Fritz Hasenohrl and E = mc^2

Abstract

In 1904, the year before Einstein's seminal papers on special relativity, Austrian physicist Fritz Hasenohrl examined the properties of blackbody radiation in a moving cavity. He calculated the work necessary to keep the cavity moving at a constant velocity as it fills with radiation and concluded that the radiation energy has associated with it an apparent mass such that E = 3/8 mc^2. Also in 1904, Hasenohrl achieved the same result by computing the force necessary to accelerate a cavity already filled with radiation. In early 1905, he corrected the latter result to E = 3/4 mc^2. In this paper, Hasenohrl's papers are examined from a modern, relativistic point of view in an attempt to understand where he went wrong. The primary mistake in his first paper was, ironically, that he didn't account for the loss of mass of the blackbody end caps as they radiate energy into the cavity. However, even taking this into account one concludes that blackbody radiation has a mass equivalent of m = 4/3 E/c^2 or m = 5/3 E/c^2 depending on whether one equates the momentum or kinetic energy of radiation to the momentum or kinetic energy of an equivalent mass. In his second and third papers that deal with an accelerated cavity, Hasenohrl concluded that the mass associated with blackbody radiation is m = 4/3 E/c^2, a result which, within the restricted context of Hasenohrl's gedanken experiment, is actually consistent with special relativity. Both of these problems are non-trivial and the surprising results, indeed, turn out to be relevant to the "4/3 problem" in classical models of the electron. An important lesson of these analyses is that E = mc^2, while extremely useful, is not a "law of physics" in the sense that it ought not be applied indiscriminately to any extended system and, in particular, to the subsystems from which they are comprised.