Far-reaching statistical consequences of the zero-point energy for the harmonic oscillator

TL;DR

This paper demonstrates that the zero-point energy inherently leads to Planck's radiation law through a statistical approach, without relying on quantum assumptions, and explores its implications for energy quantization and fluctuations.

Contribution

It introduces a purely statistical derivation of Planck's law from zero-point energy, avoiding quantum postulates and connecting classical and quantum perspectives.

Findings

Zero-point energy implies Planck's spectrum without quantum assumptions

Discontinuous energy behavior is identified at certain points

Statistical fluctuations include thermal and zero-point contributions

Abstract

In a recent thermodynamic analysis of the harmonic oscillator and using an interpolation procedure, Boyer has shown that the existence of a zero-point energy leads to the Planck spectrum. Here we avoid the interpolation by adding a statistical argument to arrive at Planck's law as an inescapable result of the presence of the zero-point energy. No explicit quantum argument is introduced along the derivations. We disclose the connection of our results with the original analysis of Planck and Einstein, which led to the notion of the quantized radiation field. We then inquire into the discrete or continuous behaviour of the energy and pinpoint the discontinuities. Finally, to open the door to the description of the zero-point fluctuations, we briefly discuss the statistical (in contrast to the purely thermodynamic) description of the oscillator, which accounts for both thermal and temperature-independent contributions to the energy dispersion.