(recall that R^ = 0 in the Riemannian case because of Eq. 17.29). Eddington
therefore suggested that R^ play the role of electromagnetic field.
Note further that
(17.47)(17.48)
is a scalar, where A is some constant. Define g^ by
(17.46)
(17.45)
where the first (second) term is the symmetric (antisymmetric) part. Not only is
R(^ antisymmetric, it is a curl: according to Eq. 17.27
342 THE LATER JOURNEYsiasm, and an ability to drop without pain, regrets, or afterthought, one strategy
and to start almost without pause on another one. For twenty years, he tried the
five-dimensional way about once every five years. In between as well as thereafter
he sought to reach his goal by means of four-dimensional connections, now of one
kind, then of another. He would also spend time on problems in general relativity
(as was already discussed in Chapter 15) or ponder the foundations of quantum
theory (as will be discussed in Chapter 25).
Returning to unified field theory, I have chosen the device of a scientific chro-
nology to convey how constant was his purpose, how manifold his methods, and
how futile his efforts. The reader will find other entries (that aim to round off a
survey of the period) interspaced with the items on unification. The entries dealing
with the five-dimensional approach, already discussed in Section 17b, are marked
with a f. Before I start with the chronology, I should stress that Einstein had three
distinct motives for studying generalizations of general relativity. First, he wanted
to join gravity with electromagnetism. Second, he had been unsuccessful in obtain-
ing singularity-free solutions of the source-free general relativistic field equations
which could represent particles; he hoped to have better luck with more general
theories. Third, he hoped that such theories might be of help in understanding the
quantum theory (see Chapter 26).
1922.} A study with Grommer on singularity-free solutions of the Kaluza
equations.- Four short papers [E35, E36, E37, E38] on Eddington's program for
a unified field theory. In 1921 Eddington had proposed a theory inspired by
Weyl's work [E39]. As we just saw, Weyl had introduced a connection and a
fundamental tensor, both symmetric, as primary objects. In Eddington's proposal
only a symmetric F^, is primary; a symmetric fundamental tensor enters through
a back door. A theory of this kind contains a Ricci tensor /?„, that is not symmetric
(even though the connection is symmetric). Put