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Re: REFRACTION - REFLECTION



This is of course not an explanation, just an anthropomorphic analogy. But
it suffers the same problem as Fermat's principle: it seems to require that
the light have a foreknowledge of the territory ahead, which doesn't seem
to make much sense. Now maybe it is possible to rearrange your world-view
in order to get around this.

I always thought that was the appeal of any "Least Action" approach. In
teaching, it gives an alternative way to look at the world. It's
particularly interesting in mechanics where the idea of cause and effect is
so thoroughly ingrained. Contrary to that, Hamilton's Principle seems to
say that all motion comes about as a result of "nature striving to achieve
a certain result" (an approximate quote from Marion's book); namely the
minimization of the Lagrangian. It's not often in physics when we can ask
students how they feel about two different world views. Of course, Newton's
Laws imply Hamilton's Principle and vice versa, so the solution to any
mechanics problem is indifferent to your choice.
To be truthful, I think my students were always kinda baffled by the
question. I was never able to elicit much of an argument from them.

--Jim Pengra, Walla Walla, Washinton 99362 mailto:pengra@whitman.edu