Suggestions as to metric in a non-conservative mechanics

The purpose of this note is to give tentative consideration to the dependence of space-time metric on the distribution of energy and momentum, in the case of a mechanics which abandons the principle of the conservation of energy. The question is a difficult one, and its final correct answer might necessitate some new conceptual apparatus. In the present note, however, we shall merely try to show the consequences of a direct and somewhat plausible method of attack, which can be made with familiar tools.