“Perhaps, there exists a covariant 6-vector by
which the appearance of electricity is explained and which springs
lightly from the , not forced into it as an alien
element.” 43
Einstein replied:
“The aim of dealing with gravitation and
electricity on the same footing by reducing both groups of
phenomena to has already caused me many
disappointments. Perhaps, you are luckier in the search. I am
totally convinced that in the end all field quantities will look
alike in essence. But it is easier to suspect something than to
discover it.” 44
(16 November 1917 [320
], Vol. 8A, Doc. 400, p. 557)
In his next letter, Förster gave results of his
calculations with an asymmetric ,
introduced an asymmetric “three-index-symbol” and a possible
generalisation of the Riemannian curvature tensor as well as
tentative Maxwell’s equations and interpretations for the
4-potential
, and special solutions (28 December
1917) ([320
], Volume 8A, Document 420, pp. 581-587). Einstein’s next letter of 17
January 1918 is skeptical:
“Since long, I also was busy by starting from a
non-symmetric ; however, I lost hope to get behind the
secret of unity (gravitation, electromagnetism) in this way.
Various reasons instilled in me strong reservations: [...] your
other remarks are interesting in themselves and new to me.” 45
([320
], Volume 8B, Document 439, pp. 610-611)
Einstein’s remarks concerning his previous efforts must be seen under the aspect of some attempts at formulating a unified field theory of matter by G. Mie [228, 229, 230]46 , J. Ishiwara, and G. Nordström, and in view of the unified field theory of gravitation and electromagnetism proposed by David Hilbert.
“According to a general mathematical theorem,
the electromagnetic equations (generalized Maxwell equations)
appear as a consequence of the gravitational equations, such that
gravitation and electrodynamics are not really different.” 47
(letter of Hilbert to Einstein of 13 November
1915 [100])
The result is contained in (Hilbert 1915, p. 397)48 .
Einstein’s answer to Hilbert on 15 November 1915 shows that he had also been busy along such lines:
“Your investigation is of great interest to me
because I have often tortured my mind in order to bridge the gap
between gravitation and electromagnetism. The hints dropped by you
on your postcards bring me to expect the greatest.” 49
[101]
Even before Förster alias Bach corresponded with
Einstein, a very early bird in the
attempt at unifying gravitation and electromagnetism had published
two papers in 1917, Reichenbächer [269, 268
]. His paper amounts
to a scalar theory of gravitation with field equation
instead of Einstein’s
outside the electrons. The electron is considered as
an extended body in the sense of Lorentz-Poincaré, and described by
a metric joined continuously to the outside metric50
:
“The disturbance, which is generated by the
electrons and which forces us to adopt a coordinate system
different from the usual one, is interpreted as the electromagnetic
six-vector, as is known.” 51
([269], p. 136)
By his “coordinate rotation”, or, as he calls it
in ([268], p. 174),
“electromagnetic rotation”, he tries to geometrize the
electromagnetic field. As Weyl’s remark in Raum-Zeit-Materie ([398
], p. 267,
footnote 30) shows, he did not grasp Reichenbächer’s reasoning; I have
not yet understood it either. Apparently, for Reichenbächer the metric deviation
from Minkowski space is due solely to the electromagnetic field,
whereas gravitation comes in by a single scalar potential connected
to the velocity of light. He claims to obtain the same value for
the perihelion shift of Mercury as Einstein ([268], p. 177). Reichenbächer was slow to fully
accept general relativity; as late as in 1920 he had an exchange
with Einstein on the foundations of
general relativity [270, 71].
After Reichenbächer had submitted his paper to Annalen der Physik and seemingly referred to Einstein,
“Planck was uncertain to which of Einstein’s papers Reichenbächer appealed. He urged that Reichenbächer speak with Einstein and so dissolve their differences. The meeting was amicable. Reichenbächer’s paper appeared in 1917 as the first attempt at a unified field theory in the wake of Einstein’s covariant field equations.” ([261], p. 208)
In this context, we must also keep in mind that
the generalisation of the metric tensor toward asymmetry or complex
values was more or less synchronous with the development of Finsler
geometry [126]. Although
Finsler himself did not apply his geometry to physics it soon
became used in attempts at the unification of gravitation and
electromagnetism [273].