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Zero-postulate classical derivation of Planck's law - at the APS Meeting in March
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 a sci.physics subgroup 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/...anck-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 may positively influence the clarity of the poster.] Sincerely, -prasad --------------------- http://www.inspiredresearch.com |
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