I. Identifications

Abstract

1. The general object of the following papers is to ascertain what form the equations of electromagnetism take when derived on a purely kinematic basis. Maxwell’s theory is not assumed. The only physical assumption made, namely, that a system of moving charges conserves its energy (defined kinematically) when the accelerations of the charges vanish, is a very slight one and is certainly satisfied in classical electromagnetism, but the resulting equations and laws, whilst coinciding with the classical theory to a considerable extent, differ in certain essential particulars. This arises from the avoidance of the empirical laws and hypothetical assumptions from which Maxwell’s theory starts. In particular we avoid the formal inconsistency in the classical theory by which a magnetic intensity H is defined via the mechanical force on an isolated magnetic pole, yet isolated magnetic poles do not occur in the classical “theory of electrons”. In the present treatment a magnetic intensity is defined via the mechanical force on a moving “charged” particle, as an element entering into the calculation of such force. The general method is, adopting the dynamics constructed in previous papers on a purely kinematic basis (Milne 1936, 1937), to formulate equations of motion containing the next most general type of “external” force arising after “gravitational” forces have been dealt with. Such forces arise from the double differentiation of scalar “superpotentials”, but we do not lay down what form these scalars are to take. Instead we allow them to determine themselves, by imposing the single physical assumption above-mentioned, after the equation of energy has been derived. Once the scalar superpotentials have been so determined, their double differentiation yields symbols E, H, which are then compared with the empirical laws governing the interaction of “charges”; this allows us to identify the adopted definition of charge and the symbols E, H with the similar quantities occurring in the experimental formulation. Lastly, we derive the identities satisfied by the resulting E, H; these partly coincide with, and partly differ from, the “field equations” with which the classical theory starts, and thus we end with theorems which play the part of the “laws of nature” assumed at the outset in the classical theory.