The Two-body Problem in Milne's Theory of Gravitation

Abstract

IN a recent communication¹, Dr. Camm has answered Schild's contention², that Milne's theory of the gravitational interaction of two massive particles in the field of the substratum is not Lorentz invariant and hence either invalid or else dependent on an arbitrary additional principle. Camm has shown that: (1) the consequences of Milne's theory are independent of any particular simultaneity convention, Lorentz-invariant or otherwise; and (2) the choice of such a convention, if Lorentz-invariant, is much more restricted than Schild supposes. While the particular convention, arbitrarily chosen by Schild, is shown to be invalid, Camm gives plausible reasons for adopting the convention, linking the event (t₁,P₁) at the particle m₁ with the event (t₂,P₂) at the particle m₂. A conclusive reason, however, can be given for imposing this condition uniquely, as the following argument shows.