A Theory of the Gravitational Field in the Light of Maxwell's Theory

Abstract

In this paper, a complete physical theory of the gravitational field is formulated, which, without recourse to the hypothesis of equivalence or of non-Euclidean geometry, has yet all the advantages of Einstein's theory for describing inertial and gravitational phenomena. The theory starts from the fact that gravitational forces obey the inverse square law in common with electric and magnetic forces; from this it is inferred that Newton's law of gravitation must be developed into a theory of field-action on much the same lines as Coulomb's law has followed; as a first step towards this, the two principles, namely, Hamilton's principle and the special principle of relativity, on which Maxwell's theory is founded, are shown to be sufficient to determine uniquely Lorentz's law of electromagnetic force. Analogous considerations on the same two principles are also found to determine uniquely the law of motion in a gravitational field represented by an invariant potential. The law is found to be a comprehensive law of motion under both inertia and gravitation---the two effects being recognised as only different aspects of the same phenomenon; all the principles of mechanics including the theorems of energy and momentum are actually deduced from the laws of gravitation and the equality of inertial and gravitational mass is proved. Newton's inertial frame is also shown to mark a fundamental physical medium in which matter is embedded---a conclusion confirmed by the experimental detection of this frame by Foucault's pendulum and by the gyro-compass.Applications of the theory.---The theory also shows that this medium is modified near large masses such as the sun and this modification is found to be responsible for the observed values of the spectral shift and of the deflection of light. The fine-structure of spectral lines and the so-called variation of electronic mass with velocity also follow from the theory. The question of Mercury's perihelion is also discussed and it is considered that the problem of perturbations must be treated as a whole in the light of the present law, and a re-examination on the observational side also must be entered into, before the Mercury problem can be dealt with with certainty.