Bell ’ s theorem in the presence of classical communication

I explain what kinds of correlation or even direct classical communication between detectors invalidate Bell's theorem, and what kinds do not. [1] of my simple demonstration [2] that their refutation [3] of an elementary version of Bell's theorem [4] cannot be correct. Rather than belabor misconceptions 1 in [3], I prefer to examine a question of more general interest. Let us turn Hess and Philipp upside down and explore the extent to which Bell's theorem survives, not only if, following Hess and Philipp, we take advantage of properties of the detectors correlated by the time on local synchronized clocks, but even if we allow further correlation of the detectors through direct straightforward ongoing classical communication between them. How much censorship must be imposed on the content of that communication for Bell's theorem to remain valid? The answer, which will surprise few who have thought much about Bell's theorem, is that the theorem remains valid even if the detectors are allowed to communicate with each other continuously throughout a long series of runs, provided only that each detector is forbidden during the course of each run from giving the other any information whatever about the setting it has randomly been given in that run. Aside from that single necessary 2 constraint the detectors can conspire in each run in any way they like. 3 To make things clear and simple I examine the question for the particular geometry used in [2] and [4], but the argument can easily be generalized. In each of a long series of 1 Among other problems, their rejection of [2] relies on a misunderstanding of what I mean by " extended instruction sets ". 2 If information on the settings of the detectors can be communicated before the detectors signal a result then the quantum mechanical data (or any other data) can be trivially simulated classically. 3 Clearly detector responses that are driven by non-communicating but internal computer programs, correlated only by synchronized clocks, satisfy this constraint, so the proof below that Bell's theorem survives such coordination of the detectors provides an alternative demonstration to that in [2] that Hess and Philipp are mistaken.