Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site brl-tgr.ARPA Path: utzoo!watmath!clyde!bonnie!akgua!whuxlm!harpo!decvax!genrad!panda!talcott!harvard!seismo!brl-tgr!gwyn From: gwyn@brl-tgr.ARPA (Doug Gwyn) Newsgroups: net.physics Subject: Re: Least Time Principle Message-ID: <11372@brl-tgr.ARPA> Date: Wed, 3-Jul-85 11:43:32 EDT Article-I.D.: brl-tgr.11372 Posted: Wed Jul 3 11:43:32 1985 Date-Received: Fri, 5-Jul-85 06:00:52 EDT References: <1033@phs.UUCP> Organization: Ballistic Research Lab Lines: 31 > Is there some known physical reason why light *must* follow the least > time path? Many of the fundamental laws of physics can be expressed as "minimum" principles, or rather, as variational principles. One needs to be a bit subtle in formulating a "minimum" principle. In the case of reflection, an even shorter path (or time) would be obtained by a direct beam from transmitter and receiver, instead of bouncing off the mirror. In general relativity, the path of light is a maximum (in 4 dimensions), not a minimum. The general form of a variational principle is: The actual behavior of a system is such that some quantity computed from its behavior is "stationary" with respect to small variations in behavior from the actual behavior. That is, the computed quantity (typically, an energy or path length) is the same for all possible system behaviors that are "close" to the one that actually happens. If you know some calculus, this should remind you of max or min of a function occurring at the point where the derivative is zero. (The variational principle amounts to a strange sort of "variational derivative" being zero.) Why it is possible to derive the fundamental equations of several areas of physics from variational principles has not been satisfactorily explained. My own view is that a variational principle is just a statement of structural stability, and the only physical laws we can hope to find are those that are structurally stable.