From: paul@mtnmath.UUCP (Paul Budnik)
Newsgroups: sci.physics
Subject: Re: The instantaneous transfer of information in QM calculations
Date: 12 Jan 93 18:02:50 GMT
Organization: Mountain Math Software, P. O. Box 2124, Saratoga. CA 95070

In article <1993Jan12.011324.3713@cs.wayne.edu>, atems@igor.physics.wayne.edu (Dale Atems) writes:
> [...]
> 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.

I make the point *again* you are not testing Bell's inequality unless you
have a controllable device. Correlations by themselves can violate the
mathematical relationship, but this relationship is only predicted to
hold under certain conditions. It is only the correlation between a settable
experimental parameter and observations affected by that parameter that
are predicted to hold in Bell's theorem. You can generate any correlation
function you choose using local processes. This will not violate Bell's
inequality under the conditions in which that inequality is predicted to
hold.

It is nonetheless true that the standard QM calculations to predict P(a,b)
do involve collapse and do involve the nonlocal transfer of information.
An experiment of this type cannot provide a conclusive demonstration that
locality is violated, but the predictions of quantum mechanics still imply
that it is. When you observe the spin at one location you collapse the wave
function in accord with that observation. You use the results of this
projection operation to compute the probability for the second observation.
The probability for the second observation is dependent on the other
observation and that dependence requires that wave function you use for
the calculation be affected by the first observation. 

You cannot assume that the spin was determined at the time the particles
separated. If that were the case you could use a linear evolution of the
wave function to compute the probabilities. The spin is only determined
when it is observed. The observation *changes* the singlet state wave
function (it does not simply reveal additional information about it,
it *changes* the function) and this change must be taken into account
when computing the probability of a particular observation on the particle
paired with the one you observed.

> 
> >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.

I claim they must *both* be false. If the observables were determined
before measurement you cannot get a violation of Bell's inequality even
with instantaneous transmission of information. What use would such
information transfer be since you are only observing what has already
been predetermined long ago.

>[...] 
> >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.

The singlet state wave function before any observation is different
that the singlet state wave function after observing one of the
two particles. If you use the former to compute the probability densitys
for detecting *both* particles you will get the wrong answer.

> [...] 
> 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 you can use shorthand techniques to compute these results.
However, in a discussion of this sort, you need to go to the original theory
and understand how those techniques are derived from that theory. I think
if you do this exercise you will see the need for collapse in that derivation.

> 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.

As I explained earlier it is not a case of either but a case of both.
Eberhard's derivation of Bell's theorem makes no reference to hidden
variable theorys or predetermined states. It only talks about an
experimental manipulation instantaneously influencing an experimental
observation in a nonlocal way. See "Bell's Theorem without Hidden
Variables", P. H. Eberhard, Il Nuovo Cimento, 38 B 1, p 75, (1977).

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

Please read Eberhard's proof. If you still believe this I will be extremely
interrested in hearing you explain why.

Paul Budnik
Newsgroups: sci.physics