Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site phs.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxn!ihnp4!houxm!mtuxo!mtunh!mtung!mtunf!ariel!vax135!timeinc!phri!pesnta!amd!amdcad!decwrl!decvax!mcnc!duke!phs!paul From: paul@phs.UUCP (Paul C. Dolber) Newsgroups: net.physics Subject: Least Time Principle Message-ID: <1033@phs.UUCP> Date: Sat, 29-Jun-85 21:53:16 EDT Article-I.D.: phs.1033 Posted: Sat Jun 29 21:53:16 1985 Date-Received: Wed, 3-Jul-85 08:17:53 EDT Organization: Dept. Physiol., DUMC Lines: 42 A rather off-the-wall question for net.physics, I suppose, but no more so than some of what I've seen here lately, and definitely a physics question. From George Owen's "The Universe of the Mind" (Johns Hopkins Press, Baltimore, 1971): "Heron of Alexandria made a major contribution to the theory of reflection by observing that when light is emitted from a point A and is reflected from a plane surface to a point B, the path corresponding to equal angles of incidence and reflection is the shortest path. He assumed that the ideal path, i.e., the shortest, represented the physical situation, and in this assumption he was quite correct... This approach to the question of reflection has much greater significance than the result shown above. The implication is that the laws of nature obey some ideal principle -- in this case, that the time for a ray to proceed via a reflection from A to B is a minimum, although in Heron's age it was not realized that the velocity of light is finite. When one incorporates the finite velocity of light and the fact that the velocity of propagation along both segments is the same, the result of Heron's construction implies that the transit time of a light ray along the reflected path is a minimum. Recognition of this fact led Fermat to the Least Time principle, in deriving the law of refraction of light rays" [pp 56-7]. "Attempting to derive Snell's law of refraction, Fermat, like Heron of Alexandria in his analysis of reflection, suggested that a light ray in passing from a point A to a point B in a medium of variable refractive index (or in a medium wherein the velocity of light varied) would make the passage in the least possible time" [p 108]. While I don't know that George really meant that part about the laws of nature obeying some ideal principle, the utility of the Least Time principle does strike me as a very odd thing indeed. Unfortunately, I don't recall what else he said about it in the course he taught for which this book was used. 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? Please don't get more detailed in your replies than is absolutely necessary; the course was known (until the year I took it) as "Physics for Poets," which ought to give you a good idea of the depth of my understanding of physical principles. Regards, Paul Dolber (...duke!phs!paul).