Via Aristotle, Leibniz & Mach to a relativistic relational gravity

Abstract

In previous work we have shown how a worldview that has its origins in the ideas of Aristotle, Leibniz and Mach leads to a quasi-classical (that is, one-clock) metric theory of gravitation (astro-ph/0107397) which, for example, when applied to model low surface brightness spirals (astro-ph/0306228), produces results that have, hitherto, only been matched by Milgrom's MOND algorithm. In this paper we show how the natural generalization of this worldview into a properly relativistic two-clock theory, applied to model a spherically symmetric gravitational source, produces results that cannot be distinguished from the canonical picture for all the standard local tests and which, when interpreted as a radiation model, produces no dipole radiation. Furthermore, although black-holes within this picture have an event horizon at the usual Schwarzschild radius, they do not have an essential singularity at the origin - the solutions are perfectly regular there.