Joy Christian wrote:Let me respond to each of the points made by Gill:
Gill: “…there are two quite distinct models in the paper we are discussing.”
This is incorrect. There is only one model — the 3-sphere model:
https://arxiv.org/abs/1405.2355 . To be sure, in my paper there are two different representations of the 3-sphere considered, each with some advantages and some disadvantages. Both representations are valuable, and they complement each other quite nicely.
Gill: “They seem to be hardly connected to one another at all.”
This is incorrect. How can there be no connection between two representations of one and the same manifold, namely a 3-sphere? This is why I am sometimes forced to stress that Gill has never published a single peer-reviewed paper in Clifford algebra (which, by the way, he learned from me) or general relativity to understand the physical model presented in my paper.
Gill: “The first model reproduces the quantum correlations, but is non-local – it is Pearle’s detection loophole model.”
This is incorrect, on both counts. Both representations of the 3-sphere model are manifestly local. Gill here makes an empty statement without a proof. And contrary to his claim, the first representation is by no means Pearle’s detection loophole model. His claim makes me suspect whether he has actually read my paper at all. To be sure, I use some of the formal mathematical constructs used by Pearl, but there is no exploitation of a “detection loophole”, or any other “loophole” for that matter, in my local model. There is a one-to-one accounting in the model between the initial (or complete) state (e, s) and the measurement outcomes A and B. So Gill once again makes a false claim without providing a proof for his claim.
Gill: “Christian learnt [Pearle’s model] from me.”
This is incorrect. I did not learn Pearle’s model from Gill. I learnt it from my former Ph.D. adviser, Prof. Abner Shimony, in the mid 1980’s, and few years later from Philip Pearl himself (whom I know personally). And while I am at it, let me also mention that I learnt about Bell’s theorem also from Abner Shimony (the “S” in the Bell-CHSH inequality) while I was his student in the mid 1980’s, and a few years later from John. S. Bell himself (with whom I was also well acquainted, thanks to my mentor Abner Shimony).
Gill: “The second is the crazy model A(a, lambda) = -B(b, lambda) = lambda = +/-1 which is clearly local but which clearly does not reproduce the quantum correlations.”
This is incorrect, on several counts. As anyone can see Gill is confusing the measurement outcomes A and B with the hidden variable lambda when he writes A = +lambda and B = -lambda. Look carefully. That is what he has written, just as he has done many times in the past. This shows that he has not really understood my model. And it is quite extraordinary that he confuses the measurement outcomes A and B with the hidden variable lambda. Also, contrary to his claim, my model evidently reproduces the quantum correlations, as anyone can see by simply studying my paper carefully and investigating the details of the analytical as well as numerical evidence presented therein. But Gill has got one thing right –- my model is indeed manifestly local, as anyone knowledgeable in the subject can readily see.
Gill: “I suggest study of one of the simpler proofs of Bell’s theorem, if you want to understand what Christian is up against.”
I recommend that too. And then, if you think you have understood Bell’s argument, I suggest that you take up my challenge to Bell’s theorem and prove me wrong. Here is my challenge, which is open to anyone, and can be taken anywhere on the Internet, not only at Fred’s forum:
viewtopic.php?f=6&t=275#p6681Gill: “You can’t even define what is a local hidden variables model without using the language of probability theory.”
This is incorrect. John S. Bell, in his famous paper of 1964, used only expectation values, not probabilities, to define a local hidden variables framework, and then produced an explicit analytical local model of his own, without using any unnecessary notion from the probability theory.
Finally, I will not quit participating at RW. I will be here to answer any questions, or respond to any reasonable criticism that I have not addressed already over the past nine years.