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From: gwyn@BRL.ARPA
Newsgroups: net.physics
Subject: Re:  Faster than light.
Message-ID: <390@sri-arpa.ARPA>
Date: Mon, 15-Jul-85 00:32:18 EDT
Article-I.D.: sri-arpa.390
Posted: Mon Jul 15 00:32:18 1985
Date-Received: Wed, 17-Jul-85 05:20:38 EDT
Lines: 50

From:  Doug Gwyn (VLD/VMB) 

I agree that there is a logical problem.  I was pointing out that
the instantaneous collapse of the wave function in a special frame
was indicative of the logical problem.  I too think we need a better
quantum theory of measurement.

The logical relativistic problem is perhaps best seen by considering
the following slight modification of the passing spaceship scenario:

	observer A	E		observer B

			spaceship -->

E is an emitter of two particles in exactly opposite directions
with exactly correlated spin.  Due to the quantum nature of the
particle emission, nothing is known about the spins except that they
are correlated so that if one measures a spin component of one of
them, the statistical distribution (call this D1) of a tilted
component measurement of the other one will be different (involves
cosine of the relative component tilt angle) than it would have been
if the first measurement had not been done (call this distribution
D2).

Now, observer A measures a spin component of a particle sent in his
direction, and shortly thereafter (separated by a spacelike interval
w.r.t. the frame in which A, B, & E are all at rest) observer B,
who is slightly farther away from E, measures the tilted spin
component of the other correlated particle.  According to QM, the
result of an ensemble of such experiments is that B measures
statistical distribution D1.  The state of B's particle is supposed
to be established "instantaneously" when A makes his measurement.

There is no real paradox so long as we think in the rest frame.  Now
consider the situation from the viewpoint of a passing spaceship
traveling at very high speed in the direction shown.  If the
collapse of the wave function is "instantaneous" as seen by the
spaceship, and if B is not too much farther from E than A, then B
will measure the spin "before" A does.  QM says that B will find
statistical distribution D2 (and A something like D1) in this case.
Now, we all know that the statistics at B will really still be D1,
not D2 (since the spaceship is irrelevant to the quantum phenomenon
going on here).  Surely there is something fundamentally wrong with
the idea that the wave function collapses "instantaneously".  What
is a correct replacement for this bogus idea?

This is more or less the thinking of Einstein that led him to reject
the conventional formulation of quantum theory.  (He also did not
like the idea that there was a fundamental randomness, but that is a
separate issue.)