Re: Total Internal Reflection

[Bernard Cleyet <anngeorg@PACBELL.NET>]

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
Fermat.

* Not the optician.

http://www.asa3.org/archive/evolution/199704/0038.html

"
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 ...."

http://www.21stcenturysciencetech.com/articles/fall01/fermat/Fermat.html

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


bc

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



RAUBER, JOEL wrote:

> | -----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?