I Is Einstein Causality Proven in Preferred Frame SR?

[PeterDonis]

Bell has later emphasized that formula (2) of his paper was not postulated but derived, and here is the derivation from the original paper (emph. mine)

That's not a "derivation". A "derivation" would be a mathematical derivation of the mathematical statement that Bell uses in his paper from some other mathematical premise.

The emphasized part.

That's not what I asked for. What I asked for was which mathematical statement in Bell's paper is violated. It appears that your answer to that would be formula (2) of his paper.

I can understand your position, but it would require renaming of established terms

Yes, I know that (I assume that by "renaming" you actually mean "redefining"). But your position also requires redefining a term: "interpretation". This whole subthread started because you objected to my statement that all interpretations of QM use the same math. As far as I know that statement is just as "standard" as the usage of "theory" that you are saying is standard.

 

[Elias1960]

That's not a "derivation". A "derivation" would be a mathematical derivation of the mathematical statement that Bell uses in his paper from some other mathematical premise.
That's not what I asked for. What I asked for was which mathematical statement in Bell's paper is violated. It appears that your answer to that would be formula (2) of his paper.

If you want to restrict Bell's theorem to the part of the article beginning with formula (2), your choice. If I refer to Bell's theorem, I refer to the full paper.

The derivation is of the necessary level for a physics paper and is certainly sufficient to classify (2) as derived, and to identify the EPR criterion of reality and Einstein causality as the assumptions necessary to derive it. One should not forget that there is the EPR paper as the background which is presupposed to be known, and the derivation is rather trivial given the EPR criterion and Einstein causality. Both are formulated in a verbal way, thus, to insist on some formula written down for it makes no sense.

This whole subthread started because you objected to my statement that all interpretations of QM use the same math. As far as I know that statement is just as "standard" as the usage of "theory" that you are saying is standard.

The standard use is AFAIK that all interpretations make the same empirical predictions.

But this does not mean the same math, dBB theory in quantum equilibrium makes the same empirical predictions, but it also uses math which is not part of standard QM math, namely the guiding equation. Of course, I do not object against naming it a different theory too, given that it is a well-defined theory even outside the quantum equilibrium, and makes completely different predictions outside this equilibrium. But naming it an interpretation is also sufficiently standard.

 

[PeterDonis]

If you want to restrict Bell's theorem to the part of the article beginning with formula (2)

I have said no such thing. I simply asked which mathematical statement the theory you were referring to violated. You never answered that question, so I had to make my best guess.

 

[Elias1960]

I have said no such thing. I simply asked which mathematical statement the theory you were referring to violated. You never answered that question, so I had to make my best guess.

If Einstein causality is sufficiently mathematical for you, then it is Einstein causality. In a theory with preferred frame, classical causality, as defined by absolute time, is what defines causality.

 

[PeterDonis]

If Einstein causality is sufficiently mathematical for you, then it is Einstein causality. In a theory with preferred frame, classical causality, as defined by absolute time, is what defines causality.

Oh, for goodness' sake. Bell's paper has mathematical statements in it. Each one has a number. Which number points to a false statement? I fail to see why you can't just answer that question without going off into the vagaries of ordinary language terms like "Einstein causality".

 

[Elias1960]

Oh, for goodness' sake. Bell's paper has mathematical statements in it. Each one has a number. Which number points to a false statement? I fail to see why you can't just answer that question without going off into the vagaries of ordinary language terms like "Einstein causality".

(2) points already to a statement that cannot be proven in SR with a preferred frame. I refer to Einstein causality because I thought a precise answer has to identify the principle which holds in spacetime SR but not in preferred frame SR and to explain why (2) cannot be derived in preferred frame SR. Such an explanation has to compare how (2) is derived for spacetime SR, and to show why it fails in preferred frame SR. This derivation is given in informal, verbal form, so my explanation has an informal, verbal form.

But once you insist, no problem, (2) cannot be proven in preferred frame SR.