XII
Relativistic kinematics required a relativistic dy-
namics for which Newtonian concepts were not well
suited. But the success of Newtonian dynamics for
speeds small compared with c had created habits of
thought that could not be easily broken. Accordingly,
Einstein and others sought to distort Newtonian con-
cepts to fit relativistic kinematics. Mass became rela-
tive, increasing in value with increasing relative speed.
Thus the greater the relative speed of an object, the
greater its inertial resistance to change in its speed.
If the object could attain speed c its mass would be-
come infinite, and no increase in speed would be possi-
ble. While this sounds like dynamics and uses Newto-
nian concepts, it is basically a reflection of the existence
of the speed limit c, which, as we saw, is an immediate
kinematic consequence of Einstein's two postulates.
(For ordinary matter and radiation, c is the upper speed
limit. For tachyons, if they exist, c is the lower speed
limit. In either case, c is a speed limit.)
In a second paper on relativity in 1905 Einstein
made a daring extrapolation. He began by showing
mathematically that if a body gives off an amount of
energy L in the form of electromagnetic radiation, its
mass decreases by L/c2. Now came these momentous
words: “The fact that the energy... [is] energy of
radiation evidently makes no difference.” Therefore,
Einstein concluded, all energy, of whatever sort, has
mass. And herein lay the germ of the famous equation
E = mc2.
In 1907 Einstein completed the derivation by a
further daring step. Arguing that a body of mass m
has the same inertia as an amount of energy mc2, and
that one should not make a distinction between “real”
and “apparent” mass, he concluded that all mass should
be regarded as a reservoir of energy. At the time, and
for many years after, there was not the slightest direct
experimental evidence for this, yet Einstein not only
asserted the equivalence of mass and energy, but rec-
ognized it in 1907 as a result of extraordinary theoret-
ical importance.
