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From: AI.Mayank@MCC.ARPA
Newsgroups: net.physics
Subject: Re: Faster than Light
Message-ID: <404@sri-arpa.ARPA>
Date: Mon, 15-Jul-85 20:25:37 EDT
Article-I.D.: sri-arpa.404
Posted: Mon Jul 15 20:25:37 1985
Date-Received: Thu, 18-Jul-85 06:32:29 EDT
Lines: 77

From:  Mayank Prakash 

>
>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 -->
>
.
.
.
.
.
>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.)
--------
>I think your discussion of the spin-experiment might confuse some
>readers into thinking that there is a *real* paradox (in the sense that
>properly applied QM would give conflicting predictions in the two
>frames).  Of course, that is not the case.
>
>Referring to your example:
>
>        observer A	E		observer B
>
>        		spaceship -->
>
.
.
.
.

>Mark
-------

>What I really had in mind in the (A E B spaceship) thought experiment
>was that observer A would be doing something nonsymmetric with
>respect to the two spin states, so that there would be a way of
>telling whether he had "interfered" with what is going on at
>observer B.  Perhaps this is not possible, which would save the
>situation in the way you describe, but offhand it is hard to see
>why not..

The argument of Mark can be generalized easily to any system that will be
correlated in the way you describe. Let us suppose you are trying to measure
the operator Q. Let us label the two particles 1 (A) and 2 (B) respectively. Q
must satisfy the following conditions - (1) It must be measurable on both
particles seperately, (2) It must be additive, i.e., its value on the whole
system must be the sum of its values on each particle individually, and (3) It
must be a constant of motion (for otherwise, the correlation between its values
on the two particles will be lost in time). Now, suppose that its eigenstates
on particle 1 are u(p), and on particle 2 are v(q), where p and q are the
corresponding eigenvalues respectively. Then, u(p)v(q) is the state in which
particle 1 has value p, particle 2 has value q, and the entire system has value
p+q for the observable Q. A general state of the system is a linear
superposition of these states. However, we are interested in a state in which
the system as a whole has a fixed value, say, P. Such a state is a linear
superposition of those products u(p)v(q), for which p+q = P. Let us say the
coefficient of u(p)v(q) in this state is a(p,q). Rest of the argument is a
repeatition of Mark's argument. So really there is no paradox here.

- mayank.

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II  Mayank Prakash  AI.Mayank@MCC.ARPA      (512) 834-3441		II
II  9430 Research Blvd., Echelon 1, Austin, TX 78759.			II
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