380
DOC.
23
PROPAGATION OF LIGHT
dbc
(fy
d2z
I
=
0,
-LI
-
0,
--
=
-y.
dt2 dt2 dt2
For the accelerated
system
K',
this follows
directly
from Galileo's
principle,
but
for
the
system
K
at rest in
a
homogeneous gravitational field,
this follows
from the
experience
that
all
bodies
undergo
the
same,
constant,
acceleration
in such
a
field. This
experience
of the identical
falling
of
all
bodies
in
the
gravitational
field
is
one
of the
most universal
experiences
that the observation of
nature has
yielded
to
us;
nevertheless, this law has
not
been
granted a place
in
the foundations
of
our
physical
edifice.
But
we
arrive at
a
very satisfactory
interpretation
of the
empirical
law if
we assume
that the
systems
K and K'
are, physically,
perfectly
equivalent, i.e.,
if
we
assume
that
the
system
K could
likewise
be
conceived
as
occurring
in
a
space
free of
a
gravitational
field;
but
in
that
case, we
must
consider K
as uniformly
accelerated.
Given this
conception, one can no more speak
of the
absolute acceleration
of the reference
system
than
one can
speak
of
a system's
absolute
velocity
in
the
ordinary theory
of
relativity.2
With
this
conception,
the
equal
falling
of
all
bodies
in
a
gravitational
field
is
self-evident.
As
long
as we
confine ourselves to
purely
mechanical
processes
within
the
range
of
validity
of
Newton's
mechanics, we can
be
sure
of
the
equivalence
of the
systems
K
and
K'.
However,
for
our
conception
to
acquire deeper
significance,
the
systems
K and K'
must
be
equivalent
with
respect
to all
physical processes,
i.e.,
the natural
laws with
respect
to
K
must coincide
completely
with
those
with
respect
to
K'. If
we
accept
this
assumption, we
obtain
a
principle
that
possesses
great
heuristic
significance,
provided
that
it
is
really
correct.
For
through a
theoretical
analysis
of
processes
taking
place
relative
to
a uniformly
accelerating
reference
system, we
obtain information about the
course
of
processes taking place
in
a
homogeneous
gravitational
field.3
In
what
follows,
I shall
first show
that from the
point
of
view
of the
ordinary theory
of
relativity our hypothesis
has
considerable
probability.
§ 2.
On the Gravitation of
Energy
The
theory
of
relativity
has shown
that the inertial
mass
of
a body
increases
with its
energy content;
if the
energy
increase
is E,
then the increase
in
the inertial
mass
is
E/c2,
where
c
denotes the
velocity
of
light.
But
is
there
also
an
increase
in
gravitational mass
corresponding
to this
increase
in
inertial
mass?
If
not,
then
a body
would fall with
different accelerations
in
the
same gravitational field, depending on
its
energy
content.
[4]
2
Of
course, one
cannot
replace
an arbitrary
gravitational
field
by a
state
of motion of the
system
without
a
gravitational field, just
as one
cannot
transform
to rest all
the
points
of
an arbitrarily
moving
medium
by means
of
a
relativistic
transformation.
3
It
will
be
shown in
a
subsequent
paper
that the
gravitational
field
considered here
is
homoge-
neous only
to first
approximation.