Gordon Watson wrote:.

The 3-page essay at

http://vixra.org/abs/1909.0216 is titled:"

Einstein vs Bell? Bell’s inequality refuted, Bell’s error corrected."

Bell's inequality (BI) is refuted in 8 lines of elementary mathematics. Bell's error is defined and corrected in 11 more.

No knowledge of QM, Joy's Clifford Algebras, nor Richard's probability theory is required.

Reason:

(i) Bell (1964b) --

http://cds.cern.ch/record/111654/files/ ... 00_001.pdf -- prepares us for the derivation of BI with a valid (and elementary) physical boundary condition; his eqn (1).

(ii) He then breaches that condition; see his move from the valid first line to the invalid second line on p.198 of Bell (1964b).

To facilitate discussion, I suggest we

number the three unnumbered relations atop p.198 as (14a) to (14c).

I look forward to critical comments from both sides of this debate; and from those in the middle or on the side-lines.

Reinforcing the view that it is all rather elementary; and with best regards: Gordon Watson

http://vixra.org/abs/1909.0216.

Your logic is faulty, Gordon. I found your paper extremely difficult to read. You succeed in making simple things very difficult, and this enables you to make incorrect logical deductions.

It is indeed all extremely elementary. No knowledge of QM is needed to follow Bell's arguments, though of course sooner or later, one should verify the classical QM derivation of the EPR-B correlations, by matrix algebra calculations (over the complex numbers) involving the 2x2 Pauli matrices and various 4x4 matrices built up from them. Clifford algebra and Geometric Algebra are sophisticated and beautiful mathematical structures which one can use to elegantly reproduce classical QM calculations. Joy Christian uses them for other purposes.

I don't understand what your problem is with "Richard's probability theory". Bell does an elementary probability calculation using the notations and terminology of 60's physicists since he was a physicist writing in the 60's for physicists.

But to get to the heart of the matter, you compare a new inequality of your own, labelled (5) in your new paper, to Bell's original three correlations inequality, reproduced and labelled (6) in your new paper. You note that a particular set of three correlations E(a, b) = -1/2, E(b, c) = -1/2, E(a, c) = +1/2 violates Bell's inequality but satisfies yours.

The reason they violate Bell's inequality is actually because it is impossible to find functions A(a, lambda), B(b, lambda), and rho(lambda) satisfying the usual constraints *and* such that E(a, b) = int A(a, lambda)B(b, lambda) rho(lambda) d lambda, etc. If you had wanted to disprove Bell by a counterexample featuring these values of the three correlations, you would have had to exhibit functions A, B and rho which reproduce your three correlations E while at the same time satisfying the standard requirements (A and B take values +/-1; rho is nonnegative and integrates to 1). But you don't do this! So your paper is empty of any content! It just exhibits muddled thinking!

I suggest you do try to find a concrete example of functions A, B and rho which do the job you want them to do. (Joy Christian thinks he did manage to do that).

I can tell you in advance that you will not succeed, since Bell's inequality is a true and trivial result in probability theory, known already by George Boole in the 1850s, and since then independently discovered again and again by many others, as Karl Hess points out (yet again) in his most recent paper.

If you do succeed, then please program the resulting model and let's do my computer challenge. 10 thousand Euro's says you'll fail.