From: paul@mtnmath.UUCP (Paul Budnik)
Newsgroups: sci.physics
Subject: Re: A proof that QM is an incomplete theory
Date: 15 Oct 92 16:26:57 GMT
Organization: Mountain Math Software, P. O. Box 2124, Saratoga. CA 95070

In article <1992Oct12.182352.12128@lmpsbbs.comm.mot.com>, bhv@areaplg2.corp.mot.com (Bronis Vidugiris) writes:
> In article <311@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:
Regarding experimental tests of Bell's inequality:
> )The passage of a photon through a polarizer is different then the passage
> )of the associated wave-function through the polarizer. It is an all
> )or nothing event like the detection of a particle. The relevant question
> )is not when does the wave-function pass through the polarizer, but when does
> )the particle pass through it. QM is not only silent on where a particle is
> )between detections. It forbids us from making assumptions about this.
> )Yet this is the question we need to answer to calculate the distribution
> )of these delays. Thus there is an experimentally measurable
> )parameter of a QM system that QM does not predict a value for.
> )QM is an incomplete theory.
> 
> It depends on the polarizer.  If you use a calcite crystal which splits the
> incoming beam into a horizontally and vertically polarized components, you
> do *not* have an all or nothing event.  You pass a beam of light 'through'
> such a polarizer, then pass the two resulting beams through a similarly
> constructed but oppositely aligned crystal to re-combine them optically, and
> you restore your original beam.  This works even if the 'beam' is a single
> photon.

This is not the all or nothing I had in mind. The problem concerns how
one computes the predictions of a test of Bell's inequality when the
polarizers are changing rapidly. This calculation must invoke collapse
in some form. When you collapse the wave function you must make a decision
about what angle the polarizer was at when the photon traversed it.

> However, you are right (IMO) about the problems wrt the meaning of 'passing
> through' - this is a problem in specifying the theory to be tested, however
> (IMO again) rather than a problem with QM.

I think it is a problem in quantum mechanics. Consider Eberhard's description
of this calculation (P. H. Eberhard, Il Nuvo Cimento 46 B, 392, 1978)
One wishes to compute P(a,A,b,B) where A and B are the respective polarizer
angles and a and b the observations. To do this one constructs the
singlet state wave function and then `collapses' it to produce a new
density matrix consistent with the observation at one of the sites. Doing
this is not a problem if the polarizer is not changing. If the polarizer is
changing, we do not know how to do this collapse i. e. we do not know
which of the two angles of the polarizer to use. The fact that we have
a detection at one site tells us nothing about the polarization of the
singlet state pair unless we know *when* the particle traversed the polarizer.

My knowledge of the machinery of quantum mechanics is limited, but I am
not aware of anything that would allow us to make such a computation.
There is no way to avoid invoking collapse in this calculation. You cannot
get the standard results from just the density matrix because it evolves
in a completely local fashion. In turn you cannot do the collapse calculation
without making an unwarranted assumption about when the particle traversed
the polarizer. I do not see how to compute within quantum mechanics
the delays between when the polarizers change angles and when this will
have an affect on the probability distribution for joint detections.

If this is true, it means that quantum mechanics is an incomplete theory.
These delays can be observed experimentally and the the theory needs to
be extended to account for them.

Does anyone think they know how to compute these delays?

Paul Budnik
Newsgroups: sci.physics