UNIFIED FIELD THEORY 333
worked for some years on the Kaluza-Klein theory. However, Einstein had
already become actively interested in Kaluza's ideas before the appearance of
Klein's papers in 1926.
- Einstein and the Kaluza-Klein Theory. In 1922 Einstein and Grommer
addressed the question, Does Eq. 17.4 have any particle-like solutions in the
absence of 'sources,' that is, if Tm = 0? It was a question Einstein had pondered
earlier in the context of conventional general relativity. For that case we do not
know, he reasoned, how to nail down Tik(i,k = 1,... , 4) as firmly as the left-
hand side of the gravitational equations. Could we do without a TA altogether?
Perhaps, he said, since the equations for pure gravitation are nonlinear. The pos-
sibility that there are nonsingular particle-like solutions for vanishing Tik ought
to be considered. In what follows, we shall see that time and time again Einstein
kept insisting on the existence of singularity-free solutions of source-free equations
as a condition that must be met by a theory acceptable to him.
Transcribed to the Kaluza theory, the question of zero Tik becomes the question
of zero T^. Einstein and Grommer [E8] showed that 'the Kaluza theory possesses
no centrally symmetric solution which depends on the g^ only and which might
be interpreted as a (singularity-free) electron,' a conclusion which of course has
nothing to do with unified field theory per se, since it could equally well have been
asked in the context of ordinary general relativity theory.
Einstein's next papers on the five-dimensional theory are two short communi-
cations in February 1927 [E19, E20]. I should explain why these papers are a
mystery to me. Recall that in 1926 (in April, to be precise) Klein had presented
an improved version of the Kaluza theory. In August 1926 Einstein wrote to
Ehrenfest that Grommer had drawn his attention to Klein's paper: 'Subject:
Kaluza, Schroedinger, general relativity' [E21]. Ten days later, he wrote to him
again: 'Klein's paper is beautiful and impressive, but I find Kaluza's principle too
unnatural' [E22]. Then come Einstein's own two papers just mentioned, followed
by a letter to Lorentz: 'It appears that the union of gravitation and Maxwell's
theory is achieved in a completely satisfactory way by the five-dimensional theory
(Kaluza-Klein-Fock)' [E23, Fl].
There is nothing unusual in Einstein's change of opinion about a theory being
unnatural at one time and completely satisfactory some months later. What does
puzzle me is a note added to the second paper [E20]: 'Herr Mandel points out to
me that the results communicated by me are not new. The entire content is found
in the paper by O. Klein.' An explicit reference is added to Klein's 1926 paper
[K3]. I fail to understand why he published his two notes in the first place.
Einstein then remained silent on the subject of five dimensions until 1931, when
he and Walther Mayer (see Chapter 29) presented a new formalism 'which is
psychologically connected with the known theory of Kaluza but in which an exten-
sion of the physical continuum to five dimensions is avoided' [E24]. He wrote
enthusiastically to Ehrenfest that this theory 'in my opinion definitively solves the
problem in the macroscopic domain' [E25] (for the last four words read: excluding
