by hidden variable theories, which should only reconstruct quantum mechanics’ predictions.

For the interest of time and space let me only discuss Bell’s criticism of von Neumann and Gleason in this paper. Von Neumann had enormous influence in quantum mechanics due to his seminal work on axiomatizing it. He produced a “no-go” theorem on hidden variable theories which Bell found unjustified in its assumptions. In particular, von Neumann required that the linear combination of expectation values is the expectation value of the combination. While true in quantum mechanics, this is too strong to be demanded for any particular value of the hidden variable, as an elementary example can show (from Reflections on Relativity by Kevin Brown):

Suppose we have two variables X and Y and two hidden variables 1 and 2. Suppose for hidden variable 1: X=2, Y=5 and X+Y=5 while for hidden variable 2: X=4, Y=3 and X+Y=9. Averaging for hidden variables 1 and 2, avg(x) = 3, avg(Y) = 4, and avg(X+Y)=7 and the sum of the averages is the average of the sums. On each hidden variable however, this property is not valid. (If you are worried about the funny math X+Y = 5 when X = 2 and Y = 5, “X”, “Y”, and “X+Y” are three separate experiments requiring separate experimental setups and the number appearing to the right hand side of the equal sign is the experimental outcome. The “+” in “X+Y” is only part of the label for an experimental setup and not a genuine plus operator.)

Gleason’s theorem improves on von Neumann’s result because it makes it a mathematical necessity to have a particular form of the average (the trace formalism) which does obey von Neumann’s condition for compatible (commuting) observables. Bell’s criticism on Gleason’s result is much more subtle and only here “Bohr’s contextuality” becomes a mandatory part of the argument. One can argue that von Neumann’s condition from above can be dismissed even without the toy example (which is not part of the paper, but I use it for the clarity of the argument), by pointing out that it is nonsensical for non-commutative variables which requires a different experimental setup. However, for compatible commutative variables it is a natural requirement (and this is what is used by Gleason).  Here Bell’s analysis becomes subtle.  To rule out hidden variables Gleason uses this requirement for commuting observables on spaces of dimensionality higher than two, meaning it has to be applied at least twice: on variables X and Y as well as X and Z, and while X and Y are compatible (commute), and X and Z are compatible as well, X and Z may not be (and the funny math from above can happen). It is only at this point where Bell says: “the result of an observation may reasonably depend not only on the state of the system (including hidden variables) but also on the disposition of the apparatus.”

So, Bell’s main argument was a defense of the freedom to construct a hidden variable theory. Unjustified requirements were also proven unjustified by showing they violate Bohr’s contextuality (but this is only a secondary supporting idea in the paper).

But why bother splitting hairs over the meaning of contextuality? Because it critically appears in many proposals of hidden variable theories aimed at recovering the predictions of quantum mechanics. Everyone agrees that quantum mechanics accurately describes nature, but not everyone is satisfied with quantum mechanics’ interpretation. Why is this so? In the traditional quantum world, there are no safe harbors for quantum objects (pure states are not immune to “collapse”) and you get epistemology (a statistical description) without ontology (objective reality) which generates a sense that something is fundamentally missing in this scheme. Hidden variables are supposed to fill this missing ontological gap and restore the “ignorance interpretation“ for the statistical nature of quantum mechanical predictions. First and foremost, in my opinion, hidden variables have to have a rock solid ontological value (ontological definiteness – typically known as non-contextuality). (Ontological definiteness is a stronger property than mere objective definiteness, which can be claimed for example by some parts of Bohm’s theory. Still, all hidden variable theories corresponding to Hilbert spaces of a dimension higher than two suffer in one form or another of ontological indefiniteness. In the case of Bohm’s theory--a contextual algebraic hidden variable theory--momentum is ill defined but still has objective definiteness. However spin is treated just like in standard quantum mechanics with ontological indefiniteness. I would challenge anyone to name a single hidden variable theory with dimensions higher than two which does not have ANY ontological problems.)

For measurement results, a dependency on the experimental context is completely acceptable. However, if hidden variables or their meaning changes with the experimental context, we are back to square one in terms of the strangeness of quantum mechanics. Not only do hidden variable theories suffer from strangeness, but all interpretations of quantum mechanics aimed at making it palatable to our classical intuition employ a bag of tricks: transactional interpretation is wonderful if you can swallow messages from the future; Bohm’s theory restores classicality at the expense of action at a distance; Everrett’s approach transforms “OR” into “AND” and deprives even classical physics of counterfactual definiteness, etc, etc.

So what do we call this rock solid (ontological) foundation? (Ontological) non-contextuality. If you are unhappy with standard quantum mechanics and its wave/particle complementarity, then you should not be happy with any other ontological flip-flopping explanation regardless of the packaging and other genuinely intuitive but ultimately non-essential features tied to the particular mathematical formalism used (lack of superposition, lack of entanglement, etc). The big pink elephant of epistemology without ontology remains in the middle of the room.

Ontological non-contextuality represents the golden standard for any physical theory aimed at restoring classical intuition. (As a side remark, general relativity and all other classical physical theories obey ontological non-contextuality.) Local realism obeys ontological non-contextuality too. We can now drop the ontological qualifier and simply state either contextual or non-contextual in the remainder of the text. This is the standard meaning of contextuality or non-contextuality when discussing hidden variables (and in this meaning general relativity is non-contextual). All non-contextual hidden variable theories are ruled out by many no-go theorems, and the majority of physicists consider contextual hidden variables unphysical with no experimental evidence ever backing their existence. There are also many flavors of contextual hidden variable theories and we already encountered the algebraic type in Bohm’s theory.

Now we are in a position to put everything together.

What does Bell’s theorem assert (regardless of any fine mathematical print)? Any locally realistic theory obeys certain inequalities which are violated by quantum mechanics and ultimately by nature in experiments. What is Joy’s challenge to Bell’s theorem? Non-commutative beables allows him to go over Bell’s inequality precisely like quantum mechanics. Is Joy’s theory noncontextual as he claims? No. Non-commutative beables are ruled out by Clifton’s theorem for non-contextual theories, meaning Joy’s theory cannot be non-contextual (and I clarified some more what kind of contextual theory it is in my preprint: http://arxiv.org/abs/1107.1007).

But let’s assume that both Clifton and I are mistaken. There is a simple way to put this to the test: if Joy’s claim of non-contextuality is correct, then one can write a computer program modeling his theory and obtain Tsirelson’s bounds. (This is not my idea; I got it from researching the web for reactions to Joy’s results.) I claim this cannot be done. If anyone manages to actually write such a program which goes above Bell’s limit then I admit I am completely wrong and Joy is right in his non-contextuality claim. And if he is right on his theory’s non-contextuality claim, then he did manage to disprove Bell’s theorem as usually understood by the physics community.

In the meantime, let me explain why I think Joy’s theory cannot be modeled on a computer and why it is not a strictly locally realistic theory.

Recently Joy published http://arxiv.org/abs/1106.0748. It is relevant to note that the state space (encoding the complete information) for spin 1/2 is SU(2) which is isomorphic with SO(3) where geometric algebra can naturally be used. There is an additional degree of freedom coming from the double cover property of the isomorphism and this allows for the possibility of a hidden variable which encodes the information on which one-to-two map you are located. It is not hard to see that Joy’s formalism when done consistently in the geometric algebra formalism is an equivalent representation of the standard quantum mechanics and his agreement with quantum mechanics comes as no surprise. However, Joy’s formalism lacks a “Born rule” which translates his formalism into the actual experimental outcomes (real numbers). If in http://arxiv.org/abs/1106.0748 one applies at any intermediate steps a map from geometric algebra objects to real numbers, it is easy to see that one only recovers Bell’s limit. (In standard complex quantum mechanics formalism this would correspond to applying Born’s rule too early and adding probabilities instead of amplitudes resulting in incorrect classical behavior predictions). But not applying any translation mechanism until the end in Joy’s formulation means that this step is delayed until the interaction taking place during the measurement process (which has to somehow implement/model the geometric algebra operations).Tung Ten Yong (http://arxiv.org/abs/0712.1637) has criticized Joy’s model because the final results are expressed as geometric algebra objects. I do not think this is a decisive criticism of Joy’s theory as Yong claims because if nature is quantum mechanical at heart, and if Joy’s theory reproduces all quantum mechanics results, this means that geometric algebra should be the proper ontology of nature. And then it is very natural to expect interaction during measurement to realize geometric algebra operations.

But geometric algebra objects are non-local and while Joy can call his model local due to factorizability, it is non-local due to the critical usage of a geometric algebra product (during measurement). Locality does not mean only separability between Alice and Bob, but must include a notion of physical distance as well. This additional non-locality would prevent any faithful simulation on a computer program because one cannot program a way to compute the experimental outcome for Alice at one end without accessing all information encoded in SO(3), meaning the inclusion of the information at Bob’s end as well (which is unavailable due to physical separation).

Again, if you disagree with the analysis above, Clifton’s theorems, or my preprint http://arxiv.org/abs/1107.1007, write a computer program modeling Joy’s theory for EPR-Bohm and show you get Tsirelson’s bound. If you succeed, I am wrong, this post is essentially incorrect, Joy’s theory is non-contextual, and Joy did disprove Bell’s theorem by counterexample.

Joy’s theory can be considered both local due to factorizability, and non-local due to geometric algebra. It can also be considered both realistic as it employs classical three dimensional geometrical objects, and non-realistic as it is (ontologically) contextual (the local beables critically depend on the experimental setting).

Finally, the same conclusions from my prior post and preprint stand: Joy does not disprove Bell’s theorem mathematically because he starts with a different assumption, that of a non-commutative beable algebra. I really did not understand Joy’s remark: “In particular, contrary to what Florin asserts, I do not start with mathematical assumptions different from those of Bell,” Quoting Joy (http://arxiv.org/abs/quant-ph/0703244v12): “In fact, apart from the multiplicative non-commutativity, they satisfy exactly the same algebra as do the local beables of Bell. […] Bell’s algebra, by contrast, is a commutative and associative normed division algebra over the field of real numbers.” Also: “Finally, Grangier expresses his unhappiness with the choice of my running title: “Disproof of Bell’s Theorem.” He rightly points out that as a mathematical theorem Bell’s theorem cannot be disproved, since its conclusions follow from well defined premises in a mathematically impeccable manner.”

Contrary to his claims and paper titles, Joy does not disprove the importance of Bell’s theorem as the key result validated by experiments rejecting local realism. If Clifton’s theorem is right or if my spin one analysis is correct, Joy’s theory is a contextual theory not classifiable as locally realistic. This is a scientific falsifiable statement, as any computer simulation of Joy’s theory exceeding Bell’s limit would render both Clifton’s theorems and my preprint wrong.

Last, Joy’s theory does expose a weakness in Bell’s theorem. Clifton’s theorems fill this weakness and Bell and Clifton’s theorem combined do rule out all hidden variable theories obeying local realism because Bell requires commutativity of beable algebra and Clifton shows that beable algebra must be commutative for all non-contextual theories and for any relativistic quantum field theories with bounded energies. As a counterexample, Joy’s theory does limit Bell’s importance in Shimony’s interpretation for some contextual hidden variable theories. However, other physicists including myself disagree with Shimony and place Bell’s theorem’s importance solely for rejecting non-contextual hidden variable theories in an experimentally verifiable fashion (in my preprint’s abstract I presented both points of view).

Scientific conclusions aside, I did enjoy learning about Joy’s result, and I do think they represent very valuable contributions in our understanding of quantum mechanics and hidden variable theories. More interesting work remains to be done and I would be very interested to see any proofs for his “Theorema Egregium” or (Eq. 10 in my preprint). I wish Joy success in further developing his ideas.

this post has been edited by the author since its original submission

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Dear Florin,

Thank you very much for your detailed reply. I will need to write down some equations to properly address the points you are making. So instead of posting my reply here I will post it in this collection of my ongoing replies. I hope that is alright with you.

All the Best,

Joy

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Dear Joy and Florin,

If I am missing something, I would be grateful if you would explain me. I will say briefly what I think so far about Joy's theory. To make the things clear, I split the theory in two layers.

1. (a simplified version of Joy's theory, as I see it). We want to obtain the The EPR correlation for two particles in a singlet state, which is the cos of the angle between the orientations of the measurement devices. The obvious way to obtain cos is to take the dot product between the two orientations.

2. The second layer - the usage of Pauli's algebra - seems to provide a justification for the 1st layer, but I think that in fact it is just a mean to obtain the dot product, hence the cos, and it obfuscates the idea.

Being it dot or Clifford product, I fail to see other justification for it than to get the desired cos.

But let's assume that Joy's papers present a good reason for this. I don't see why this is considered local, and a disproof of Bell's theorem. The particles are "at a distance", so this operation would be non-local. Also, we can take the dot/Clifford product for any two particles, being from a singlet or not, and get the same cos, which this time is not the correct correlation. So, we would have to say that if they are entangled, we can dot them, if not, we should do something else. So we couldn't get rid of entanglement.

Briefly, I think that the "exact sequence" is this:

justify "space algebra" -> take Clifford product -> keep dot product -> get cos correlations

and at this moment I don't see other reason for this approach than to get the cos. And the approach itself sounds to me like a "spooky Clifford product at a distance" :-), so I wouldn't consider it a disproof of Bell's theorem.

Are the things really that simple as I see them, or I am missing something?

Cristi

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Dear Florin,

Both your posts, as well as your paper, are very well-written, and as usual you did a great job conveying highly abstract ideas so that they can be followed by a wide audience. Joy's response deserves equal praises, and he answered with patience the questions addressed to him.

You said: "Tung Ten Yong (http://arxiv.org/abs/0712.1637) has criticized Joy's model because the final results are expressed as geometric algebra objects. I do not think this is a decisive criticism of Joy's theory as Yong claims because if nature is quantum mechanical at heart, and if Joy's theory reproduces all quantum mechanics results, this means that geometric algebra should be the proper ontology of nature."

I must say that the very moment when I read your remark, I was convinced that Yong was in fact criticizing the use of geometric algebra objects AS EXPECTATION VALUES. This was one of the first features that stroke me when reading Joy's work.

The expectation value is a real number. The measurement device indicates real numbers. Quantum mechanics is based on complex numbers, Hilbert spaces, matrices, yet the results are real numbers, ALWAYS. Because the expectation value is a probabilistic thing. So, in this particular point, I must agree with Yong.

Joy's expectation value is an even element of the Pauli algebra. While it looks structurally similar to the expectation value for real numbers, there is no obvious meaning of it. What is the meaning of a a Clifford-valued expectation value?

But I don't want to reject this novel type of expectation value just for not being real numbers. For example, the expectation values of momentum, along the three axes, are real numbers, but you can if you really want make statistics with the vector which has them as components. So, one may be able to write "vector valued expectation values".

So, in my opinion, when introducing a novel kind of expectation value, it should come with some explanations of why is this an expectation value, and what actually is a Clifford algebra valued expectation value. I couldn't find this explanation in Joy's papers.

Of course, if we take the limit for large number of observations, the bivector part cancels and we remain with a real number - the cosine. But what if we make only one observation? Would the result have a bivector part? If so, what's its meaning?

Best regards,

Cristi

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Dear Florin,

I don't understand your remark: "geometric algebra objects are non-local". Could you please explain it more?

For example, we can rewrite Maxwell's equations using geometric algebra. Does this make the electromagnetic field non-local?

What if, instead of the geometric product in Joy's theory, we take just the dot product (which is commutative)? We obtain directly the cos, without worrying about the bivector part of the expectation value, and we avoid using geometric algebra. Does this make Joy's theorem more local?

Best regards,

Cristi

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Florin,

I am intrigued by this matter of computation. First off it sounds as if there is some scuttlebutt about this. Yet of greater interest, if one really wanted to address this question it seems to come down to an issue of algorithmic structure and computability. If you are right this means the Tsirelson bound is simply not computable by JC’s system. Unfortunately I am not familiar with Clifton’s theorem and other matters so I do not see clearly what the problem is. This issue of hidden variables and contextuality is pretty tangential to my main focus. Yet this seems to suggest that either this is some problem involving a contradiction, or it is a problem involving NP completeness, where the space is somehow to large to ever compute this, or maybe (though I doubt it) some sort of Turing machine halting problem or Godel’s theorem.

Cheers LC

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Florin,

This almost seems to boil down to asking whether a Rubik’s cube has nonlocal properties. The 4x10^{19} configurations of the cube could be a Hilbert space. If I wanted to teleport a state (Rubik's cube configuration) to Alice I would need to perform a set of Hadamard operations on an ancillary state that she and I have access to. This would demolish some entanglement. The question might amount to asking whether or not the teleportation could be completely accomplished with just the Rubik’s cube operations and nothing else. Hence the contextuality of states in a quantum setting would be defined entirely by the cube operations, without a Hadamard matrix operation for a SLOCC operation.

This might be an interesting thing to chew over for a while.

Cheers LC

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Dear Florin,

I wish to start by saying I have enjoyed the discussion between yourself and Joy and I look forward to the continuation. My own studies of Bell's work have led me to the following position. Bell's theorem can be generalized as follows:

--

IF there exists a single probability distribution p(a,b,c) from which three distributions p(a,b), p(b,c), and p(a,c) can be extracted, then the expectation values from these distributions must necessarily obey the following inequality:

|E(a,b) - E(a,c)|

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Here's how I see a software simulation of a local hidden variable theory applyed to the EPR experiment:

1. Make a computer program which generates randomly the hidden variables corresponding to each of the two particles corresponding to a singlet state (stored in a data structure).

2. Make a computer program which receives as input a data structure containing the hidden variables corresponding to one particle, and the orientation of the measurement device, and returns either +1, or -1. Give a copy of this program to Alice and another to Bob.

3. Prepare two states with the algorithm #1.

4. Send one of the states, by email, to Alice, and the other to Bob, which are at distant locations from one another.

5. Alice disconnects from the Internet, then runs the algorithm #2, with the first parameter being the hidden variables she got by email, and the second parameter the orientation of the measurement device, randomly chosen. Then she saves the orientation and the result (+1 or -1).

In the same time, Bob does the same as Alice, but for his particle.

7. Alice and Bob connect simultaneously to the Internet and send the orientations and the results to a server, to be recorded.

8. Repeat the steps 3 to 7 a large number of times.

9. Calculate the correlations between the data recorded on the server.

10. Compare the results with those predicted by Quantum Mechanics (and verified by experiments).

----------------------------

I think that it is a good exercise to think at possible ways to make the program output the two results correlated as they are in QM. The ardent practitioner of this sadhana receives the insight into the meaning of Bell's theorem :-)

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AN EXPLICIT LOCAL VARIABLES TOPOLOGICAL MECHANISM FOR THE EPR CORRELATIONS

It is based on a non-trivial topology (wormholes).

Cut two spheres out of our space, and glue the two boundaries of the space together. This wormhole can be traversed by a source free electric field, and used to model a pair of electrically charged particles of opposite charges as its mouths (Einstein-Risen 1935, Misner-Wheeler's charge-without-charge 1957, Rainich 1925).

For EPR we need a wormhole which connects two electrons instead of an electron-positron pair. A wormhole having as mouths two equal charges can be obtained as follows: instead of just gluing together the two spherical boundaries, we first flip the orientation of one of them. Since the electric field is a bivector, the change in orientation changes the sign of the electric field, and the two topological charges have the same sign.

Now associate to the two electrons your favorite local classical description. The communication required to obtain the correlation can be done through the wormhole.

----------------

This may be the basis of a mathematically correct local hidden variable theory. Also, it seems to disprove, or rather circumvent, Bell's theorem. For Bohm's hidden variable theory, it provides a mechanism to get the correlation without faster than light signals. I proposed it here for theoretical purposes only, as an example. My favorite interpretation is another one.

Cristi

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It is because being and experience and thought/ideas are integrated and interactive that there are limits to the understanding. Where do you think that ideas come from? The requirements, limits, and extensiveness of truth center upon the extent to which thought is similar to sensory experience. We all come from the center of the human body.

AND, the purpose of vision is to advise of the consequences of touch in time. Another great physical truth -- (by Berkeley).

We do not move (naturally) with regard to the Sun and photons because there are no consequences of touch in time. That is, no gravity, black space, death, destruction of vision, inability to discern distance in outer space.

Sorry folks, physics ultimately involves natural experience that gives us life.

FUNDAMENTALLY, THE ENTIRE APPROACH OF MODERN PHYSICS IS INCORRECT, AND ULTIMATELY DESTRUCTIVE.

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lET'S START FOCUSING ON CONSTRUCTIVE PHYSICS -- THE PHYSICS OF NATURAL EXPERIENCE, GROWTH, AND LIFE.

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Florin,

When I pointed out Joy's work to you I was hoping for just the type of result you've produced above. I'd like to thank you for this effort. In particular I enjoyed your clear discussion of contextual and non-contextual. One cannot even evaluate Joy's statements about the relevance of 'contextuality' without knowing what is meant by the terms. Many people are interested in this topic and you have done all of us a favor by clarifying these definitions.

I am also pleased that you are more open on this subject. You earlier claimed that I brought disgrace on my theory by even referring to de Broglie-Bohm or 'hidden variable'. Now you note that "there is no absolute agreement even between experts on the very definitions of what one means by locality, realism, or contextuality, or a no-go theorem for hidden variable theories."

In addition to Joy Christian's analysis challenging the status quo, I've also pointed out recently that weak quantum measurements resulted in the following observation:

"Single-particle trajectories measured in this fashion reproduce those predicted by the Bohm-deBroglie interpretation of quantum mechanics."

In my mind, both of these results, theoretical and experimental, challenge John Bell's test. In addition you have noted that, unlike Bell, Kochen-Specker cannot be put to any experimental test. It is from this perspective that I ask the following:

Is violation of Bell's inequality *the* basis for rejection of local realism in physics?

That is, if Bell had derived Tsirelson's bound, would most physicists today reject local realism in quantum mechanics?

Thanks again for analyzing Joy's work and sharing your analysis with us. I look forward to your answer.

Edwin Eugene Klingman

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KEEP AN EYE ON PHYSICS TODAY MAGAZINE FOR MY UNIFIED AND FUNDAMENTAL EXPLANATION OF PHYSICS (AND OUR ORIGIN).

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Hi Florin,

I regret that I just got around to your arXiv paper ("Comments on 'disproof of Bell's theorem')but things have been flying pretty thick and fast.

I stumbled on this point:

"Joy Christian then attempts a generalization and makes an extraordinary claim without proof [4]: for any Hilbert space H of arbitrary dimension there exist a topological space corresponding to EPR counterfactual elements of reality and a morphism m : H -> Omega such that the following relation holds:

m(|psi_a> + |psi_b>) = (m|psi_a>) + (m|psi_b>) = A_aA_b members of Omega (10)

with A_a and A_b two points in the topological space. From this it is not hard to prove that exact local-realistic completion of any arbitrary entangled state is always possible. At this point, it is not clear if Eq. 10

can always be achieved, and this is a very interesting open problem."

I wasn't aware it was an open problem; however, it is simply proved by consequence of Joy's condition of 4pi (vice 2pi) rotation, q.e.d. Details from my results in the "Quantum music ..." blog, 16 August, text and attached figure.

His whole framework is, as he has claimed, is complete in its generalization.

Tom

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Tom,

I have been following both Joy's and Florin's forums from the start. It has been fascinating and it seems to me that your analysis is "spot on". Florin has represented the opposing view admirably, and I believe Joy benefits from the communications he's received from both of you. Unfortunately, my math skills aren't sufficient to contribute or even distinguish between the "subtle" and the "malicious", but it does make me want to learn more.

Keep up the good work,

Dan

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Dear Florin,

I miss your participation. Out of ignorance, I ask for further clarification. Joy used geometric algebra. I am still looking into that. However, I assumed that geometric algebra would have already had the connection that you mention here:

"All I would say is that at some point some consistent translation mechanism has to be found from Joy's formulation to standard statistics. I disagree with Joy not on his math, but on his interpretation. And if his math is right I am confident such a mechanism does exist and will be eventually discovered. In other words, if Joy found an equivalent way of formulating QM, Born rule's translation into the new formalism will follow. It is just not done at this point."

Does your point have to do with something other than geometric algebra or are you saying that there is no current link between geometric algebra and standard statistics? If so, how important is this missing link? Missing links seem very important to me. As I have said to Joy, if my questions or remarks are off the mark please just say so and I will study your messages again.

James

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Tom,

I have to acknowledge your superior skill. I read your previous powerpoint presentation. It was somewhat abrupt for me. However, you presentation:

"Let's see how this makes out:

joy christian local realism experiment"

is way too thin for me. However, I am satisfied just to see what the professionals say in response.

Thank you,

James

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Florin,

Sez who?

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TH Ray wrote: "Overcoming spacetime curvature -- now, that's an accomplishment."

Many of your masters have overcome it but did not inform you:

http://www.newscientist.com/article/mg20026831.500-what-
makes-the-universe-tick.html

"It is still not clear who is right, says John Norton, a philosopher based at the University of Pittsburgh, Pennsylvania. Norton is hesitant to express it, but his instinct - and the consensus in physics - seems to be that space and time exist on their own. The trouble with this idea, though, is that it doesn't sit well with relativity, which describes space-time as a malleable fabric whose geometry can be changed by the gravity of stars, planets and matter."

Pentcho Valev pvalev@yahoo.com

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Jason Wolfe wrote: "Some may argue that the relationship between gravity and light is already well known. Let me be more specific. There is more to learn, by experiment, about phase/frequency shift of light AND gravitational time dilation."

Consider this:

http://student.fizika.org/~jsisko/Knjige/Klasicna%20Meh
anika/David%20Morin/CH13.PDF

David Morin: "The equivalence principle has a striking consequence concerning the behavior of clocks in a gravitational field. It implies that higher clocks run faster than lower clocks. If you put a watch on top of a tower, and then stand on the ground, you will see the watch on the tower tick faster than an identical watch on your wrist. When you take the watch down and compare it to the one on your wrist, it will show more time elapsed."

Is it true? Clever Einsteinians know that there is no gravitational time dilation. The gravitational redshift arises from the change in the speed of light signals in the presence of gravitation:

http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/d
p/0486406768

Banesh Hoffmann: "In an accelerated sky laboratory, and therefore also in the corresponding earth laboratory, the frequence of arrival of light pulses is lower than the ticking rate of the upper clocks even though all the clocks go at the same rate. (...) As a result the experimenter at the ceiling of the sky laboratory will see with his own eyes that the floor clock is going at a slower rate than the ceiling clock - even though, as I have stressed, both are going at the same rate. (...) The gravitational red shift does not arise from changes in the intrinsic rates of clocks. It arises from what befalls light signals as they traverse space and time in the presence of gravitation."

Pentcho Valev pvalev@yahoo.com

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attachments: 48_Gill.pdf

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I am glad seeing this continuation, it is very much informative where I can be motivated.

technical content

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