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Re: Total Internal Reflection

This is what I suspected. i.e. not provable, like existence of WMD.
[Absence of proof is not proof of absence.] But, experience organizer.
Before asking the question, I skimmed a number of interesting sites, and
found Noether's principle (?) is involved in a couple, and one discussed
Feynman. The most interesting was Hecht's * discussion of teleology and

* Not the optician.

Feynman did for teleology in mechanics what Darwin did for teleology in
biology. Feynman's PhD thesis showed how the principle of least action
in classical mechanics is an *automatic consequence* of the deeper
quantum mechanical principle of superposition of complex amplitudes. In
the quantum formulation all conceivable trajectories democratically
contribute on an equal footing to the complex probability amplitude for
a given process. In the small (DeBroglie) wavelength limit of the
quantum formulation where the accumulated action ...."

bc, who should read the parts of Goldstein he didn't as a grad. student
and F., L., and S.


p.s. Another did the reverse ("proved" N. via Fermat! as suggested by JR)


| -----Original Message-----
| > Is there a simple proof of Fermat's principle?
| Feynman, volume II chapter 19.
| Probably as simple as it's going to get.
| Recommended. Really, really, recommended.

In the context of say "Mechanics" then what Feynman says can be said to
prove Fermat's principle from Newton's laws and their generalization to
energy concepts (KE and PE). So I think this is an excellent reply to the
question of "Is there a simple proof of Fermat's principle for mechanics
starting from Newton's laws. Or even the question as originally stated.

Similar statements could be said in the context Fermat's principle in the
context of quantum mechanics, optics etc.

However, in another sense one could reply to the question by stating that
one can view Fermat's principle as fundamental organizing principle and
hence it requires not proof other than how well it serves as an organizing
principle for the data.

In the context of mechanics this is how one might respond to the question of
"Is there a simple proof of Newton's 2nd law?" typically, assuming one
wants to use it as a central organizing principle of mechanics, one states
it without proof and appeals to experiment (data) for its validity.

Of course, one could say, yes, starting with Fermat's principle for
mechanics one can easily derive Newton's 2nd law.

Subnote: I would argue that Fermat's principle (I really mean least action
principles) serve as a broader organizing principle in Physics and are
therefore probably preferable as such, than say Newton's laws.

Discussion? Opinion?