Hilbert’s Axiomatic Method and His “Foundations of Physics”: Reconciling Causality with the Axiom of General Invariance

Abstract

AbstractIn November and December 1915, Hilbert gave two presentations to the Royal G?ottingen Academy of Sciences under the common title ‘The Foundations of Physics’. Distinguished as ‘First Communication’ (Hilbert, 1915b) and ‘Second Communication’ (Hilbert, 1917), the two ‘notes’, as they are widely known, eventually appeared in the Nachrichten of the Academy. The first quickly entered the canon of classical general relativity but has recently become the object of renewed scholarly scrutiny since the discovery (Corry, Renn and Stachel 1997) of a set of printer’s proofs dated December 6, 1915 ((Hilbert, 1915a), henceforth ‘Proofs’). Hilbert’s second presentation has not received the same detailed reconsideration, with the recent exception of an extended study offered by Renn and Stachel (1999/2007). While we agree with much of their detailed technical reconstruction, we profoundly disagree with the assessment of Renn and Stachel that the second note shows that Hilbert had abandoned his own project (set out in the first note), and is working on a variety of largely unrelated problems within Einstein’s. In our opinion, this assessment rests on misunderstandings concerning the aims, content, and significance of the second communication, as well as its links to the first. Our aim in this paper is to offer an alternate narrative, according to which Hilbert’s second note emerges as a natural continuation of the first, containing important and interesting further developments of that project, and above all shedding needed illumination on Hilbert’s assessment of the epistemological novelty posed by a generally covariant physics.KeywordsGeneral CovarianceGeneral InvarianceTimelike CurveCovariant TheoryCausality PrincipleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.