Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxn!ihnp4!qantel!hplabs!sri-unix.ARPA!MJackson.Wbst@Xerox.ARPA 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