What if Planck had known about these calculations?

TL;DR

This paper explores a classical derivation of blackbody radiation and the Unruh-Hawking effect using zero-point fluctuations, suggesting alternative pathways for quantum mechanics development if Planck had known these results.

Contribution

It provides a classical derivation of quantum phenomena like blackbody spectrum and the Unruh-Hawking effect without quantum assumptions, using zero-point fluctuations.

Findings

Derivation of Planck's spectrum without quantized energy levels

Classical derivation of the Unruh-Hawking effect

Implications for the development of quantum theory

Abstract

Here we present some results that would possibly have attracted the attention of the physics community in the early days of quantum mechanics in such a way that its development could have been different from what we see today. We will first present a derivation of Planck's blackbody spectrum radiation without the hypothesis of quantized energy levels of the oscillator, the only additional hypothesis to the classical theory being the existence of zeropoint fluctuations in the electromagnetic field, and this would stand as a nontrivial vacuum which could be inferred by classical means. After doing this, we derive the Unruh-Hawking effect for the electromagnetic field in a purely undulatory context, without dualities and without photons, and one question, among many others, arises after these statements: What would be the development of quantum mechanics if Planck was aware of these possibilities?