From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!usc!cs.utexas.edu!uunet!pmafire!mica.inel.gov!guinness!opal.idbsu.edu!holmes Tue Jun  9 10:07:17 EDT 1992
Article 6106 of comp.ai.philosophy:
Newsgroups: comp.ai.philosophy
Path: newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!usc!cs.utexas.edu!uunet!pmafire!mica.inel.gov!guinness!opal.idbsu.edu!holmes
>From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: Quantum mechanics (no AI here, sorry)
Message-ID: <1992Jun5.165532.26362@guinness.idbsu.edu>
Sender: usenet@guinness.idbsu.edu (Usenet News mail)
Nntp-Posting-Host: opal
Organization: Boise State University Math Dept.
References: <1992Jun4.201614.10240@oracorp.com>
Date: Fri, 5 Jun 1992 16:55:32 GMT
Lines: 113

In article <1992Jun4.201614.10240@oracorp.com> daryl@oracorp.com (Daryl McCullough) writes:
>holmes@opal.idbsu.edu (Randall Holmes) writes:
>
>[about quantum nonlocality]
>
>>It's local properties of the _waves_ that are involved.  Such an
>>experiment is carried out by setting up a state in two widely
>>separated locations which depends on an unobserved factor in a single
>>earlier event.  One then makes observations at the widely separated
>>points, and, lo, they agree with one another.  These results make
>>perfect sense (require no explanation at all, in fact) on a hidden
>>variables interpretation, i.e., on the interpretation that there was a
>>real underlying value to the unobserved factor in the earlier event
>>which we did not in fact observe (we couldn't observe it and do the
>>experiment, in fact).
>
>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!).  Bell's Theorem says that a
certain class of hidden-variables theories cannot explain the Mermin
results; these theories are deterministic, among other things
(determinism is not needed; a suitably simplistic notion of what the
hidden variables look like will get one into trouble by itself)..  I
am not advocating a deterministic position, nor do I think that the
hidden state is very simple (it is not anything like a macroscopic
spin).  Suppose that a device emits two electrons with opposite spin
in opposite directions.  Whenever the spin of an electron along a
given axis is measured, it will be found to have its axis of rotation
pointing in that direction or in the opposite direction.  Set up two
measuring devices to catch the two electrons emerging from the device,
which are set up to measure spin along an axis which can be adjusted
(independently for the two devices).  The events of the two devices
capturing the two electrons emitted in a given trial have space-like
separation.  When a given pair of electrons is emitted, if the two
devices are at the same setting, they will measure the electrons as
having opposite spin.  Now suppose that we adjust one of the
detectors; there is suddenly a fall-off in correlation of the two
measurements, depending on the angle of adjustment.  Now suppose
detector A is at a slight angle from detector B, so we are set up to
expect a certain failure of correlation.  We send off a pair of
electrons.  While they are in flight, we twiddle detector B back into
line with detector A -- notice that no information can be transferred
from detector B to detector A in time to affect detector A in any way
-- suddenly, we have a perfect correlation between the two spins.
This is supposed to establish superluminal communication between the
two detectors.  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.


>
>>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.  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..."



>
>Daryl McCullough
>ORA Corp.
>Ithaca, NY


-- 
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


