DOC.
4
THEORY
OF
STATIC GRAVITATIONAL
FIELD
163
Published
in
Annalen der
Physik
38
(1912):
443-458. Received
23
March
1912, published
23
May
1912.
[1]See
Einstein 1912c
(Doc. 3).
[2]See Einstein
1907j (Vol. 2,
Doc.
47),
§20.
[3]See
Einstein 1912c
(Doc.
3).
[4]See
Born
1909, §5;
see
also
Einstein 1912c
(Doc.
3),
p.
356.
[5]In
all
earlier versions of Maxwell's
equations (in
vector notation) in
Einstein's
published
writings,
"curl"
is
used instead of "rot."
In
his
manuscript
on
the
special theory
of
relativity
(Doc.
1),
he
changes
notation from "curl"
to
"rot"
on [p.
61].
See
also
[pp.
38-39]
of Einstein's
"Scratch Notebook"
(Vol. 3, Appendix A),
where Maxwell's
equations are
written with
"curl"
as
well
as
"rot."
[6]See
Einstein 1912c
(Doc. 3),
p.
359.
[7]"dt" should
be
"dt."
[8]The
second
term
on
the
right
should have
no
factor
1/c.
[9]The
second
equal
sign
should
be
a
minus
sign.
[10]These
equations appear
in
a
similar
context
on [pp.
38-39]
of Einstein's "Scratch
Notebook"
(Vol.
3,
Appendix A).
[11]Einstein
met
Ehrenfest for the
first
time when the latter visited him
in
Prague
from
23
to
29
February
1912 (see
Einstein
to Paul Ehrenfest, 12
February
1912
[Vol. 5,
Doc.
357],
and
Einstein
to Paul Ehrenfest,
10
March
1912
[Vol. 5,
Doc.
369]).
For
an
account
of
this meeting,
see
Klein,
M.
1970,
pp.
175-179.
[12]See
Einstein 1912c
(Doc. 3),
p.
367.
[13]"v"
should
be
"r."
[14]This
expression
for
the
energy density
as
well
as
the
expressions
below for
the
energy
flux
and for the
x
and
y
components
of the
stresses
are
also written
on [p. 39]
of Einstein's
"Scratch
Notebook"
(Vol. 3,
Appendix
A).
[15]See,
e.g.,
Lorentz
1895,
§12.
[16]See
Einstein 1912c
(Doc. 3), pp.
363-364.
[17]See
Einstein 1911h
(Vol.
3,
Doc.
23).
[18]The
problem
of
(special)
relativistic
thermodynamics
was
first
treated
in
Planck 1907
and
is
also discussed
in
Einstein
1907j
(Vol.
2,
Doc. 47),
§15.
Einstein did
not
publish anything
further
on
this
subject.
[19]See
Einstein 1912c
(Doc.
3),
p.
367,
for the conclusion
that,
according
to
Einstein's
theory
of static
gravitation,
the
energy
of
a
system
should
be
proportional
to
c.
[20]Since Einstein had
already
used
equation
number 4
on
p.
449,
the
numbering
of the
equations
becomes inconsistent
at this
point.
[21]See
Einstein 1912c
(Doc.
3),
p.
360,
for the derivation of
the field
equation
(3a).
In fn.
1
on
the
same
page
Einstein
announces a
detailed discussion of
the problems
connected with
this
equation.
On
[p. 38]
of
the
"Scratch Notebook"
(Vol. 3,
Appendix
A)
the
equation
appears
together
with the remark "untenable"
("unhaltbar").
[22]The
reference
is to
equation
(4) on p.
449.
All
further references
to
equations
(3)
and
(4)
concern
the
equations
on
p.
452
(see also
note 20).
[23]See
Einstein 1912c
(Doc. 3),
p.
364.
[24]The
factor "dc" should be omitted.
[25]See
Einstein 1912c
(Doc. 3),
p.
364.
[26]The
conclusion that
the equivalence principle
can
only be valid in infinitely small fields
puzzled
Einstein for
some time;
he mentioned
it,
for
instance,
in
a
letter
to
Paul Ehrenfest
(Einstein
to
Paul
Ehrenfest,
before
20
June
1912
[Vol.
5,
Doc.
409]).
For
a
historical discussion
of
this
problem,
see
Stachel 1980 and Norton
1985.
[27]This
and the
following equation appear
on [p. 39]
of Einstein's "Scratch Notebook"
(Vol.
3, Appendix A),
under
the
heading
"static
gravitational
field"
("Statisches Schwerefeld").
[28]The
equations
in the
second
line
of
(5) are
written
on
[p.
39]
of Einstein's "Scratch
Notebook"
(Vol.
3,
Appendix A).