From: paul@mtnmath.UUCP (Paul Budnik)
Newsgroups: sci.physics
Subject: Re: The instantaneous transfer of information in QM calculations
Date: 11 Jan 93 16:24:04 GMT
Organization: Mountain Math Software, P. O. Box 2124, Saratoga. CA 95070

In article <1993Jan11.031132.1521@cs.wayne.edu>, atems@igor.physics.wayne.edu (Dale Atems) writes:
[...]
> Consider an experimental setup designed to test the version of Bell's
> inequality that applies to spin-half particles in the singlet state. [...]
>  
> Bell's inequality for this situation takes the form of a relationship
> between correlation functions < (S(1,a) S(2,b) > where S(i,a) is the
> component of particle i's spin along a, and similarly for b. To determine
> such a correlation function experimentally, *in principle* all you need
> to do is repeat the experiment a sufficient number of times, measuring
> the spins of both particles and forming the product S(1,a) S(2,b) for
> each pair, sum the products and divide by the number of pairs detected.
> I don't see where you need to assume anything about what happens to the
> wave function of one particle after the other is detected. One simply
> measures spin components and computes a statistical average.

Of course you do not need to make any such assumption to analyze the
statistics of the experimental results. You do need to use the
collapse postulate in some from to prove what quantum mechanics *predicts*
in such an experiment. What is crucial about Bell's inequality is that
the observation at one site was *affected* by the *measurement* made
at the other site. If it were simply a matter of the two particles having
parameters that were correlated at the time they split apart you *cannot*
get a violation of Bell's inequality. To get the QM prediction you have
to use more then the assumption that the two particles are in a singlet
state. If you just used this assumption then the probability density of
a detection at one site would be independent of the observations at the
other site because those observations cannot influence the distant probability
density. You have to assume that when you make an observation at one site
this *changes* the probability density you use in your *calculations* at
the other site to be in accord with information you obtained from that
distant measurement. This may not sound like quantum collapse. You may
just think about it as using all the information you have, but it terms
of the mathematical theory you are forced to use the collapse postulate to
get the correct probability density.

> Of course, a finding that the observed correlations violate Bell's
> inequality says nothing about locality if they could have been produced
> by an exchange of information. As I understand it, the basic
> premise behind Bell's proof is that all components of each particle's
> spin are fixed when the singlet state is prepared and do not change
> afterward. [...]

This is dead wrong. If it were true you would not get a violation of
Bell's inequality. There is a real instantaneous information transfer
whenever there is a violation of Bell's inequality. In quantum
mechanics it is not a form of information transfer that can be used for
communication, but a distant experimental setting instantaneously influences
the observational results at a local site. This comes from the central
assumption of quantum mechanics that a state *does not exist* until it
is observed. All that is *determined* from the assumption that the two
photons are in a singlet state is that observations of them will have a
certain correlation. The actual orientation of the spins *is not determined*
until an observation is made. If you assume it is predetermined you
have a hidden variables theory and will get results in contradiction with
the predictions of QM.

Paul Budnik
Newsgroups: sci.physics