Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxt!houxm!mtuxo!mtunh!mtung!mtunf!ariel!vax135!cornell!uw-beaver!tektronix!hplabs!sri-unix!AI.Mayank@MCC.ARPA From: AI.Mayank@MCC.ARPA Newsgroups: net.physics Subject: Re: Faster than light. Message-ID: <364@sri-arpa.ARPA> Date: Tue, 9-Jul-85 14:49:37 EDT Article-I.D.: sri-arpa.364 Posted: Tue Jul 9 14:49:37 1985 Date-Received: Sat, 13-Jul-85 09:36:34 EDT Lines: 61 From: Mayank Prakash>Please define "instantaneously" in a generally-invariant way. Instantaneity cannot be defined even in a specially invariant way, forget a generally invariant definition. You are missing the point entirely and we are getting on a tangential discussion. Perhaps my inability to express myself clearly is at least partially to blame, but let me make another attempt to clarify my position. All I am claiming is that QM does not give rise to any *observable* contradictions with SR. Logically, there are problems and I am not claiming that a good solution exists. For sake of concreteness, let us consider your earlier example of a photon starting from the north star. Its wave function expands at the velocity of light, (in ANY inertial frame). The important property of the wave-function to remember is that the wave-function of a *given photon* in a *given state* cannot be observed (measured). We can only measure the wave-function corresponding to a *given state* of photons. The reason of course is the uncertainty principle - any attempt to measure it at one space-time point alters it irreversibly at all other points, and hence a measurement at one point makes a measurement at other points meaningless. (Footnote1: The probability distribution corresponding to a given state of photons can be measured by preparing a large number of photons in that state, and then recording the distribution of these photons. This gives us the mod-squared of the wave-function. To get its phase, one could do interference experiments). Now consider an observer at Earth. As soon as she sees the photon, the wave function collapses to within a small region (the speck on a photographic plate, a cell in her retina or whatever) **instantaneously in her frame**. In particular, the wave-function at the point diametrically opposite from her on the pther side of the north star suddenly reduces to zero as soon as the observation is made. Suppose another person is moving along in, say a spaceship. In the moving frame, the wave function at the same diametrically opposite point would collapse to zero either before or after the photon is observed on Earth. Does this mean we have a contradiction? Logically, yes; empirical, no. The reason there is no empirical paradox is simply that the wave function is not itself observable. Therefore, the collapse of the wavae function cannot be observed by any other observer. A real contradiction with SR arises only if *information* can be transmitted faster than light, for in that case, causality can be violated. I:n this situation, *WE* cannot use this setup to transmit information faster than light, and hence cannot *observe* causality violations. However, the wave function does receive a signal to collapse instantaneously (in some frame), and therefore, in some frames it would collapse before the observation was made, and this is far from a satisfactory situation. However, since the wave function is not an observable entity itself, no *empirical* contradictions arise in conventional QM, making the situation *tolerable*, at least pending a better understanding of the measurement process in QM. That was the whole point I was trying to make, and I would welcome criticisms or comments on this issue, but please do not send me any more messages on the meaning of simultaneity etc. - mayank. ========================================================================== II Mayank Prakash AI.Mayank@MCC.ARPA (512) 834-3441 II II 9430 Research Blvd., Echelon 1, Austin, TX 78759. II ========================================================================== -------