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I've the kinetic approach in mind. There the "coarse-graining" is done via gradient expansion. I've to think harder, whether this leads to a violation of Bell's theorem. Maybe this is a loophole in my argument!atyy said:Can you show that the coarse-graining is local and preserves relativistic causality? Peres talks about coarse-graining such that the Wigner function becomes entirely positive, which means that the theory resulting from the coarse-graining is a classical probabilistic theory and therefore realistic. If the coarse-graining is local, the resulting theory is presumably a local realistic theory. However, the Bell theorem forbids local realistic theories, so the theory that results from local coarse-graining presumably cannot explain violations of the Bell inequalities at spacelike separation.
I think the paper you are thinking about is Braam Gaasbeek's "Demystifying the Delayed Choice Experiments" http://arxiv.org/abs/1007.3977. I agree with this paper completely. Section 3 does not correct Figure 1. Section 3 says Figure 1 is correct, but that collapse is not necessarily physical (not an frame-invariant event). Quantum mechanics in the minimal interpretation is an FAPP theory, and the predictions of FAPP collapse are thus far completely successful and consistent with special relativity. So this paper does not support your point (unless we are agreeing, but using different language). Rather it supports my point that collapse is part of the standard postulates of quantum mechanics, and is not in conflict with relativity.
Yes, that's the paper. Sorry, I forgot to cite it properly again. Here's the crucial point (at the end of Sect. 3):
If "nothing happens along these slices" in Fig. 2 then the instantaneous collapse proposed in Fig. 1 doesn't happen, or did I get this wrong?B. Gaasbek:
We can now solve the problem we started with in the
introduction. If the measurement is nothing but an iso-
lated event in space time, there is no point whatsoever in
trying to associate a spatial slice to it. So the horizontal
and tilted lines in Figure 2 actually have no meaning at
all! Nothing happens along these slices - the only place
where something physical happens is the place of the
measurement, and the implications on conditional prob-
abilities hold for other measurements throughout the en-
tire spacetime, present and past.