John D. Norton


home >> research >> history of general relativity  
My most important contribution to the history of relativity was
the presentation of the first analysis of Einstein's "Zurich
Notebook." It turned out to contain Einstein's private calculations
for the crucial period of the making of his greatest discovery, the
general theory of relativity. The notebook enabled a reconstruction
of Einstein's path from the earliest insight of an essential
connection between gravitation and the curvature of spacetime
through to the juggling of the complicated expressions that
eventually become the Einstein equations. The notebook also
explained in detail the outstanding puzzle of why Einstein rejected
these famous equations in 1913, only to return to them ruefully two
years later. My work on this notebook has continued in collaboration
with a group of historians of science under the auspices of the Max
Planck Institute for History of Science in Berlin and has lead to
our joint publication of the definitive multivolume work on the
notebook. 
"How Einstein Found His Field Equations: 19121915,"
Historical Studies in the Physical Sciences, 14
(1984), pp. 253315. Reprinted in D. Howard and J. Stachel (eds.), Einstein
and the History of General Relativity: Einstein Studies Vol.
I, Boston: Birkhauser, pp101159. Download.
"Einstein, the Hole Argument and the Reality of Space," in J. Forge (ed.), Measurement, Realism and Objectivity (Reidel), 1987,pp. 153188. Download. Contributing editor to Collected Papers of Albert Einstein, Vol. 4: The Swiss Years: Writings, 19121914. Princeton Univ. Press, 1995. With Don Howard, "Out of the Labyrinth: Einstein, Hertz and Göttingen Answer to the Hole Argument," pp. 3062 in J. Earman, M. Janssen and J. Norton The Attraction of Gravitation: New Studies in History of General Relativity. Boston: Birkhäuser. Download. "'Nature in the Realization of the Simplest Conceivable Mathematical Ideas': Einstein and the Canon of Mathematical Simplicity," Studies in the History and Philosophy of Modern Physics, 31 (2000), pp.135170. Download With Juergen Renn, Tilman Sauer, Michel Janssen, John Stachel, “A Commentary on the Notes on Gravity in the Zürich Notebook” in Juergen Renn (ed.), The Genesis of General Relativity. Vol. 2 Einstein's Zurich Notebook: Commentary and Essays. Springer, 2007 pp. 489714. "A Peek into Einstein's Zurich Notebook." Goodies. 

Two fundamental errors led Einstein to reject generally covariant
gravitational field equations for over two years as he was
developing his general theory of relativity. The first is now well
known. It was the presumption that weak, static gravitational fields
must be spatially flat and a corresponding assumption about his weak
field equations. I conjecture that a second hitherto unrecognized
error also defeated Einstein's efforts: he unwittingly reified his
spacetime coordinate systems. The same error, months later, allowed
the hole argument to convince Einstein that all generally covariant
gravitational field equations would be physically uninteresting. 
"A Conjecture on Einstein, the Independent Reality
of Spacetime Coordinate Systems and the Disaster of 1913," pp.
67102 in A. J. Kox and J. Einsenstaedt, eds., The Universe of
General Relativity. Einstein Studies Volume 11. Boston:
Birkhaeuser, 2005. Download.
"What Was Einstein's 'Fateful Prejudice'?" in Juergen Renn (ed.), The Genesis of General Relativity. Vol. 2 Einstein's Zurich Notebook: Commentary and Essays. Springer, 2007, pp. 71583. Download. 

Other related work includes a study of the Nordstroem theory of gravitation, which Einstein identified as the serious competitor to his newly emerging general relativity. Einstein was able to show that even this most conservative of theories led to the same outcome, the association of gravitation with a curvature of spacetime.  "Einstein, Nordström and the early Demise of
Lorentzcovariant, Scalar Theories of Gravitation," Archive for
History of Exact Sciences, 45 (1992), pp.1794. To be
reprinted in J. Renn (ed.), Relativity and its Alternatives.
Download "Einstein and Nordström: Some Lesser Known thought Experiments in Gravitation," pp.329 in J. Earman, M. Janssen and J. Norton The Attraction of Gravitation: New Studies in History of General Relativity. Boston: Birkhäuser, 1993. Download 

In the late 1890s, Seeliger showed that the simplest and most natural Newtonian cosmology was paradoxical. This paradox, which even tripped up Newton, was used by Einstein to motivate introduction of his cosmological constant. I have surveyed and catalogued the many responses in the literature to this paradox.  "The Cosmological Woes of Newtonian Gravitation
Theory," in H. Goenner, J. Renn, J. Ritter and T. Sauer, eds., The
Expanding Worlds of General Relativity: Einstein Studies, volume 7,
Boston: Birkhäuser, pp. 271322. Download


Einstein insisted that his principle of equivalence was a founding heuristic for his general theory of relativity. However this principle was in tension with his theory of 1912 and flatly contradicted by his theory of 1913. Instead conservation of energy and momentum provided a pathway to unique gravitational field equations in both theories.  "Einstein’s Conflicting Heuristics: The Discovery of General Relativity," draft.  