THE NEW KINEMATICS 155We have now discussed special relativity from its nineteenth century antece-
dents to Einstein's motivation, his paper of 1905 and its sequels, and the early
reactions to the new theory. I shall not discuss the further developments in classical
special relativity. Its impact on modern physics is assessed in papers by Wolfgang
Panofsky [Pll] and Edward Purcell [P12].
Remaining unfinished business, mainly related to the roles of Einstein, Lorentz,
and Poincare, will be discussed in Chapter 8. By way of transition, let us consider
the problem of electromagnetic mass.7e. Electromagnetic Mass: The First Century*
Long before it was known that the equivalence of energy and inertial mass is a
necessary consequence of the relativity postulates and that this equivalence applies
to all forms of energy, long before it was known that the separate conservation
laws of energy and of mass merge into one, there was a time when dynamic rather
than kinematic arguments led to the notion of electromagnetic mass, a form of
energy arising specifically in the case of a charged particle coupled to its own
electromagnetic field. The electromagnetic mass concept celebrates its first centen-
nial as these lines are written. The investigations of the self-energy problem of the
electron by men like Abraham, Lorentz, and Poincare have long since ceased to
be relevant. All that has remained from those early times is that we still do not
understand the problem.
'A close analogy to this question of electromagnetic mass is furnished by a sim-
ple hydrodynamic problem,' Lorentz told his listeners at Columbia University
early in 1906 [L8]. The problem he had in mind was the motion of a solid, per-
fectly smooth sphere of mass m 0 moving uniformly with a velocity ~v in an infinite,
incompressible, ideal fluid. Motions of this kind had been analyzed as early as
1842 by Stokes [S4]. Stokes had shown that the kinetic energy E and the momen-
tum p of the system are given by E = %mv^2 and p = mv, where m = m 0 + /u.
The parameter fj,—the induced, or hydrodynamic, mass—depends on the radius
of the sphere and the density of the fluid. The analogy to which Lorentz referred
was first noted by J. J. Thomson, who in 1881 had studied the problem 'of a
charged sphere moving through an unlimited space filled with a medium of spe-
cific inductive capacity K.... The resistance [to the sphere's motion]... must
correspond to the resistance theoretically experienced by a solid in moving through
a perfect fluid' [T2]. Thomson calculated the kinetic energy of the system for small
velocities and found it to be of the form E = %mv^2 , where m = m 0 + fj.: 'The
effect of the electrification is the same as if the mass of the sphere were
*Some of the material of this section was presented earlier in an article on the history of the theory
of the electron [PI3],