Is this a question or comment or what?
Marchildon's consideration of "Hardy’s Setup and Elements of
Reality" concludes: "there seems to be no way to assign elements of reality in a relativistically invariant way". I.e. Lorentz invariance is incompatible with independent elements of reality, a la EPR.
Next he analyzes this conclusion against several interpretations of QM. Assuming I read him correctly (a big if), he is saying that standard collapse theory and Bohmian mechanics have problems with achieving Lorentz invariance; while MWI and Cramer's Transactional Interpretation do not.
Yes, he is saying that. But he was not aware of
http://xxx.lanl.gov/abs/0811.1905 [accepted for publication in Int. J. Quantum Inf.]
which, I believe, solves these problems. (When I saw Marchildon's paper few days ago, I have sent him a note regarding the paper above and he seemed to be interested about it. Maybe he will take it into account in a revised version of his paper.)
I saw some interesting stuff following Towler's lecture notes. He was saying that the Lorentz version of space-time should be kept, and the Einstein version of SR should be dropped. He says that makes things play nicer with Pilot Wave (BM/dBB) theory and perhaps solves some of the issues. I had not heard such a strong perspective on the matter before. Is this a viable option? I would guess that it would run afoul of General Relativity pretty quickly. Although I guess the Lorentz version of spacetime would have a lot of similarities with SR and therefore GR anyway.
It certainly is a viable option, even in curved spacetime (needed by general relativity). Nevertheless, such a version certainly looses some of its mathematical elegance. (The mathematical elegance is one of the reasons why I become interested in non-relativistic Bohmian mechanics in the first place.) If Bohmian mechanics is hoped to be a fundamental theory, then it is natural to require the mathematical elegance. For that reason, I prefer searching for a completely relativistic-covariant formulation. For the case in which particle creation can be neglected, the paper I mentioned above completely achieves that goal. Moreover, it provides a simple counterexample to various "theorems" claiming that relativistic-covariant nonlocal hidden variable theory is impossible. The crucial "new" idea in this paper that makes Lorentz covariance possible is the observation that |psi|^2 is not a probability density in space, but in SPACETIME. Such an idea may look as a deviation from experimentally confirmed probabilistic interpretation of psi, but, as explained in the paper, this idea is in a complete agreement with experiments.
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