https://doi.org/10.1140/epjh/e2012-30061-5
Fritz Hasenöhrl and E = mc2
Haverford College, 19041
Haverford, PA, USA
a
e-mail: sboughn@haverford.edu
Received:
28
November
2012
Received in final form:
17
December
2012
Published online:
21
January
2013
In 1904, the year before Einstein’s seminal papers on special relativity, Austrian
physicist Fritz Hasenöhrl 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 
. In a subsequent paper, also in 1904, Hasenöhrl
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 
. This result, i.e., 
, has led many to conclude that Hasenöhrl fell victim to
the same “mistake” made by others who derived this relation between the mass and
electrostatic energy of the electron. Some have attributed the mistake to the neglect of
stress in the blackbody cavity. In this paper, Hasenöhrl’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 
or 
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, Hasenöhrl concluded that
the mass associated with blackbody radiation is , a result which, within the restricted context of
Hasenöhrl’s gedanken experiment, is actually consistent with special relativity. (If one
includes all components of the system, including cavity stresses, then the total mass and
energy of the system are, to be sure, related by
m = E/c2.)
Both of these problems are non-trivial and the surprising results, indeed, turn out to be
relevant to the “
problem” in classical models of the electron. An
important lesson of these analyses is that
E = mc2, 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. We suspect that similar problems have plagued attempts to model the
classical electron.
© EDP Sciences, Springer-Verlag 2013
