History of General Relativity
My Ph.D. advisor Peter G. Bergmann has long been recognized as a co-inventor of a technique that lies at the core of modern attempts at unifying the fundamental laws of nature. The Dirac-Bergmann Hamiltonian constrained dynamics formalism is a method for reformulating, as so-called initial value problems, theories that enjoy a high degree of symmetry. In this form a conventional method exists for converting classical theories into quantum mechanical theories. Einstein’s general theory of relativity, his geometrical theory of gravity, is the supreme example a theory admitting this high degree of symmetry. His dynamical equations take the same form regardless of the choice of spatial and temporal coordinates.
Following his tenure as Einstein’s young assistant at the Institute
for Advanced Study in Princeton from 1936 through 1941, and work for the US
Navy during World War II, Bergmann began at Syracuse University in 1948 an
attempt to convert Einstein’s theory into a quantum theory of gravity.
Although no one has yet succeeded in synthesizing general relativity with
quantum theory, the Dirac-Bergmann technique is one of the mathematical foundations
of all of today’s unified theories, including theories unifying weak
and electromagnetic forces, grand unified theories, and even superstrings
and branes.
I have recently been able to start a long-planned investigation into the origins
of constrained Hamiltonian dynamics, and in particular into the contributions
of Peter Bergmann and his collaborators. My first published article dealing
with Bergmann is a short piece appearing in Albert Einstein: Engineer of the
Universe: One Hundred Authors for Einstein, Jürgen Renn ed. (Wiley-VCH,
Weinheim, 2005) ISBN 10:3-527-40574-7. A gave a talk, "Peter Bergmann
and the invention of constrained Hamiltonian dynamics", at the Seventh
International Conference on the History of General Relativity in the Canary
Islands in March, 2005. The Proceedings preprint is available here.
In July 2006 I gave an invited talk in Berlin at the Eleventh Marcel Grossmann
Meeting on "Rosenfeld, Bergmann, Dirac and the invention of constrained
Hamiltonian dynamics". The Proceedings preprint is available here.
I have translated and annotated a groundbreaking 1930 paper by Leon Rosenfeld on this theme, and it will soon be available as a Max Planck Institute for the History of Science preprint. An historical analysis will appear in Archive for History of Exact Sciences.
I look forward to a sabbatical semester at the Max Planck Institute
for the History of Science in the Spring of 2008, where I will be able to
devote full time to this historical research.