The celebrated defect of a theory of gravitation modeled after Maxwell electromagnetism was first pointed out by Maxwell himself (Maxwell 1864, 571). In such a theory, due to the change of signs, the energy density of the gravitational field is negative and becomes more negative as the field becomes stronger. In order not to introduce net negative energies into the theory, one must then suppose that space, in the absence of gravitational forces, must contain a positive energy density sufficiently great to offset the negative energy of any possible field strength. Maxwell professed himself baffled by the question of how a medium could possesses such properties and renounced further work on the problem. As it turns out it was Einstein’s foe, Abraham, shortly after his exchange with Einstein, who refined Maxwell’s concern into a more telling objection. In a lecture of October 19, 1912, he reviewed his own gravitation theory based on Einstein’s idea of using the speed of light as a gravitational potential. (Abraham 1912e) He first reflected (pp. 193–94), however, on a gravitation theory modeled after Maxwell electromagnetism. In such a theory, a mass, set into oscillation, would emit waves analogous to light waves. However, because of the change of sign, the energy flow would not be away from the mass but towards it, so that the energy of oscillation would increase. In other words such an oscillating mass would have no stable equilibrium. Similar difficulties were reported by him for gravitation theories of Maxwellian form due to H.A. Lorentz and R. Gans.
