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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
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