124
EINSTEIN
ON
THE
STATIC
FIELD
In
the letter
to
Wien
accompanying
the
paper,
Einstein
emphasized
that
he
had
full
confidence
in his
theory
and added that
he
was now searching
for the
dynamics
of
gravitation.[12]
Not
very
long
after the submission of
his
paper
Einstein
wrote to
Wien
to
withdraw
it
because he had found inconsistencies
in his
theory,
but later that
same day
he
reversed his decision
and
asked Wien
to
publish the
paper
after
all,
"so that those
who
are
interested
in
the
problem
can see
how
I
have arrived
at
the
formulas."[13] He
did add
a
footnote,
pointing
out
the
error
to the
reader and
announcing a
correction
in
a
future
paper.[14]
In
Einstein 1912d
(Doc. 4),
submitted
on
20 March
1912,
he
explains
in
detail
why
the
gravitational field
equation
of his earlier
paper
cannot be
correct.
He considers
a
set
of
masses
fixed
by a
massless
rigid
frame
and
concludes
from the
field
equation
that the
masses
would
start
to
move,
thus
violating
the
principle
that action
equals
reaction.
As
a consequence
of
this
problem,
Einstein
finds
himself
forced
to
modify
his
original
field
equation, replacing
it
by[15]
cAc

(1/2)
(grad
c)2
=
kc2p.
He
argues
that the additional
term
(1/2
c) (grad c)2
can
be
interpreted
as
the
energy
density
of the
gravitational field,
which itself
acts
as a source
of the
gravitational
potential.
Since
this
equation
does
not,
however,
admit linear solutions
in
the
matter
free
case,
it
implies
that the
principle
of
equivalence
is
valid
only
for
infinitely
small
spatial regions.
Since the
principle
of
equivalence
had been
Einstein's main heuristic
guide,
its
failure for
finite
regions
was
quite puzzling
for
him.[16] He
nevertheless
completed
his
theory
by
showing
how the
equations
of
electrodynamics
and thermo
dynamics
have
to be
modified
in
the
presence
of
a
static
gravitational
field.
Despite
the unresolved
difficulty
that the restriction of the
equivalence principle constituted,
Einstein
was pleased
with his
achievement.[17]
III
Three months
earlier,
in
January 1912,
when
Einstein
was
still
working
on
the
first
version of
his
theory,
Max Abraham had
published
a theory
of
gravitation
which took
[12]See Einstein
to
Wilhelm
Wien,
24
February
1912
(Vol. 5,
Doc.
365).
[13]"damit
diejenigen,
welche sich für das Problem
interessieren, sehen, wie
ich
zu
den
Formeln
gekommen
bin"
(Einstein
to
Wilhelm
Wien,
11
March
1912
[Vol.
5,
Doc.
371]).
[14]See
Einstein 1912c
(Doc.
3),
p.
360.
[15]See
Einstein 1912d
(Doc. 4), p.
456.
[16]See
Einstein 1912h
(Doc.
8), p.
1063;
see
also Einstein
to
Paul
Ehrenfest,
before
20
June
1912
(Vol.
5,
Doc.
409).
For
a
discussion of the role of
the
principle
of
equivalence
in
the
subsequent development,
see
the editorial
note,
"Einstein
on
Gravitation and
Relativity:
The
Collaboration
with Marcel
Grossmann,"
pp.
294295.
[17]See, e.g.,
Einstein
to
Paul
Ehrenfest,
10
March
1912
(Vol.
5,
Doc.
369).
Einstein
gave
a
brief
summary
of his achievements
in
a
letter
to
Michele Besso of 26 March
1912
(Vol.
5,
Doc.
377).