From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!psinntp!psinntp!scylla!daryl Tue Jun  9 10:07:32 EDT 1992
Article 6127 of comp.ai.philosophy:
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>From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: Quantum mechanics (no AI here, sorry)
Message-ID: <1992Jun6.133052.2816@oracorp.com>
Organization: ORA Corporation
Date: Sat, 6 Jun 1992 13:30:52 GMT

holmes@opal.idbsu.edu (Randall Holmes) writes:

>>Randall, I think you are behind the times on this. Einstein *thought*
>>that a hidden-variables interpretation would explain the seeming
>>nonlocality of quantum mechanics, but John Bell in fact showed just
>>the opposite: the nonlocality *cannot* be explained by hidden
>>variables theories (Bell's Theorem).

>It just isn't so.  I produced a hidden variables explanation of the
>behaviour of Mermin's device after about an hour of reflection (the
>reflection was required to recover my earlier thinking on the subject,
>which took a lot more than an hour!).

>...Suppose that a device emits two electrons with opposite spin
>in opposite directions. [Describes EPR experiment]

>This is supposed to establish superluminal communication between the
>two detectors.

No, it is supposed to establish that Einstein's realism requires
superluminal communication. The idea that a particle has a definite
spin in each direction, we just don't know what it is, is ruled out
unless one wants to allow superliminal communication.

>It establishes no such thing.  Here is an alternate
>hypothesis.  The state of a particle, when it is emitted, consists of
>a definite yes-no answer for each angle (not a hidden single axis of
>polarization -- Bell's argument does kill this). Each of these
>answers is diametrically opposed as between the two electrons.  The
>answers vis-a-vis two angles for a given one of the two electrons are
>correlated probabilistically in the appropriate degree determined by
>the angle.  This kind of hidden state, decided at the source, not by
>random events with space-like separation at the detectors, will
>exhibit the exact behaviour seen in the Mermin experiment and does not
>involve non-locality.  What is unclear is what the physical meaning of
>the state is, but that is already unclear in QM as it stands.

Randall, research along these lines has already been done. It leads to
the idea of "spin-1/2 functions", which are functions from the surface
of a 2-sphere into +/- 1 such that the correlations are in accord with
the predictions of quantum mechanics. The existence of such functions
is very difficult to establish, and has a very high set theoretic
consistency strength. (I can't remember whether their existence is
actually independent of ZFC, or not.) Such a function would have to
be wildly discontinuous almost everywhere.

Anyway, while I agree that there are *mathematical* possibilities to
circumvent Bell's Theorem, I don't think that there are any that a
physicist would take seriously. In the spin-1/2 function approach, it
is as if an *enormously* convoluted conspiracy were being perpetrated
to give the illusion of the simplicity of quantum mechanics.

>>
>>>The "non-locality" has to do (on my interpretation) with the fact
>>>that getting extra information about event A may immediately give
>>>me extra information about event B even if A and B have space-like
>>>separation
>>
>>That explanation has been pretty much ruled out. There is no way
>>to reproduce the statistical predictions of quantum mechanics by
>>such a hidden variables theory.
>
>I just did it.  The point is that the rather stringent conditions on
>Bell's Theorem are not satisfied by this hidden state hypothesis.
>Read the conditions.  What is true is that the hidden states have to
>be very complicated and the resulting theory will not be
>deterministic. A more succinct answer is that this is a hidden
>variables theory, but it is not "such" a hidden variables theory.
>
>The question of cost arises; is this too complicated an expedient for
>avoiding the non-locality in the QM formalism revealed by Bell's
>Theorem?  I think the answer is that it is necessary at any cost to
>avoid the confusion of physical objects (particles) with mathematical
>constructs (probability waves) which are not physical objects [of
>course, I maintain that they are real objects, but they are not
>physical objects]; as long as the probability waves are treated as if
>they were an independent reality, we are evading the difficult problem
>of "explaining" the reasons why the probability waves work to describe
>the behaviour of particles with information restrictions imposed by
>the quantum of action.

Your approach eliminates the mathematical construct of the wave
function in favor of the equally mathematical construct of spin-1/2
functions. Your approach doesn't recover a particle picture, but
instead a particle turns out to be a locus for an enormous conspiracy.
I don't think it is an improvement, and neither do most physicists,
which is why spin-1/2 functions have been regarded as more or less
a curiosity.

I have to admit that it is possible that spin-1/2 functions (and their
analogs for properties other than spin) could possibly give rise to a
consistent, satisfying interpretation of quantum mechanics, but much
work needs to be done before that time. The way I feel about it, such
an approach currently seems much less satisfactory than ordinary
interpretations of quantum mechanics.

I will repeat that I think field quantities are as real as particles.
What makes a particle physical and a field quantity, such as the
electric field, the magnetic field, the space-time metric, not
physical. While for nonrelativistic quantum mechanics, you may be able
to think of particles as fundamental, with the wave function as a
measure of our ignorance about their positions, this doesn't extend to
relativistic quantum field theory. For Bosons (such as photons), the
wave function cannot be interpreted as a probability density, at all,
since it is not positive-definite.

>As regards unobservable factors, there is nothing to choose between
>the theories; hidden states of which only a part can be observed
>in a single operation versus superluminal communication which cannot
>be used to transmit information make an unappealing choice either way.
>"I was thinking of a plan to dye one's whiskers green..."

The many-worlds interpretation is, to me, a preferable alternative,
although it shares with the spin-1/2 formulation the problem that
only a tiny fraction of the universe is actually detectable.

Daryl McCullough
ORA Corp.
Ithaca, NY



