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Article 6161 of comp.ai.philosophy:
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>From: holmes@opal.idbsu.edu (Randall Holmes)
Newsgroups: comp.ai.philosophy
Subject: Re: Quantum mechanics (no AI here, sorry)
Message-ID: <1992Jun8.150305.5307@guinness.idbsu.edu>
Date: 8 Jun 92 15:03:05 GMT
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In article <1992Jun6.133052.2816@oracorp.com> daryl@oracorp.com (Daryl McCullough) writes:
>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.
>

Well, at least I'm not behind the times!  Could you e-mail me a
reference for spin 1/2 functions?  It actually occurred to me that
constructing the array of random variables needed might be
nontrivial...  I actually do think of the underlying reality behind QM
as being a necessarily elaborate conspiracy to deny us certain
information!

>>>
>>>>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 agree.  Again, I think that the "conspiracy" metaphor is a good one.

>
>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.

If the mathematical complexities of spin 1/2 functions are bad enough,
I would tend to agree, and switch my endorsement to many-worlds.

>
>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

I agree that the many-worlds hypothesis is attractive.  Chalmers,
please note that I actually do know what I am talking about...











-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu


