DOC.
9
FORMAL FOUNDATION OF RELATIVITY
129
Published
in
Königlich
Preußische
Akademie der
Wissenschaften (Berlin). Sitzungsberichte
(1914):
1030-1085. Submitted
29
October
1914, published
26
November
1914.
[1]See
Einstein and Grossmann
1913
(Vol.
4.
Doc.
13),
1914b
(Doc.
2),
and
Einstein 1913c
(Vol. 4,
Doc.
17)
for Einstein's work with Marcel Grossmann
on
general
relativity
and later
developments;
see
also
Vol.
4,
the editorial
note,
"Einstein
on
Gravitation and
Relativity:
The
Collaboration with Marcel
Grossmann,"
pp.
294-301,
for
a
historical discussion.
In
a
letter
from
1915
Einstein claimed that Grossmann "did
not
contribute
substantially
to
the results"
("trug
aber materiell nichts
zu
den
Ergebnissen
bei." Einstein
to
Arnold
Sommerfeld,
15
July
1915).
[2]For historical discussions of the
present paper,
see
Norton
1984 and
Cattani and
De
Maria
1989.
[3]See
also Einstein's discussion of
the
physical
and
epistemological
reasons
to
include
non-
linear transformations in Einstein
to
H. A. Lorentz, 23 January 1915.
[4]See
Mach
1897, chap.
2.6.
See
also Einstein 1916c
(Doc.
29),
note
4,
for
more on
the role
that Mach's ideas
played
in
Einstein's
thinking.
[5]This is
a
version of the
equivalence principle,
which
was
first
formulated
by
Einstein
in
1907 (see
Einstein
1907j [Vol. 2,
Doc.
47],
§17).
It had
played
an
important
heuristic role
in
Einstein's search for
a
relativistic
theory
of
gravitation (see
Vol.
4,
the editorial
note,
"Einstein
on
Gravitation and
Relativity:
The Static
Field,"
pp.
122-128,
for
a
discussion).
See
also Ein-
stein
1916p
(Doc. 40)
for further elucidation.
[6]"idt" should be "it."
[7]The
superscripts
a
should
be
subscripts.
[8]See
Ricci and Levi-Civita
1901.
[9]The
derivatives
should
be
partial
derivatives.
[10]"(2)"
should be
"(20)."
[11]Here and
in
the
equation
below the
subscript
"k" should
be
"k."
[12]The
superscript pairs
"tax,"
"Kß,"
"wß,"
and "Ka" should be
subscripts.
[13]"Faß"
should be
"Faß."
[14]"Linse"
should
be
"Linie."
[15]Note
that
equation
numbers
(23), (24), and (23a)
are
used twice
in
this
paper.
[16]See Christoffel
1869,
p.
48.
[17]See
Christoffel 1869,
p.
49.
[18]See
Christoffel 1869,
p.
57.
[19]"a-1"
should be
"al-1."
[20]There
should
be
a
minus
sign
between the
two
derivatives
in
the second
term
in
the
sec-
ond
summation.
[21]In
the
second and
third
terms
on
the
right-hand
side
a
summation
over
x
is
implied,
as
are
summations
over
a
and
x
in
the
following terms.
[22]A
summation
over a
is
implied.
[23]Following
Weyl,
V-tensors
were
later named "tensor densities"
("Tensordichten."
Weyl
1918b).
[24]See,
e.g.,
Laue
1911
for Max Laue's
formulation.
Einstein
had used Laue's
approach
ear-
lier
in
an
unpublished manuscript
on
the
special theory
of
relativity (see Vol.
4,
Doc.
1).
[25]"o
=
1" should be "a
=
2" and vice
versa.
[26]"(42)"
should
be "(42a)."
LIV
[27]In
eq.
(46)
"g"
should be
"g^v."
Earlier,
Einstein
had
denoted the
quantities
gmv as
the
components
of the
gravitational
field
(see
Einstein 1914e
[Vol. 4,
Doc.
25],
p. 177).
[28]"(44)"
should be
"(42a)."
[29]"(44)"
Should
be
"(42a)."
[30]"dx2"
should be
"dx1."
[31]"1
+
p
+
P"
in
this
equation
and in
the
one
below should
be
"1 +
pp0-1
+
P
."\
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