2.00 David Rowe (Mainz), What Einstein learned from mathematicians - and
not just Marcel Grossman
4.00 Roger Penrose (Oxford), General Relativity Theory since 1960
(This is the weekly Mathematics Colloquium.)
There is an abstract of David Rowe's talk below.
For further information, contact me or Jeremy Gray (j.j.gray@open.ac.uk).
David Rowe, What Einstein Learned from the Mathematicians (and not just
Marcel Grossmann)
Standard accounts of Einstein's early work on general relativity theory
have stressed the role of a single mathematician, Marcel Grossmann. It was
he who came to Einstein's rescue when it became clear to Einstein around
1912 that generalizing special relativity in order to accommodate
gravitation brought with it a number of delicate geometrical problems.
Grossmann provided the necessary technical machinery, namely Riemannian
geometry and the tensor calculus of Ricci and Levi-Civita. Their
collaboration led to the Entwurf theory, which was bolstered by Einstein's
belief that, however desirable, generally covariant gravitational field
equations could not be obtained.
In October 1914, Einstein published his notorious "hole argument" to prove
this contention, and he surely repeated this argument in July 1915 when he
delivered six lectures on general relativity theory in Goettingen. We know
that he succeeded at that time in convincing Hilbert of the merits of the
Entwurf theory, which maintained that only a more limited form of
covariance was possible. By November 1915, however, both Einstein and
Hilbert had come to realize that the hole argument was unsound, although
the issue of preserving causality geometrically remained a major issue that
Hilbert grappled with for another year.
Thanks to some diligent archival work by Leo Corry, we now know that the
standard story of how both Hilbert and Einstein found the "correct" field
equations nearly simultaneously can no longer be taken seriously. This
recent revelation, however, only raises many more interesting questions
with regard to the "race" between Hilbert and Einstein such as the issue of
causality in GRT alluded to above. After touching on these matters, I will
go on to argue that they only mark the beginning in a fascinating story
involving remarkably intense interactions between leading mathematicians
and the man who launched both special and general relativity theory.
Indeed, the recently published Einstein correspondence from the period 1914
to 1918 makes abundantly clear the importance of Einstein's contacts with
Tullio Levi-Civita, Hermann Weyl, Felix Klein, Emmy Noether, and a number
of other mathematicians. Given the precarious reception of GRT among
physicists and astronomers (notwithstanding the support of such notable
figures as Eddington, DeSitter, Laue, and Mie), the enthusiastic response
of mathematicians and, in particular, the Goettingen mathematical community
is all the more striking. This enthusiasm reached its high point with the
work of Hilbert and Weyl, both of whom attempted to lay the groundwork for
the first unified field theories.
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