Relationism and Relativity

Abstract

In the seventeenth century a famous debate occurred between Newton and Leibniz on the question of whether space is an entity in its own right, or merely a system of relations of bodies. Near the end of the nineteenth century Mach attempted to defend the Leibnizian relationist view by putting forth what is now called Mach's principle: (roughly) that the fixed stars can play the role in physics which Newton attributed to space. And early in the twentieth century Einstein claimed to have vindicated Mach's critique of Newton by embodying this principle in his general theory of relativity. Eventually, however, it became apparent that in many respects general relativity is inconsistent with Mach's point of view. Supporters of Leibniz and Mach may therefore be heartened by the recent development of a new version of general relativity-the initial-value formulation-which is in many ways closer to the Machian point of view than Einstein's original version. The main purpose of this paper is to determine just how close it is. I will argue that the roles which space and spacetime play in the new formulation-especially their causal roles in certain senses-make it fundamentally anti-Machian. There is already a massive literature on the issues surrounding absolute vs. relational theories of space, Mach's principle, and general relativity. But it seems to me that even the best of this literature suffers from two rather serious defects: (i) it does not take account of the post-Einsteinian