I have read carefully what you have written and I have discovered inconsistencies. I believe that what you write is impossible to understand. But this is already obvious: there is a known mathematical theorem whose proof is completely correct. You claim to have a counterexample. Hence your example must be wrong.Joy Christian wrote: ↑Sun May 08, 2022 3:20 amEither you are getting too old for this stuff or your eyesight needs checking. Or maybe you just don't read stuff anymore. Please read my paper or my above comment again. What I have used to define mu_1 and mu_2 is the initial spin direction s^i, not s_1 or s_2. Here the superscript "i" refers to the initial spin direction at the source, and the subscripts 1 and 2 refer to the observation stations at the two ends of the experiment. This is not difficult to understand.gill1109 wrote: ↑Sun May 08, 2022 2:43 amOK, but in that case the notation and/or explanation needs some improvement. You are using s^1 twice in the same expression (once explicitly, once implicitly), and similar for s^2, but the two occurrences are not supposed to be the same.Joy Christian wrote: ↑Sun May 01, 2022 11:35 pm That is not correct. In eq. (11) mu_1 and mu_2 are defined to be fixed for each run. They are defined in terms of the initial spin direction s^i at the source.
It is important to read what I have defined carefully.
You must also define the initial two spin directions.
Notice that my presentation of Gull’s proof of Bell’s theorem using Fourier analysis has now been published. It forms my response to a challenge made by you and Fred Diether. You are thanked in the acknowledgments. https://arxiv.org/abs/2012.00719