From: paul@mtnmath.UUCP (Paul Budnik)
Newsgroups: sci.physics
Subject: Re: The instantaneous transfer of information in QM calculations
Date: 12 Jan 93 17:06:23 GMT
Organization: Mountain Math Software, P. O. Box 2124, Saratoga. CA 95070

In article <1993Jan12.004853.10698@noose.ecn.purdue.edu>, muttiah@thistle.ecn.purdue.edu (Ranjan S Muttiah) writes:
> [...] 
> Paul you said that the projection postulate doesn't involve some sort 
> of "collapse." On second reading of Anthony Sudbery, I have to eat my words as 
> well as your's and say that we were both wrong.  Here's why (from page 186):

Rather than eat my words I would prefer to clarify them. The projection
postulate assumes a `collapse' but this does not result in any nonlocal
effect. It only changes the wave function *after* the measurement and
thus cannot generate a nonlocal macroscopic effect. A second invocation
of the projection postulate on this *changed* wave function is necessary
to get a nonlocal prediction.

> [...]
> Now Bell's in inequality, locality is 
> defined in terms of the independence of probability events i.e., given two results
> of experiments, a and b, with state vectors A and B:
> 
> 	P   (a . b| A . B) = P (a|A) P (b|B)
> 	 E&F                  E       F
> 
> I don't think this necessarily precludes less than speed of light (please 
> explain to me if you think otherwise).

You need to talk about more than just the probability of
detections when you talk about tests of Bell's inequality. It is simple
using local processes to generate absolutely any correlation function
you care to define. Just `preprogram' the two particles to behave as
demanded. You can even have the detections of these particles be space-like
separated. There is no problem in generating such correlation functions.
What is crucial in tests of Bell's inequality is that you have a
controllable device that affects the probability of joint detections. You
need two of them and if you want to be certain that a local
hidden variables model could not account for the result. You must change the
settings on both devices. The time delay between when you change these
settings and when this change has a measurable effect on the probability
of joint detections *must* be less than the the time it takes light to
travel for either controllable device to the more distant detector.
To understand why this is the case you have to read a derivation
of the proof that no local theory can produces results in contradiction
with Bell's inequality and understand the conditions necessary for that
proof to hold. It is proably better to read Eberhard's rather than
Bell's version because Eberhard's result does not involve any reference
to local hidden variables theorys. See: "Bell's Theorem without Hidden
Variables", P. H. Eberhard, Il Nuovo Cimento, 38 B 1, p 75, (1977); and
"Bell's Theorem and the Different Concepts of Locality", P. H. Eberhard,
Il Nuovo Cimento 46 B, p 392, (1978).


> Now to be sure (but _only_ to be sure), 
> you might want the measurements E and F to be seperated such that there
> is no speed of light communication (what you call space-like seperation I believe).
> And that's it.  I don't know what else to say.  If Bell's inequality is
> violated then the assumptions about probability must be wrong (I think Daryl
> M. pointed this out as well).  The information about spins could have been 
> exchanged before the experiment had even begun/during/any fancy you want.

The intriguing thing about Bell's result is that information must be exchanged
instantaneously *at the time* the observation is made.  If you do not
believe this please check out the references I cited above. There is no
other way to get such results except by revising fundamental laws of
mathematics.  I think the latter suggestions are premature. There is
no adequate justification for the claim that Bell's inequality is
violated in nature or the claim that the wave function changes
instantaneously when an observation is made.
I guarantee you without the assumption that the wave function changes
instantaneously you cannot prove Bell's inequality is violated.

I believe information transfer does occur in singlet state wave function
experiments. I do not think the information is transferred instantaneously.
An effective test of Bell's inequality will measure delays long enough to
preserve locality. I think it is more than a coincidence that quantum mechanics
is incomplete in the sense that it does not provide a clear prediction
about what these delays are, but only constrains them so that locality
must be be violated in some experiments. We have always known that the
collapse postulate was vague. I have shown that it is too vague to predict
these delays and this casts considerable additional doubt on what was
already a pretty dubious law of physics.

I think the singlet state wave function is a mathematical
fiction and the decay process that creates it is an extended process in
space in time that generates these correlations using local mechanistic means.

Paul Budnik