Hasenohrl and the Equivalence of Mass and Energy

TL;DR

This paper revisits Fritz Hasenohrl's early 20th-century work on blackbody radiation and mass-energy equivalence, clarifying misconceptions and providing a modern relativistic analysis that resolves longstanding confusions.

Contribution

It offers a new, accurate relativistic solution to Hasenohrl's thought experiment, correcting historical misunderstandings and clarifying the relation between radiation energy and mass.

Findings

Hasenohrl's original calculations were incomplete and led to misconceptions.

The correct relativistic treatment shows the proper relation between energy and mass.

Many previous interpretations, including Fermi's, are found to be misleading or incorrect.

Abstract

In 1904 Austrian physicist Fritz Hasenohrl (1874-1915) examined blackbody radiation in a reflecting cavity. By calculating the work necessary to keep the cavity moving at a constant velocity against the radiation pressure he concluded that to a moving observer the energy of the radiation would appear to increase by an amount E=(3/8)mc^2, which in early 1905 he corrected to E=(3/4)mc^2. Because relativistic corrections come in at order v^2/c^2 and Hasenohrl's gedankenexperiment evidently required calculations only to order v/c, it is initially puzzling why he did not achieve the answer universally accepted today. Moreover, that $m$ should be equal to (4/3)E/c^2 has led commentators to believe that this problem is identical to the famous "4/3 problem" of the self-energy of the electron and they have invariably attributed Hasenohrl's mistake to neglect of the cavity stresses. We examine Hasenohrl's papers from a modern, relativistic point of view in an attempt to understand where exactly he went wrong. The problem turns out to be a rich and challenging one with strong resonances to matters that remain controversial. We give an acceptable relativistic solution to the conundrum and show that virtually everything ever written about Hasenohrl's thought experiment, including a 1923 paper by Enrico Fermi, is misleading if not incorrect.