DOC.
3
STATICS OF GRAVITATIONAL FIELD
95
Doc.
3
The
Speed
of
Light
and the Statics of the Gravitational Field
by
A.
Einstein
[Annalen
der
Physik
38
(1912):
355-69]
In
a
paper
that
appeared
last
year,1
I
drew from the
hypothesis
that the
gravitational
field and the
state
of acceleration of the coordinate
system
are
physically equivalent
a
few
conclusions that tie in
very
well with the results of the
theory
of
relativity
(theory
of
relativity
of uniform
motion).
But
at
the
same
time it turned
out
that
one
of the basic
principles
of that
theory, namely,
the
principle
of the
constancy
of
the
velocity
of
light,
is
valid
only
for
space-time regions
of
constant
gravitational
potential.
Even
though
this result rules
out
the universal
applicability
of the Lorentz
transformation, it
should
not
frighten
us away
from the further
pursuit
of the
path we
have
taken; at
the
very
least the
hypothesis
that the "acceleration field" is
a
special
case
of
the
gravitational
field
has,
in
my opinion,
such
a
high degree
of
probability,
especially
in view of the conclusions
regarding
the
gravitational mass
of the
energy
content,
already
drawn
in
the first
paper,
that
a more
exact
consideration of the
conclusions of the above
equivalence
hypothesis
seems
indicated.
[3]
Since
then,
Abraham has
proposed
a
theory
of
gravitation2
that contains the
conclusions drawn in
my
first
paper
as
special
cases.
However,
we
shall
see
in what
follows that Abraham's
system
of
equations cannot
be reconciled with the
equiva-
lence
hypothesis,
and that his
conception
of time and
space
does
not
hold
up even
from
a purely
formal,
mathematical
point
of view.
§1. Space
and
Time in the
Acceleration Field
Let the reference
system
K
(coordinates
x,
y,
z)
be in
a
state
of
uniform acceleration
in the direction of
its
x-coordinate. Let this
acceleration
be
uniform in Born's
sense,
i.e.,
the
acceleration
of
its
origin,
referred
to
a
nonaccelerated
system
with
respect
to
which
the
points
of K
possess
no
velocity
or
infinitely
small
velocity,
shall
be
a
constant
quantity.
According
to
the
eqivalence hypothesis,
such
a
system
K
is
strictly
[4]
1A. Einstein, Ann. d.
Phys.
35
(1911): 35.
2M.
Abraham, Phys.
Zeitschr.
13
(1912).
[1]
[2]