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Are the Androids Dreaming Yet?

This is quite a complex piece of mathematics so let me show you how it works. Again, our thought experiment relies on an analogy involving clothing – sorry.
In the Bell Test experiment three polarizers are set up at 0, 1/3 and 2/3 of the way around a circle, 120 degrees apart. For Einstein to be correct photons must each carry at least three pieces of information:

If I meet the 0 degree polarizer do I go through or not?
If I meet the 120 degree polarizer do I go through or not?
If I meet the 240 degree polarizer do I go through or not?

If a photon had only one piece of information, say that it was vertically polarized, it would not know what to do if it came across a polarizer at 45 degrees. In that case the photon would sometimes go through and sometimes not, with a fifty-fifty probability. But Einstein did not want to countenance probability. “God does not play dice with the Universe.” He required certainty. “I like to think the Moon is there when I am not watching it.” The photons must know enough to handle, with certainty, any eventuality they may come across. (We could set up experiments with a more complex set of choices, dividing the photons into quarters, fifths and so on, but thirds are simple numbers and we can use the children’s clothing analogy to demonstrate the mathematics.)

[Diagram Labels: Hats, Gloves, Scarfs, A, B, C, D, E, F, G]
[Table Headers: H, G, S, HG, GS, SH, Prob]
[Table Data Rows containing Y, N, S, D, and probabilities]
[Mathematical Formula: ( + ) + ( + ) ≥ ( + )]

Hats, Scarves, and Gloves

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