Application of Bell’s theorem to computer simulation
Posted: Tue Sep 07, 2021 6:16 pm
Suppose A and B are two functions with domain [0, 2 pi) x [0, 1] and range {-1, +1}, programmed in some programming language such as R, Python, Matlab or Mathematica. Suppose we use the programming language’s built in pseudo-random number generator to create numbers u_1, ..., u_N, simulating independent realisations of a random number uniformly distributed on [0, 1]; take N to be 1 million. Suppose we compute the average of the N numbers A(a, u_n) * B(b, u_n), for some specified values of a and b.
Can one find programs which compute some A and B with the just specified domain and range, such that the simulation experiment just described is very likely to very well approximate -cos(a - b), for all pairs of angles a, b corresponding to half degree steps between 0 and 360 degrees?
This question comes from a recent discussion in another thread.
Michel wrote:
I replied:
Can one find programs which compute some A and B with the just specified domain and range, such that the simulation experiment just described is very likely to very well approximate -cos(a - b), for all pairs of angles a, b corresponding to half degree steps between 0 and 360 degrees?
This question comes from a recent discussion in another thread.
Michel wrote:
Joy is 100% right. There is no such thing as a mathematical theorem with loopholes. Richard is wrong, the so-called "loopholes" in Bell's theorem are directly related to oversights in Bell's analysis. In other words, the "loopholes" disprove the theorem. Why else will Richard (and Larsson) try to create a new theorem if the original one was valid? Notwithstanding the fact that Fine first identified the time synchronization flaw in Bell's theorem. It is not simply a problem with practical application.
I replied:
Joy is not 100% right. There can be a loophole in an attempt to apply a mathematical theorem to a practical matter. Larsson and my theorem is a different theorem to the “Bell theorem seen as a math theorem”. The conditions are different, and the conclusion is different. The theorem of Lasrsson and myself, for instance, applies to the computer simulation “epr-simple”. Bell’s theorem doesn’t. See https://arxiv.org/abs/1507.00106