THE MASS-ENERGY RELATION
classical mechanical recoil process would not have led to the mass-
energy relation. It is therefore erroneous to contend, as R. T. Smith did,
that Einstein’s 1906 derivation is “purely classical and has nothing to do
with relativity.”
36
Just as Einstein’s 1905 derivation became the prototype of numerous
modified versions belonging to class I, so his 1906 derivation initiated
a long series of class II variants, of which each was intended to be more
rigorous than all those that preceded it. Since Adel F. Antippa’s detailed
survey of class II derivations is readily available a brief summary of this
development will suffice.
37
In his contribution to the Schilpp book, Max von Laue reformulated
Einstein’s 1906 derivation with only one minor change.
38
He added
to the physical scenario two bodies or disks, one at each end of the
cylinder, one of which transfers 1E back from right to left. He thus
replaced Einstein’s “imagined massless carrier,” which he regarded
as physically unrealistic by a mechanical process. Another disturbing
feature of Einstein’s 1906 derivation is his assumption of the rigidity
of the cylinder, an assumption which, in his third (1907) derivation,
he showed to be incompatible with the relativity of simultaneity. This
deficiency in the 1906 derivation was criticized in 1960 by Eugene
Feenberg, who pointed out that “the recoil generates an elastic wave
traveling with finite velocity from the source point; the far end does
not begin to move until the radiation has been absorbed, and then
the first motion is away from the source.”
39
It is only after some time,
when the elastic waves are damped out by dissipative processes that the
cylinder is finally at rest, having undergone the displacement. However,
as Feenberg shows, these complications do not invalidate the correctness
of the mass-energy relation.
In the early 1920s, in the wake of an international wave of general
interest in the theory of relativity, Max Born was invited to deliver
36
R. T. Smith, “Classical Origins of ‘E = mc
2
’,” Physics Education 27, 248–250 (1992).
37
A. T. Antippa, “Variations on a Photon-in-a-Box by Einstein,” UQTR-TH-8, Universit
´
e
du Qu
´
ebec
`
a Trois-Rivi
`
eres, pp. 1–48; “Inertia of Energy and the Liberated Photon,”
American Journal of Physics 44, 841–844 (1976). See also the earlier survey on some of
Einstein’s derivations by W. Kantor, “Inertia of Energy,” American Journal of Physics 22,
528–541 (1954). A thorough analysis of Einstein’s 1906 and 1907 derivations as well as
their elaborations by Planck and von Laue has also been given by A. I. Miller in his Albert
Einstein’s Special Theory of Relativity (Reading, Mass.: Addison-Wesley, 1981), pp. 353–367.
38
Van Laue in P. A. Schilpp, ed., Albert Einstein, pp. 524–527.
39
E. Feenberg, “Inertia of Energy,” American Journal of Physics 28, 565–566 (1960).
79