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Article 3719 of comp.ai.philosophy:
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>From: bill@NSMA.AriZonA.EdU (Bill Skaggs)
Newsgroups: comp.ai.philosophy
Subject: Re: QM nonsense
Message-ID: <1992Feb13.202401.28326@organpipe.uug.arizona.edu>
Date: 13 Feb 92 20:24:01 GMT
References: <jbaxter.697533284@adelphi> <406@tdatirv.UUCP> <65812@netnews.upenn.edu> <17872@castle.ed.ac.uk>
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Reply-To: bill@NSMA.AriZonA.EdU (Bill Skaggs)
Organization: Center for Neural Systems, Memory, and Aging
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  This is not exactly related to AI, but there seems to be a lot of
puzzlement related to quantum mechanics on this newsgroup, so it might
be useful to lay out some of the issues.

  Most of the philosophically perplexing aspects of QM arise in one
simple, easily understood experiment, the "two-slit experiment."  The
setup consists of a barrier with two small holes ("slits") and a
detector screen behind it, which lights up wherever an electron hits
it.  A beam of electrons is aimed at the barrier; the beam is weak
enough that it is virtually certain that no more than one electron
will be present at a time.  Some of the electrons pass through the
slits and strike the detector.

  There are three stages.  First, close the left slit, and keep a
record of how many electrons strike the detector at each location.
Second, close the right slit, and keep track of where the electrons
strike.  Third, leave both slits open, and again record the number of
electrons striking at each point.

  Common sense predicts that each electron must pass through either
the left or the right slit, and that an electron passing through one
slit cannot "know" whether the other slit is open -- therefore the
number recorded in stage 3 at each location should be the sum of the
numbers recorded in stages 1 and 2.

  Quantum mechanics predicts differently.  The wave function for a
single electron will pass through *both* slits, and the portions
coming through each slit will interfere with each other, like light
being diffracted by a grating.  Quantum mechanics predicts that the
number recorded in stage 3 will be systematically different from the
sum of the numbers recorded in stages 1 and 2.  It predicts that the
stage 3 pattern will show interference fringes.

  This is the paradox:  the electron is a particle, because when you
measure its location, you always find it at a single, specific place.
But before the position is measured it acts like a wave, because its
ensemble of possible states can interfere with each other.  

  This *interference* is what distinguishes an uncollapsed wave
function.  The paradox of Schrodinger's cat (for those who know about
it) is that both the dead and alive states must be simultaneously
present, because they will interfere with each other, and the
interference can, at least in principle, be measured.

  Now, collapse of wave functions is not actually part of quantum
mechanics.  QM is a set of differential equations, and those equations
do not show any behavior that can appropriately be described as
"collapse".  Collapse arises out of the attempt to interpret the
differential equations in experimental terms -- out of the attempt to
connect the microscopic equations of QM with the macroscopic reality
we live with.

  It is important to realize that the occurrence of collapse is, in
principle at least, empirically verifiable, because it implies the
loss of interference between the different possible states of the
system.  Quantum mechanics (i.e. the Schrodinger equation) predicts no
such loss of interference, so collapse, whenever it occurs, is a
violation of QM.  

  It is unreasonable to expect QM to tell us the circumstances in
which QM will be wrong.  Whether collapse occurs in brains, or in any
sort of macroscopic measuring device, in either case it is a violation
of QM, and so we cannot expect QM to give us insight.

  My feeling is that collapse probably does not occur at all.  Quantum
mechanics has always in the past been correct when it predicted
interference between states; why should it be wrong now?  There may be
a sort of *effective* collapse, though.  It may be generally
impossible for a measuring device to detect interference between its
own internal states.  If this is so, then whatever you look at is,
from your point of view, collapsed.  But somebody else, looking at
you, could still in principle detect interference between various
possible states of you.

	-- Bill


