From: atems@igor.physics.wayne.edu (Dale Atems)
Subject: Re: The instantaneous transfer of information in QM calculations
Organization: Wayne State University, Detroit, MI
Date: Tue, 12 Jan 1993 01:13:24 GMT

In article <485@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:
>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. 

Please show me where. In this case QM predicts a certain value for the
quantity P(a,b) = < (S(1,a) S(2,b) >, this is the expectation value
for the product of the spin components in a singlet pair. What you
need to predict is P(a,b), P(a,c), and P(b,c). For some choices of the
unit vectors a,b,c, the QM predictions (using only the linear theory)
violate Bell's inequality.

>What is crucial about Bell's inequality is that
>the observation at one site was *affected* by the *measurement* made
>at the other site. 

This cannot be said with certainty. The most one can say, I believe,
is that the correlations are inconsistent with the assumptions that all
the observables are fixed before measurement, *and* that no
observation affected the outcome of a distant measurement. The
violations of Bell's inequality mean that at least one of these
assumptions is incorrect.

>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. 

Agreed.

>To get the QM prediction you have
>to use more then the assumption that the two particles are in a singlet
>state. 

No, I believe this is all you need.

>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. 

I don't use the probability density for a detection at all. Everything
is expressed in terms of average values of products of spin
components. I suspect we are having trouble communicating because of
the difference in experimental setups -- in the photon experiment, the
detection of a photon that has passed through a polarizer means that
it was "found" to be in a particular linear polarization state.

>[...]
>> 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. 

Yes, that is the point! If the assumptions behind Bell's proof are
correct, you *shouldn't* see his inequality violated. If you do even
though no subluminal signal could have influenced the results, then
either you are dealing with superluminal signals -- instantaneous
transfer of information in some frame -- or else it is not the case
that all spin components were determined when the state was prepared.

>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. 

In QM it is not information transfer at all. The correlations are
inconsistent only with assumptions that the standard interpretation of
QM denies.

>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.

Agreed.

------
Dale Atems
Wayne State University, Detroit, MI
Department of Physics and Astronomy
atems@igor.physics.wayne.edu
Newsgroups: sci.physics