FIELD THEORIES OF GRAVITATION: THE FIRST FIFTY YEARS 229on the gravitation theory which the Finnish physicist Gunnar Nordstrom had
been developing since 1912. Furthermore, he was going to comment on yet another
recent gravitation theory, this one by Abraham (whom we encountered earlier in
the discussion of special relativity). He would also be confronted, he knew, with
still a further theory of gravity of recent vintage, one by Gustav Mie.* In one way
or another, this outpouring of gravitation theories in the years 1912 and 1913 was
a consequence of Einstein's Prague papers. Abraham had proposed to extend Ein-
stein's theory of variable light velocity in a static gravitational field to the nonstatic
case. Nordstrom had raised another question: could not the equivalence principle
be incorporated in a relativistic theory with constant light velocity? Mie's theory
was yet another variant in which c is constant. These activities during 1911-13
do not by any means mark the beginnings of the search for a field theory of grav-
itation, however. As a preface to the discussion of the confused situation at the
Vienna congress of 1913 let us briefly go back half a century.
The search began with Maxwell's remarks on a vector theory of gravitation.
These are found tucked away in his great memoir, A Dynamical Theory of the
Electromagnetic Field, completed in 1864, the purpose of which is 'to explain the
[electromagnetic] action between distant bodies without assuming the existence of
forces capable of acting directly at sensible distances. The theory I propose may
therefore be called a theory of the Electromagnetic Field. ..' [Ml]. After devoting
some forty printed pages to this problem, Maxwell abruptly and briefly turns to
gravitation: 'After tracing to the action of the surrounding medium both the mag-
netic and the electric attractions and repulsions, and finding them to depend on
the inverse square of the distance, we are naturally led to inquire whether the
attraction of gravitation, which follows the same law of the distance, is not also
traceable to the action of a surrounding medium.' But how can one explain, Max-
well asks, that the gravitational force is attractive whereas the force between elec-
tric charges of the same sign is repulsive? He notes that this requires an ad hoc
change of sign when going from the electromagnetic to the gravitational pon-
deromotive force (recall: this is a vector theory). Therefore the gravitational energy
also needs an additional minus sign. This leads to paradoxes: 'the presence of
dense bodies influences the medium so as to diminish this energy [of the medium]
wherever there is a resultant attraction. As I am unable to understand in what
way a medium can possess such properties, I cannot go any further in this direc-
tion in searching for the cause of gravitation.'
Maxwell's wise words were not generally heeded, not even by physicists of great
stature. Oliver Heaviside discussed the gravitational-electromagnetic analogy
without mentioning the negative energy difficulty [HI]. So, remarkably, did
Lorentz, in one of his rare speculative papers [LI], written in 1900. He proposed
that the repulsive forces between two particles with respective charges ( + e, + e)
equal those for (— e, —e) but are slightly weaker (in absolute magnitude) than
the attractive force for the case (+ e, — e). Then if one has, for example, two
'References to other work on gravitation from that period are found in a review by Abraham [Al]