Between equilibrium and fluctuation: Einstein's heuristic argument and Boltzmann's principle

TL;DR

This paper critically examines Einstein's 1905 heuristic argument for lightquanta, analyzing its coherence, historical context, and the role of Boltzmann's principle, revealing limitations in extending the concept across the spectrum.

Contribution

It offers a nuanced reinterpretation of Einstein's argument, emphasizing the importance of occupancy number over frequency and clarifying conceptual ambiguities.

Findings

Einstein's reasoning can be seen as fluctuation-based or equilibrium comparison.

The role of Boltzmann's principle evolved in Einstein's work.

Limitations of lightquanta concept depend on occupancy number, not frequency.

Abstract

We critically revisit Einstein's 1905 heuristic argument for lightquanta, considering its internal coherence and the scope of its applicability. We argue that Einstein's reasoning, often celebrated for its originality, is ambiguous because it can be understood as a fluctuation or as a comparison between equilibrium states. A historical and conceptual analysis of Einstein's use of Boltzmann's principle in those years reveals his evolving stance on its meaning and the role of probability, as well as his persistent doubts about the nature of radiation. We use our analysis to examine the limitations of extending the notion of Einstein's lightquanta across the electromagnetic spectrum: the relevant parameter is not the frequency, but the occupancy number.