348 THE LATER JOURNEY
From 1945 until the end. The final Einstein equations. Einstein, now in his
mid-sixties, spent the remaining years of his life working on an old love of his,
dating back to 1925: a theory with a fundamental tensor and a connection which
are both nonsymmetric. Initially, he proposed [E73] that these quantities be com-
plex but hermitian (see also [E74]). However, without essential changes one can
revert to the real nonsymmetric formulation (as he did in later papers) since the
group remains the G^ of real point transformations which do not mix real and
imaginary parts of the g's and the F's. The two mentioned papers were authored
by him alone, as were two other contributions, one on Bianchi identities [E75] and
one on the place of discrete masses and charges in this theory [E76]. The major
part of this work was done in collaboration, however, first with Straus [E77] (see
also [S7]), then with Bruria Kaufman [E78, E79], his last assistant. Shortly after
Einstein's death, Kaufman gave a summary of this work at the Bern conference
[K6]. In this very clear and useful report is also found a comparison with the near-
simultaneous work on nonsymmetric connections by Schroedinger [S3] and by
Behram Kursunoglu [K7].*
As the large number of papers intimates, Einstein's efforts to master the non-
symmetric case were far more elaborate during the last decade of his life than they
had been in 1925. At the technical level, the plan of attack was modified several
times. My brief review of this work starts once again from the general formalism
developed in the previous section, where it was noted that the properties of the
third-rank tensor Q^ defined by Eq. 17.24 are important for a detailed specifi-
cation of a connection. That was Einstein's new point of departure. In 1945 he
postulated the relation
plays a role; T^ is a 4-vector (use Eq. 17.25) which vanishes identically in the
Riemann case. The plan was to construct from these ingredients a theory such
that (as in 1925) the symmetric and antisymmetric parts of g^, would correspond
to the metric and the electromagnetic field, respectively, and to see if the theory*Schroedinger treats only the connection as primary and introduces the fundamental tensor via the
cosmological-term device of Eddington. Kursunoglu's theory is more like Einstein's but contains one
additional parameter. For further references to nonsymmetric connections, see [L3, S8, and Tl].
(17.60)
From the transformation properties of the g^ (which, whether symmetric or not,
transform in the good old way; see Eq. 17.22 and the comment following it) and
of the rj, (Eq. 17.25), it follows that Eq. 17.59 is a covariant postulate. Further-
more, now that we are cured of distant parallelism, we once again have nontrivial
curvature and Ricci tensors given by Eqs. 17.26 and 17.27, respectively. In addi-
tion F,,. defined by