Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site petsd.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxt!houxm!mtuxo!mtunh!mtung!mtunf!ariel!vax135!petsd!cjh From: cjh@petsd.UUCP (Chris Henrich) Newsgroups: net.physics Subject: Re: Least Time Principle Message-ID: <558@petsd.UUCP> Date: Tue, 2-Jul-85 12:15:08 EDT Article-I.D.: petsd.558 Posted: Tue Jul 2 12:15:08 1985 Date-Received: Wed, 3-Jul-85 08:40:49 EDT References: <1033@phs.UUCP> Reply-To: cjh@petsd.UUCP (PUT YOUR NAME HERE) Organization: Perkin-Elmer DSG, Tinton Falls, N.J. Lines: 42 Summary: Yes, there is such a thing, but... [] In article <1033@phs.UUCP> paul@phs.UUCP (Paul C. Dolber) writes: >...(an example of how the path of a light ray gets to its end >point in "least time")... > What I would like to know is: Is there >some known physical reason why light *must* follow the least time >path? or can one only conclude that it's an accident? or the result >of some cosmic design? There is a mathematical reason, if not exactly a physical reason. The best description of how light propagates, for most purposes, is a "wave" model: something which is defined at each point in space and varies continuously as a function of position and time; the "wave equation" relates the change at one point to the values at neighboring points. (That's a hand-waving definition of what a partial differential equation does.) The wave equations and other differential equations of physics often imply "variational principles:" that a wave propagates (or a particle moves) along a line which happens to be the solution of the following kind of problem: find the curve which minimizes a certain function depending on all the points that it passes through. The best-written book about this connection between physical principles and variational problems known to me is "The Variational Principles of Mechanics" by Cornelius Lanczos. It is not light reading, and presumes a knowledge of calculus. Does the existence of variational principles in physics imply something about God? This question goes beyond the subject matter of science or mathematics; these are about experiments, hypotheses, equations, theorems, etc. I believe that the answer is "Yes," but this is not a thing that I try to prove by mathematics. Regards, Chris -- Full-Name: Christopher J. Henrich UUCP: ..!(cornell | ariel | ukc | houxz)!vax135!petsd!cjh US Mail: MS 313; Perkin-Elmer; 106 Apple St; Tinton Falls, NJ 07724 Phone: (201) 758-7288