342
DOC. 13 GENERALIZED THEORY OF RELATIVITY
[35]For
Einstein's earlier discussion of the effect of
a
static gravitational field
on
electro-
magnetic processes,
see
Einstein 1912d
(Doc. 4),
§§1
and
2.
[36]See note 25 above.
[37]Kottler
1912,
§3. Following
the earlier work of
Minkowski,
Sommerfeld,
and
Laue
on
four-dimensional
electrodynamics,
Kottler
was
the first to
use
the
absolute differential
calculus
of Ricci and Levi-Civita
to express
Maxwell's
equations
in
generalized
coordinates-without,
however,
relating
this
work
to the
problem
of
gravitation.
For
a
later evaluation of
his
own
work,
see
Kottler
1922,
pp.
189-190.
[38]See
also the introduction of these
quantities
in
Einstein's research
notes
on a
generalized
theory
of
relativity (Doc. 10),
[p.
53].
[39]Einstein
discusses covariant
electrodynamics
in his
unpublished manuscript
on
special
relativity
(Doc.
1),
[pp.
55-70];
see
also
[p.
48]
for
Einstein's introduction of the
term
"six–
vector"
("Sechservektor"), following Sommerfeld
1910a,
p.
753. Calculations related
to
the
equations
below
are
found
on
[pp.
53-57]
of Einstein's research
notes
on a
generalized
theory
of
relativity
(Doc. 10).
[40]Equations
similar
to the
following
ones
appear
on [p. 57]
of
Einstein's research
notes on
a
generalized theory
of
relativity
(Doc. 10).
[41]dt
in
the second
term
should
be
dy.
[42]As
is
evident from
subsequent
discussions,
the
following argument against
a
scalar
theory
of
gravitation
was
mainly
directed
against
Nordström's
theory (Nordström 1912). Shortly
after
the
publication
of the
present
paper,
Einstein retracted the
argument (see
Einstein 1913c
[Doc.
17],
p.
1253,
and Einstein 1914d
[Doc. 26], p.
261).
For Nordström's reaction
to
Einstein's
argument,
see
Nordström 1913b,
pp.
544-546. For historical discussions of Nordström's scalar
theory
of
gravitation,
see
Isaksson
1985,
Norton
1992b,
and the
editorial
note,
"Einstein
on
Gravitation and
Relativity:
The Collaboration with Marcel
Grossmann,"
pp.
298-300.
[43]See
Laue
1911a,
p.
74.
Einstein had mentioned
this
scalar earlier
in
his
manuscript
on
special relativity (Doc.
1), [p.
50].
[44]Nordström discussed
the
implications
of the
equality
of inertial and
gravitational
mass
for his scalar
theory
of
gravitation in
Nordström
1913a.
[45]Christoffel
1869.
[46]Ricci
and Levi-Civita
1901.
[47]In
chaps. 5
and 6
of
Ricci
and Levi-Civita
1901
the absolute differential calculus
is
applied
to
various
examples
from
physics,
such
as
dynamics, electrodynamics,
heat
conduction, and
elasticity.
[48]See,
e.g.,
Minkowski
1908, Sommerfeld 1910a, 1910b,
Laue
1911a,
1913.
[49]Kottler
1912.
[50]For
a
discussion of the influence of the
algebraic
tradition
in
the
study
of differential
forms
on
Grossmann's
presentation,
see
Reich
1994,
sec.
4. For
a
history
of
the
later
geometrical
interpretation
of fundamental
concepts
of
general relativity,
see
Reich 1994,
sec.
5.3.
[51]For evidence that the
general
definition of
a
tensor
given
in
the
following
was new
in
the
mathematical literature of
the
time,
see
Budde
1914,
p.
246;
see
also the editorial
note,
"Einstein
on
Gravitation
and
Relativity:
The Collaboration with Marcel
Grossmann,"
p.
296.
[52]See
Ricci and Levi-Civita
1901,
p.
131.
[53]For
this
terminology,
see
Ricci and Levi-Civita
1901,
p.
134.
[54]Minkowski
1908.
[55]Sommerfeld
1910a,
1910b.
[56]Laue 1913.
[57]Christoffel
1869,
p.
57.
Christoffel
did
not,
however,
use
the
terminology
of
tensors and
covariant differentiation
but
referred
only to
the transformation
properties
of differential forms.
See
also Einstein's
manuscript
on
special relativity
(Doc.
1), [p.
53],
and
his research
notes
on
a
generalized theory
of
relativity (Doc. 10),
[p.
15],
for earlier introductions of similar
operations.
[58]See
Ricci and Levi-Civita
1901,
p.
138,
where
they
also
refer
to
the earlier work
by
Christoffel
(Christoffel
1869).