From: paul@mtnmath.UUCP (Paul Budnik)
Newsgroups: sci.physics
Subject: Re: hidden variables
Date: 21 Jan 93 17:05:23 GMT
Organization: Mountain Math Software, P. O. Box 2124, Saratoga. CA 95070

In article <1993Jan21.000329.21085@cs.wayne.edu>, atems@igor.physics.wayne.edu (Dale Atems) writes:
> In article <505@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:
> 
> >We shall see. I claim QM is a provably incomplete theory. I have posted
>                                ^^^^^^^^
> >the argument and submitted a paper claiming this result.
> 
> As I said before, I missed this post. The argument I saw proves
> nothing because it assumes something it needs to show, namely that the
> postulate of wave function collapse is required in order to make any
> prediction about the delay.
> 
> If you have a rigorous argument that you would rather not reveal
> because your paper is still under review, then please say so. If the
> full argument was given in your earlier post, then please repost it.
> Otherwise we are just wasting our time here.
> 

It can be difficult to make a rigorous argument about a non-rigorous
axiom of quantum mechanics. However one can give an almost rigorous argument
that shows collapse is necessary to compute the delay. All the laws of
physics except the collapse postulate are local. You cannot get a
violation of Bell's inequality from these laws. Thus you need collapse to
prove that Bell's inequality is violated and to compute the delay
involved.

It is the premise of this argument, `that no law of physics except the
collapse postulate can violate Bell's inequality' that you keep objecting
to. One can step through these laws one by one and prove they are all local
but I consider this a well known fact that does not require such a proof.
You keep claiming that you can show a violation of Bell's inequality with
the linear part of quantum mechanics or the Schrodinger equation. This is an
obviously local partial differential equation. It states how a probability
at a given point in phase space changes based on the value at that point
and second order derivatives at that point. (The derivatives are second
order in the relativistic version of the equation but first order in
the version one most often uses in practical problems.)

I do not claim that this is a fully rigorous mathematical argument.
However it is obvious that it can be `almost' made into one. One needs
a mathematical definition of locality and a proof that QM violates it,
such as that provided by Eberhard. One then needs to prove that the Schrodinger
equation cannot. Such a proof is easily constructed given the mathematical
form of the equation. What gets dicey in all this is that the Schrodinger
equation talks only about probabilities in phase space. However the predictions
of locality violation in QM are predictions about macroscopic events. There
is no mathematically rigorous away around this because this aspect of
QM is not a mathematically rigorous theory. You need to prove that if
the probabilities for observations in a theory only change in a local way
then one cannot get a violation of locality from that theory. You can
no doubt do this with a suitable definition for what you mean by theory.
However quantum mechanics cannot be rigorously formalized to fit such
a definition. There is no way to formalize a theory that takes probability
as a primary concept. Thus there is no way to give a fully rigorous proof
of this. In QM fully rigorous proofs can only be done for the linear
part of the theory.

Paul Budnik
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