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From: rimey@ucbvax.ARPA (Ken Rimey)
Newsgroups: net.physics
Subject: Re: Least Time Principle
Message-ID: <8760@ucbvax.ARPA>
Date: Thu, 4-Jul-85 01:35:15 EDT
Article-I.D.: ucbvax.8760
Posted: Thu Jul  4 01:35:15 1985
Date-Received: Fri, 5-Jul-85 05:38:31 EDT
References: <1033@phs.UUCP> <558@petsd.UUCP>
Reply-To: rimey@ucbvax.UUCP (Ken Rimey)
Organization: University of California at Berkeley
Lines: 27

>>                               What I would like to know is:  Is there
>>some known physical reason why light *must* follow the least time
>>path?
>	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 ...

Here's a try at a physical reason:  Let's say that the ray of light
doesn't only follow the path of least time, but follows all possible
paths.  There is really a collection of rays, but those that don't
approximately follow the least-time path cancel each other.

Rays that follow paths close to that of the least-time ray get to the
destination slightly later, but only slightly.  These rays therefore
arrive roughly in phase, and interfere constructively.

For each ray that follows a bizarre, unphysical path, there are rays
that follow nearby paths that arrive later, and rays that arrive sooner.
These arrive with an even mix of phases, and interfere destructively.

The result is that only the rays *close* to the least-time ray are
seen at the destination.  These ideas can be expressed mathematically,
but only with difficulty.

Does anybody buy it?

						Ken Rimey