On 3/06/2016 8:22 pm, 'scerir' via Everything List wrote:
Bruce:
This relates to my current obsession with the universal applicability of
Bell's theorem (and other inequalities such as that of CHSH). Consider the
statement of the Church-Turing thesis: "the statement that our laws of physics
can be simulated to any desired precision by a Turing machine (or at any rate,
by a probabilistic Turing machine)". This is not true for Bell-type experiments
on entangled particle pairs. To be more precise, the correlations produced from
measurements on entangled pairs at spacelike separations cannot be reproduced
by any computational process. [....]
### Unless something strange is going on here. In example, I'm trying to
understand something J.Christian wrote recently.. See Appendix D, page 8 and 9
in this paper https://arxiv.org/pdf/1501.03393v6.pdf
Joy Christian has been trying to disprove Bell's theorem for ages. There
is a fundamental mistake in her argument -- She claims that Bell
replaces a sum of expectation values by the expectation value of a sum
(see equations D3 and D4 of the paper you reference). But Bell does no
such thing: such a replacement is, of course, invalid, but Bell does not
do this. What actually happens is that the hypothesis of independence
(locality) is used to replace the expectation value of the product with
the product of expectation values. This is explained very clearly in the
review I referenced by Brunner et al, arXiv: 1303.2849. In Section 1B,
Brunner gives the argument against the computability of the quantum
results that violate the inequalities. The point is that the proof of
Bell's theorem is not limited to correlations on entangled pairs -- it
applies to any sets of correlations between measurements on a series of
observables with a limited number of outcomes each. For example, an
experiment in which there are only two measurement choices (x or y), and
where the possible outcomes take two values (a,b in {-1,+1}. When the
process is truly local, the inequalities hold however the data are
generated. Computer simulations are local,so cannot reproduce the
quantum violations of the inequalities.
Bruce
BTW L. Accardi, (Accardi and Regoli, 2000, 2001; Accardi, Imafuku and Regoli,
2002) has claimed to have produced a suite of computer programmes, to be run on
a network of computers, which will simulate a violation of Bell's inequalites.
See also http://arxiv.org/pdf/1507.00106v3.pdf
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