Zero-postulate classical derivation of Planck's law - at the APS Meeting in March
- From: earthshrink@xxxxxxxxx
- Date: Wed, 15 Feb 2006 20:18:39 +0000 (UTC)
I will be presenting my now complete classical derivation of Planck's
law for the first time in the Wednesday poster session. Given the
responses previously received from learned editors of journals like the
Annalen, I believe the accepted abstract is a major milestone in my
clarity of expression as well! I hope my presentation will live up to
the strength of the result...
The key piece, which was incomplete in the derivation previously
posted on my website and advertised in this group for criticism
in 2004, is the identification of the Planck oscillators. As
authoritatively explained at
http://www.physicsweb.org/articles/world/13/12/8/1 ,
and verifiable at
http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html
, the oscillators were hypothetical in Planck's original derivation.
Planck was guided by classical thermodynamic principles, and saw the
oscillator quantization simply as a means of counting states to compute
the entropy. They were identified with radiation quantization only
years later.
I had intuitively identified the oscillators with harmonic families of
modes some years ago. However, as an EPL reviewer observed, the implied
involvement of an entire, infinite family of harmonics when observing a
single frequency was unexplained and didn't seem to make sense.
The emergent answer, explained in my slides online and to be hopefully
brought out better in the poster, the energy exchanges are not only
confined to individual harmonic families, but within each family, only
one member can be excited at any instant. This explains why a family
functions as a harmonic oscillator - all its energy is either at f, or
at hf, or at 3f, and so on, thereby leading to the _expectation_ levels
of hf, 2hf, etc. The result eliminates the conceptual difficulty of
quantization that hitherto made it seem inherently nonclassical: how a
classically continuous quantity like energy can manifest with discrete
values. (The discreteness of standing wave modes obviously concerns
static division of cavity space, not of amplitude or energy.)
In the present picture, an individual mode can have any instantaneous
energy - as explained in the online slides, its _expectation_ energy
has to be a (spatial) multiple of the _expectation_ energy of a one
half-wavelength interval. The half-wavelength intervals, under the
condition of equilibrium must have equal expectation energies, hence
the _expectation_ energy of each mode becomes constant. The mode
families then can have expectation energies of hf, 2hf, 3hf, etc.
corresponding to their member modes of half-wavelength/2 interval, 2
such intervals, 3 such intervals, and so on. Energy quantization thus
results from the spatial discreteness of modes, and the result is
clearly classical, there being _no_ assumption whatsoever in this
analysis that can be equated with _assuming_ quantization.
[I am posting this partly for the same reason as presenting the poster
- review - and partly to report progress in gratitude to those who took
the time to comment, however briefly, in 2004. I may not have the
bandwidth to respond before the APS Meeting, since I need to focus on
promised empirical testing of my oral presentation thesis - which
concerns a mundane Hubble's law wave effect and associated systematic
spectrometric error, already favourably peer-reviewed, appropriately,
in signals and radar forums in 2005. However, your comments would be
valuable and may have positive influence on the clarity of the poster.]
Sincerely,
-prasad
---------------------
V. Guruprasad,
http://www.inspiredresearch.com
.
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