338
DOC.
30 FOUNDATION OF
GENERAL RELATIVITY
Published
in Annalen
der
Physik
49
(1916):
769-822. Received
20
March
1916, published
11
May
1916. A
manuscript
of
46 pages is
in
the Schwadron Collection
at
the Hebrew
University
of
Jerusalem. There
are no
significant
variations from the
printed
version.
[1]This paper gives
a
full overview of the
final
version of the
general theory
of
relativity
after its latest revisions
as
published
in
Einstein's
papers
of November
1915,
Einstein
1915f,
1915g, 1915h,
and 1915i
(Docs.
21, 22, 24, and
25).
It
was
also
published separately
as
Ein-
stein
1916f. In mid-January 1916
Einstein had still
expressed
doubts about his
ability to
write
such
a
paper,
calling
his
writings
"correct but
quite indigestible" ("zwar richtig
aber reichlich
unverdaulich."
Einstein
to
H. A. Lorentz,
17 January
1916),
but
two
months later
he sent
the
manuscript
of the
paper
to
the editor
of
the Annalen
der
Physik,
Wilhelm
Wien
(see
Einstein
to
Wilhelm
Wien,
18
March
1916).
[2]Although the
term
"special
theory
of
relativity" ("spezielle Relativitätstheorie") already
occurs
in
Einstein
1915f (Doc. 21)
and Einstein
1915i
(Doc.
25),
this
is
Einstein's
first
system-
atic
usage
of
it.
The
term
"special principle
of
relativity" ("spezielles Relativitätsprinzip"),
which
is
used
on p.
770,
appears
here for the first
time.
[3]See
Minkowski
1908. See also, e.g.,
Einstein's
own
exposition
of
special relativity
in
an
unpublished manuscript
from
1912
to
1914 (see Vol.
4,
Doc.
1).
[4]See Vol.
4,
the editorial
note,
"Einstein's Research Notes
on a
Generalized
Theory
of Rel-
ativity," pp. 195-196,
and Reich
1994
for discussions of the mathematical
background
of
gen-
eral
relativity.
[5]See
also Einstein and Grossmann 1913
(Vol. 4,
Doc.
13)
and Einstein 1914o
(Doc.
9)
for
earlier
expositions
of these mathematical tools.
[6]Several months earlier Einstein
expressed
himself somewhat
differently,
claiming
that
Grossmann "did
not
contribute
substantially to
the results"
("trug
aber materiell nichts
zu
den
Ergebnissen
bei." Einstein
to
Arnold
Sommerfeld,
15 July 1915).
See also
Vol.
4,
the editorial
note,
"Einstein
on
Gravitation and
Relativity:
The Collaboration with Marcel
Grossmann,"
pp.
295-296,
for
a
discussion of Marcel Grossmann's
part
in
the
development
of
general relativity.
[7]See
Mach 1897. See also Einstein 1916c
(Doc. 29),
note 4,
for
more on
the role of Mach's
ideas
in
Einstein's
thinking.
[8]This
"equivalence principle"
had
played
an
important
heuristic role
in
Einstein's search
for
a
relativistic
theory
of
gravitation.
It
was
first formulated
in
Einstein
1907j (Vol. 2,
Doc.
47), §17;
see
also
Vol.
4,
the editorial
note,
"Einstein
on
Gravitation and
Relativity:
The Static
Field,"
pp. 122-124,
for
a
discussion.
In
Einstein
1916p
(Doc. 40)
Einstein
gives
a
further elu-
cidation
in
response to
criticism
by
Friedrich
Kottler.
[9]See
Eötvös 1891.
[10]See
Stachel 1980 for
a
discussion of the role that the
problem
of the
rigidly rotating
disk
played
in
the
development
of
general relativity.
[11]This
point
was
first
emphasized by
Einstein
in
his
correspondence
with Paul Ehrenfest
and Michele
Besso
(see
Einstein
to
Paul
Ehrenfest, 26
December
1915,
and
5 January 1916;
and
Einstein
to
Michele
Besso,
3 January
1916).
[12]This
is
the first time Einstein introduces his "summation convention"
in print.
He had
used it earlier
in
his
correspondence
(see
Einstein
to
Paul
Ehrenfest, 24 January
1916).
[13]See
Ricci and Levi-Civita 1901.
[14]"guv"
in
the first
term
on
the
right-hand
side should
be
"guo."
[15]"guv"
in
the first and second
terms
should be "guo"; "xo"
in
the second
term
should
be
"xv"
in
both
cases;
all "y"
in
the second and third
terms
should
be
"s."
[16]"guv"
on the
left-hand side should be
"guv"
[17]"y"
should be
"g."
[18]"gua"
should be
"gua."
[19]"(31)"
should be
"(32)."
[20]"guv"
should be "gta."
[21]In
this line
as
well
as
three lines below
Rpuot
denotes the Riemann-Christoffel
tensor.