Einstein Meets Hilbert: At the Crossroads of Physics and Mathematics

Abstract

One of the most famous episodes in the early history of general relativity involves the ''race between Albert Einstein and David Hilbert to uncover the ''correct'' form for the ten gravitational field equations. In light of recent archival findings, however, this story now has become a topic of renewed interest and controversy among historians of physics and mathematics. Drawing on recent studies and newly found sources, the present essay takes up this familiar tale from a new perspective, one that has seldom received due attention in the standard literature, namely, the mathematical issues at the heart of Einstein's theory. Told from this angle, the leading actors are Einstein's collaborator Marcel Grossmann, his critic Tullio Levi-Civita, his competitor David Hilbert, and several other mathematicians, many of them connected with Hilbert's Gö ttingen colleagues such as Hermann Weyl, Felix Klein, and Emmy Noether. As Einstein was the first to admit, Gö ttingen was far more important than Berlin as an active center for research in general relativity. Any account which, like this one, tries to understand both the actions and motives of the leading players must confront the problem of interpreting the rather sparse documentary evidence available. The interpretation offered herein, whatever its merits, aims first and foremost to show how mathematical issues deeply permeated the early history of general relativity.

Gravitational energy for GR and Poincaré gauge theories: A covariant Hamiltonian approach

“…d One reason was his famous "hole" argument. 61,98 e Einstein and Hilbert had quite different agendas; 112,115,136,141 Hilbert in his Foundation of Physics papers, based on the work of Einstein and Mie, was using his axiomatic method with the objective of finding a unified field theory of gravity and electromagnetism. 15,28,58,108,109,114 July 28, 2015 0:26 World Scientific Review Volume -9.75in x 6.5in 100GR˙Ch4˙150726v1 page 5Gravitational energy for GR and Poincaré gauge theories:a covariant Hamiltonian approach 5 l The sign in this expression is dictated by the condition for positive energy determined by the Hamiltonian using our local Minkowski signature convention: Pµ = (−E/c, p).…”

Making Mathematics in an Oral Culture: Göttingen in the Era of Klein and Hilbert

“…48 Once Einstein's mature theory came out (Einstein 1916a) -alongside Hilbert's paper and the pioneering work of Schwarzschild containing the first exact solutions of the Einstein equations -many mathematicians and physicists began 44 For the reception in Leiden, see Kox 1992. 45 Recent contributions to the literature include Corry, Renn and Stachel 1997;Corry 1997;Sauer 1999;Renn and Stachel 1999;Corry 1999a;Corry 1999b;Corry 1999c;Rowe 1999;Rowe 2001a. 46 Hilbert to Schwarzschild, 23 October 1910 Universitätsbibliothek, Göttingen (NSUB).…”

Noether Symmetries Quantization and Superintegrability of Biological Models

“…Since many mathematical tools used in physics have also been used in biology with different success, we present a somewhat forgotten and neglected tool, a tool that in one of its outcomes, Noether symmetries, helped Einstein and Klein in their quarrel with Hilbert about the energy-momentum conservation of general relativity theory [2]. This tool is Lie continuous symmetries, which yield conservation laws, calculus of variation setting, and ultimately quantization.…”