230 RELATIVITY, THE GENERAL THEORY
neutral particles at rest, each composed of a pair of subunits (+e, — e), there is
a residual Newtonian attraction between them. The formalism of his theory con-
sists of a doubled set of Maxwell equations and ponderomotive forces (the latter
with coefficients adjusted to give the desired behavior for the various charge com-
binations). Nowhere in this strange paper is it noted that there exists a doubling
of conservation laws, one for charge and one for gravitational rest mass. Lorentz
calculated velocity-dependent corrections to Newton's law and went as far as eval-
uating their influence (too small) on the perihelion of Mercury. A few others also
examined the consequences of this theory [Gl, Wl]. In 1908 Poincare mentioned
Lorentz's gravitation theory as an example of a field theory that is compatible
with the requirements of special relativity [PI].*
As late as 1912, it was still necessary to show that all these vector theories made
no sense because of Maxwell's negative energy difficulty. At that time Abraham
pointed out that the equilibrium of a gravitational oscillator is unstable [A2]: the
amplitude of the slightest oscillation increases with emission of gravitational field
energy; there is radiation enhancement rather than radiation damping. Thus the
vector theories were buried at just about the time attention shifted to scalar
theories.
This brief period began with Einstein's paper of June 1911, in which he
showed that the velocity of light cannot generally be treated as a universal constant
in a static gravitational field [E4]. Half a year later, Abraham made the first
attempt to extend this conclusion to nonstatic fields [A3]. He tried the impossible:
to incorporate this idea of a nonconstant light velocity into the special theory of
relativity. He generalized the Newtonian equation for a point particle, K —
— V<p = a, where K is the gravitational force acting on a unit of mass, <p the
potential, and a the acceleration, to
where «,, is the four-velocity and the dot denotes differentiation with respect to
the proper time r. The function
where
From Eqs. 13.1 and 13.3,* Poincare had already emphasized the need for a relativistic theory of gravitation in his memoir of
1905 [ P2], in which he discussed some general kinematic aspects of the problem without commitment
to a specific model. See also Minkowski [M2].