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From: MJackson.Wbst@Xerox.ARPA
Newsgroups: net.physics
Subject: Re: Faster than light.
Message-ID: <394@sri-arpa.ARPA>
Date: Mon, 15-Jul-85 10:41:40 EDT
Article-I.D.: sri-arpa.394
Posted: Mon Jul 15 10:41:40 1985
Date-Received: Thu, 18-Jul-85 03:44:28 EDT
Lines: 54

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 -->

Assume for definiteness that E is emitting unpolarized spin-1/2
particles.  Then D2 (what you call the distribution when the other
measurement has not been done) is just 50% up, 50% down.

In general, D1 (the distribution to be expected when A PARTICULAR SPIN
has been measured by the other observer) will depend on the angle
between the detectors.  Note that since there are two possible outcomes
of the other observer's measurement, there are TWO distributions, call
them D1up and D1down.  Let us assume (again, for definiteness) that D1up
is 25% up, 75% down and that D1down is 75% up, 25% down.

Now in the stationary frame one can say that A receives his particle
first, the wave function collapses "instantaneously," and B's
measurement is thereby affected.  We predict, and would observe
experimentally, that for the set of all cases where A receives a spin-up
particle, B receives 75% down and 25% up; similarly for the cases where
A receives a spin-down particle.  Speaking loosely, one might say that
the measurement at A "caused" the shift in B's distribution.

In the moving frame, B receives his particle first.  Now we expect his
distribution to be D2.  But that was his total distribution before!
(Note that D2 = .5*D1up + .5*D1down.)  And for those events in which B
receives a spin-up particle, it is found that A's distribution is 25% up
and 75% down, and similarly.  Now it *seems* more natural to say that
the measurement at B "caused" the shift in A's distribution, but since
the experimentally measureable facts are the same, who's to tell?.

All that has happened, of course, is that we have chosen two different
ways of looking at the fundamental relationship:

          A = up      A = down

B = up     .125        .375
B = down   .375        .125

There is *no* paradox.  There *is* a difficulty in putting together an
intuitively acceptable combination of causality, induction, and
speed-of-light limit.  Let me recommend again the recent /Physics Today/
article on Bell's inequality; I am willing to summarize it if there is
interest, although I might not have the time to key it in for a couple
of weeks.

Mark