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
selfevident.
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.