How to Teach General Relativity

Abstract

Supposing that one is already familiar with special relativistic physics, what constitutes the best route via which to arrive at the architecture of the general theory of relativity? Although the later Einstein would stress the significance of mathematical and theoretical principles in answering this question, in this article we follow the lead of the earlier Einstein (circa 1916) and stress instead how one can go a long way to arriving at the general theory via inductive and empirical principles, without invoking presumptions concerning the geometrical structure of the final theory. We focus on the construction of the kinematical structure and the terms describing the coupling of matter to gravity. General covariance, understood and employed as a straightforward extrapolation of empirical considerations, is central to our derivation, together with what we dub the 'Methodological Equivalence Principle'. We argue that our approach has a number of virtues, both for one's understanding of the general theory of relativity, but also for pedagogy, since it stresses-to the greatest extent possible (a lesson which we inherit from Bell [1976])-both the methodological precedence of dynamical considerations to interpretative issues and the theoretical continuity between general relativity and its precursors. We conclude by comparing our approach to other philosophical approaches to general relativity and discussing the significance of empirically motivated methodological principles in the philosophy of science.