Connecting blackbody radiation and zero-point radiation within classical physics: A new minimum principle and a status review

TL;DR

This paper presents a classical physics-based thermodynamic analysis linking blackbody radiation and zero-point energy, proposing a new minimum principle that explains the Planck spectrum and reviewing prior derivations involving zero-point radiation.

Contribution

It introduces a new minimum principle within classical physics that explains the Planck spectrum by connecting blackbody radiation and zero-point energy through thermodynamic analysis.

Findings

Derivation of thermodynamic functions from a single function of w/T.

Identification of a natural minimum principle for the Planck spectrum.

Numerical confirmation of the minimum principle.

Abstract

A new thermodynamic analysis is presented for the intimate connections between blackbody radiation and zero-point radiation within classical physics. First, using the thermodynamic behavior of an oscillator under an adiabatic change of frequency, we show that the thermodynamic functions can all be derived from a single function of w/T, analogous to Wien's displacement theorem. The high- and low-frequency limits allow asymptotic energy forms involving T alone or w alone, corresponding to energy equipartition and zero-point energy. It is then suggested that the actual thermodynamic behavior for a harmonic oscillator is given by the function satisfying the Wien displacement result which provides the smoothest possible interpolation between scale-decoupled energy equipartition at low frequency and scale-invariant zero-point energy at high frequency. This leads to the Planck spectrum. Second, we turn to radiation in a box with conducting walls and a conducting partition so that the discrete normal mode structure of the box becomes important. The contrasting Casimir energies are explored for the Rayleigh-Jeans and zero-point spectra. The Rayleigh-Jeans spectrum involves no change of energy with partition position, and the zero-point spectrum involves no change of entropy. It is suggested that the Planck spectrum with zero-point radiation satisfies a natural minimum principle which corresponds to greatest independence of the system energy from the position of the partition for a fixed temperature. Numerical calculation is used for confirmation. Third, we review the previous derivations of the Planck radiation spectrum in classical physics, all of which involve zero-point radiation.