UNIFIED FIELD THEORY 349could have particle-like solutions. This plan had failed in 1925. It failed again this
time. I summarize the findings.
a) The order of the indices of the F's in Eq. 17.59 is important and was chosen
such that Eq. 17.59 shall remain valid if g^ —» g^ and Fj, —» rJM. Einstein and
Kaufman extended this rule to the nontrivial constraint that all final equations of
the theory shall be invariant under this transposition operation. (R^ is not invar-
iant under transposition; the final equations are. Note that the indices in Eq. 17.26
have been written in such an order that they conform to the choice made by Ein-
stein and his co-workers.)
b) In the symmetric case, Eq. 17.21 is a consequence of Eq. 17.59. This is not
true here.
c) gf, is a reducible representation of the group; the symmetric and antisym-
metric parts do not mix under G 4. Therefore, the unification of gravitation and
electromagnetism is formally arbitrary. Tor this reason, Pauli sticks out his
tongue when I tell him about [the theory]' [E80]. An attempt to overcome this
objection by extending G 4 was not successful.*
d) As in 1925, the variational principle is given by Eq. 17.50. After lengthy
calculations, Einstein and his collaborators found the field equations to bethe first of which is identical with Eq. 17.59, which therefore ceases to be a pos-
tulate and becomes a consequence of the variational principle. The R^ and /?„,
are the respective symmetric and antisymmetric parts of R^.
These are Einstein's final field equations.
In his own words (written in December 1954), 'In my opinion, the theory pre-
sented here is the logically simplest relativistic field theory which is at all possible.
But this does not mean that nature might not obey a more complex field theory'
[E81]. It must be said, however, that, once again, logical simplicity failed not only
to produce something new in physics but also to reproduce something old. Just as
in 1925 (see Eq. 17.51), he could not even derive the electromagnetic field equa-
tions in the weak-field approximation (see [K6], p. 234). It is a puzzle to me why
he did not heed this result of his, obtained thirty years earlier. Indeed, none of
Einstein's attempts to generalize the Riemannian connection ever produced the
free-field Maxwell equations.
In 1949 Einstein wrote a new appendix for the third edition of his The Mean-
ing of'Relativity in which he described his most recent work on unification. It was
"The idea was to demand invariance under FJ, —» FJ, + 6° d\/dx', where X is an arbitrary scalar
function. This forces FJ, to be nonsymmetric and at the same time leaves R,, invariant. However,
the final equation F, = 0 is not invariant under this new transformation.