‘The tensor calculus knows physics better than the physicist’: Bachelard on the role of ‘Covariant Differentiation’ in Relativity theory

Gaston Bachelard's La valeur inductive de la relativité is arguably his most overlooked work. This paper argues that, nevertheless, it represents a noteworthy contribution to the early history of the philosophical interpretation of general relativity. In particular, Bachelard deserves recognition for identifying the central importance of the comma-goes-to-semicolon rule, referenced in modern textbooks: The principle of general relativity demands that fundamental laws of nature be expressed by tensor equations, substituting ordinary derivatives (commas) with covariant derivatives (semicolons). The equivalence principle might be taken as the claim that this formal change in non-gravitational laws for matter and fields directly leads to the discovery of the corresponding gravitational laws. The paper concludes that, among early professional philosophers working on relativity, Bachelard uniquely grasped the "inductive value" of this heuristic device: "tensor calculus knows physics better than the physicist does", as Langevin once put it.