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148 RELATIVITY, THE SPECIAL THEORY

7b. September 1905: About E = me^2

'The mass of a body is a measure of its energy content,' Einstein, technical expert

third class at the patent office in Bern, concluded in September 1905 [E9]. 'The

law of conservation of mass is a special case of the law of conservation of energy,'

Einstein, technical expert second class, wrote in May 1906 [E10]. 'In regard to

inertia, a mass m is equivalent to an energy content ... me^2. This result is of

extraordinary importance since [it implies that] the inertial mass and the energy

of a physical system appear as equivalent things,' he stated in 1907 [Ell]. For

special cases the equivalence of mass and energy had been known for about

twenty-five years.* The novelty of 1905 was the generality of this connection.

Einstein's proof of 1905** for the relation

Now, Einstein said, note that Eq. 7.21 for the energy differential is identical in
structure to Eq. 7.17 for the kinetic energy differential of a particle, so that 'if a
body gives off the energy L in the form of radiation, its mass diminishes by L/c^2.
The fact that the energy withdrawn from the body becomes energy of radiation
evidently makes no difference.'
This brief paper of September 1905 ends with the remark that bodies 'whose
energy content is variable to a high degree, for example, radium salts,' may per-
haps be used to test this prediction. But Einstein was not quite sure. In the fall of
1905 he wrote to Habicht, 'The line of thought is amusing and fascinating, but

*See Section 7e on electromagnetic mass. Also before September 1905, Fritz Hasenohrl had discov-

ered that the kinetic energy of a cavity increases when it is filled with radiation, in such a way that

the mass of the system appears to increase [HI].

**He gave two proofs in later years. In 1934 he gave the Gibbs lecture in Pittsburgh and deduced

Eq. 7.20 from the validity in all inertial frames of energy and momentum conservation for a system

of point particles [El2]. In 1946 he gave an elementary derivation in which the equations for the

aberration of light and the radiation pressure are assumed given [E13].

runs as follows. Consider a body with energy E{ at rest in a given inertial frame.

The body next emits plane waves of light with energy L/2 in a direction making

an angle (j> with the x axis and an equal quantity of light in the opposite direction.

After these emissions the body has an energy Es, so that A£ = E, — E, = L.

Consider this same situation as seen from an inertial frame moving with a velocity

v in the x direction. According to Eq. 7.18, A.E^1 ' = E[ — E'f = yL indepen-

dently of $. Thus

or, to second order