Classical derivation of Bose-Einstein statistics
- URL: http://arxiv.org/abs/2308.02069v2
- Date: Tue, 22 Aug 2023 17:54:17 GMT
- Title: Classical derivation of Bose-Einstein statistics
- Authors: Paul Tangney
- Abstract summary: I prove that, at thermal equilibrium, the observed distribution of energy is a Bose-Einstein distribution.
I identify characteristics of the classical independent-oscillator Hamiltonian that make my derivation of the distribution possible.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Without invoking quantum mechanics I prove that, at thermal equilibrium, the
observed distribution of energy among any set of non-interacting harmonic
oscillators is a Bose-Einstein distribution, albeit with an unknown constant,
${h_?}$, in place of Planck's constant, $h$. I identify characteristics of the
classical independent-oscillator Hamiltonian that make my derivation of the
Bose-Einstein distribution possible, and I point out that other classical
physical systems, such as an ideal gas, have Hamiltonians that can be
transformed canonically into forms with these characteristics. If ${h_?=h}$,
among the implications of this work are that (i) there is no discrepancy
between the experimentally-observed spectrum of a blackbody and what should be
expected if light was a mechanical wave in a bounded medium; (ii) there is no
discrepancy between the experimentally-observed temperature dependence of a
crystal's heat capacity and what should be expected of classical lattice waves;
and (iii) when a cluster of massive particles is cold enough, the classical
expectation should be that almost all of its vibrational energy is possessed by
its lowest-frequency normal mode. Therefore, below a certain temperature, all
but one of its degrees of freedom are almost inactive and it is a Bose-Einstein
condensate.
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