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The Earl of Snowden December 19, 2016 at 11:02 am wrote:I would be surprised because if I took an Nx4 matrix with every cell filled by a +1 or a -1, which we agree cannot exceed the bound 2, and tried to turn it in to a matrix like one would see in an actual experiment, by randomly replacing one of the two Alice observations with an NA and one of the two Bob observations with an NA, then for a LARGE number of rows, the lhs calculation would have almost no chance of exceeding the bound 2 by a statistically significant amount. Try it in R. (The choice of where to put the NA’s must be random and independent of what the rows look like.)

That argument which was first proposed by Gill fails for several reasons:

1) The 4 Nx2 spreadsheets you generate in this way are not statistically independent, but the 4 Nx2 spreadsheets in experiments used to calculate ⟨A₁B₁⟩ + ⟨A₂B’₂⟩ + ⟨A’₃B₃⟩ – ⟨A’₄B’₄⟩ are independent.

2) Even if they were independent (which they aren’t cf (1)), it is not true that Local Realistic theories MUST produce an Nx4 spreadsheet of outcomes. The EPR elements of reality do not have to be the outcomes themselves. Just because the outcomes may not be simultaneously available does not mean the hidden elements of physical reality are not simultaneously present.

3) It is a fact that the outcomes in the EPRB experiment are not simultaneously available so a 4xN spreadsheet does not exist for that experiment, irrespective of the kind of theory you want to use to model it.

4) Even if a 4xN spreadsheet of outcomes existed (which it does not cf (3)), and even if the 4 disjoint Nx2 spreadsheets were independent (which they are not cf(1)), the cyclical recombination of rows in the paired Nx2 spreadsheets means that it is not always possible to faithfully sample the Nx4 spreadsheet using data from 4 separate disjoint Nx2 spreadsheets (see http://www.panix.com/~jays/vorob.pdf)

5) Anything you try in R will be one specific model (your imagination) of what a hidden variable theory is. Just because your imagined model does not exceed the bound says absolutely nothing about the possibility of any other model violating it. In other words, the probability of find a model which violates it may be 0.00001. So long as it is not 0, the argument fails. It does not help pro-Bell one iota to suggest that the probability of finding a model which exceeds 2 is low. You need to show that it is P=0.

6) See https://arxiv.org/pdf/0907.0767.pdf, https://arxiv.org/pdf/1108.3583.pdf, https://arxiv.org/pdf/1605.04887.pdf

Dirkman wrote:Quick layman question: Is your S3 theory related in any way to space-time symmetries ?

Dirkman wrote:It looks like so far Jay Yablon has reached the conclusion that bell is a self fullfilling tautology because one already excludes strong correlations from the definition of locality.

Which is funny cause I have seen a lot of talk on physicsforums about locality in QFT being based on the Cluster Decomposition Property which already excludes correlated systems.