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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).