gill1109 wrote:Joy Christian wrote:Here is a published paper by Richard D. Gill:

https://link.springer.com/article/10.10 ... 015-2657-4. It is a critique of one of my papers, published in the same journal. I have criticized Gill's paper before for different reasons in this unpublished preprint:

https://arxiv.org/abs/1501.03393. But here I want to point out the mistake in all Bell-type arguments I have been highlighting in this thread. This mistake is conspicuous in Gill's published paper, which I reproduce below:

It is the second unnumbered equation seen above that is wrong. Gill is referring to me and my published paper in the above paragraph. Mind you, there is nothing mathematically wrong in his equation. Mathematically it is a trivial equation and its LHS is indeed equal to its RHS. But physically the equation is nonsense. It assumes that the sum of expectation values is equal to the expectation value of the sum.

That is not valid for hidden variable theories.

Strange that a trivial arithmetical identity, in whose truth there is no doubt whatsoever, as Joy Christian himself agrees, should suddenly fail to be true *for physical reasons* when the numbers involved happen to be the values taken on by *hidden variables*. The hidden variables theory is a physical theory of what is going on behind the scenes which supposes that there are physical properties of physical objects, which take on numerical values in any particular instance but which happen not to be directly observable by human experimenters. The odd thing is that they apparently do not obey ordinary rules of arithmetic. What rules they do follow is never revealed. The physical meaning of the word "hidden" is that only certified physicists can talk about them. I don't think it makes sense to call such a theory a "theory" at all. It sounds more like a mystery religion to me. The high priest makes pronouncements which make no sense to anybody, but since his actions seemed to ensure that Winter gave way to Spring every year (because he performed those ritual incantations every Winter and so far, hey presto, every year, Spring did come again), the faithful continue to make sacrifices and offerings at his temple, enabling the high priest to live a cushy life, and giving him lots of political influence, since the rich and powerful need to consult him and get scientific backing for their policy decisions.

The amusing thing about Christian's proposed experiment involving colourful exploding balls which disintegrate into pairs of contrarywise spinning hemispheres, tracked by state of the art video cameras and video processing software, is that the so-called hidden variables are not hidden at all, but are in fact directly observed.

Your emotional rambling has near-zero scientific content. You say:

Richard D. Gill wrote:

The odd thing is that they apparently do not obey ordinary rules of arithmetic. What rules they do follow is never revealed. The physical meaning of the word "hidden" is that only certified physicists can talk about them.

There is no truth in these statements, except perhaps in the last one. Yes, you have to be a certified physicist, such as von Neumann, Bell, Wigner, or Shimony, to truly understand what is meant by "hidden variables." But that is true about any science. All editors of physics journals seek approval of only certified physicists. Why? Because there are very good reasons for that.

But I digress. The rules that must be respected by any hidden variable theory are precisely known since the work of von Neumann and others in the early 1930s. The main rule is so simple that even uncertified non-physicists can understand it. The rule is that, unlike in quantum theory, every observable in a hidden variable theory must have a definite value, which must be an eigenvalue of the corresponding quantum mechanical operator. That is it. The rule is hardly mysterious or imprecise. Therefore the mistake in Richard D. Gill's second unnumbered equation I have quoted above is also crystal clear. The RHS of his equation is not summing over the correct eigenvalue. The correct eigenvalue, for the current case, is given in Eq. (35) of

my paper.

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