[General] closed paths

[Andrew Meulenberg]

Dear Andre,

In your replies to Chip, you show what I consider to be a sign of the true
scholar "the desire and ability to acquire, remember, and utilize
information from many diverse sources." Thank you for your link to de
Broglie's 1923 paper. My French is not good enough to be sure that I was
not interpreting his points as (rather than because of) his supporting of
some of my views. In particular:

   1. His emphasis on frequency (or period) rather than wavelength.
   2. His mention of closed path,
   3. I'm not quite sure what to do with his association of the
   relativistic gamma factor with the wave frequency. It looks interesting;
   but, I need to figure out the implications. Do you have an answer? It does
   get included in his resonant energy relationship (which has a mv^2 rather
   than 1/2(mv^2) basis).

His single mention of closed path, compared to his wave-based emphasis on
frequency, misses statement of the importance of path independence of the
closed or contour integral about non-singular regions. While his wave
functions provide cyclic examples of these closed paths, the importance to
conservation laws is seldom (if ever?) mentioned in physics.

I also have a question on a comment you made to Chip. In

"Heisenberg equation turns out to be de Broglie's equation for the Bohr
orbit adapted to account for a* precision *drift of the chosen velocity on
either side of the selected velocity value on the ground orbital of the
hydrogen atom."
you mention "precision drift."  Could you explain this a bit? I had
originally thought that you meant *precession drift*, which I consider to
be very important (the basis of the de Broglie frequency). However, I don't
think you had that in mind.

Andrew M.
André Michaud <srp2 at srpinc.org>

Hi Chip,

As I signaled the typo in your equation on page 36, I forgot to mention
something else that struck me (this is a part that I read carefully)

I notice that you mention that you noticed what you named a "beat
frequency" with regard to the hydrogen ground state.

Just to mention that this the exact term that de Broglie used in French (un
battement) to describe the resonance state that he associated with the
hydrogen ground state. Here is a link to the paper that inspired
Schrödinger to introduce the wave function on account of this observation
by de Broglie:

http://www.academie-sciences.fr/pdf/dossiers/Broglie/
Broglie_pdf/CR1923_p507.pdf

The interesting part is in page 509.

I also noted that your outer and inner radii for the ground state can be
directly related to Heisenberg's equation

Heisenberg equation turns out to be de Broglie's equation for the Bohr
orbit adapted to account for a precision drift of the chosen velocity on
either side of the selected velocity value on the ground orbital of the
hydrogen atom.

This range lies between your outer and inner radii.

But you probably already were aware of this latter detail

Best Regards
--- André Michaud
GSJournal admin
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