DOC.
23
PROPAGATION OF LIGHT
381
The
very
satisfying
result of the
relativity theory,
according
to which
the
principle
of
the
conservation of
mass
merges
into the
principle
of the conservation of
energy,
would not
be
possible
to
maintain,
because the
old
formulation of
the
principle
of
the
conservation
of
mass
would
indeed
have to be
abandoned for the
inertial
mass,
but maintained
for
the
gravitational
mass.
This must
be considered
very unlikely.
On the other
hand,
the
ordinary theory
of
relativity
does
not
provide
us
with
any
argument
from which
we
could
conclude that the
weight
of
a body depends
on
its
energy
content.
But
we
will
show
that the
gravitation
of
energy
is
a
necessary consequence
of
our hypothesis
of the
equivalence
of
the
systems
K and K'.
Consider
two
material
systems
S1
and
S2
which
are
equipped
with
measuring
instruments and situated
on
the
z-axis
of K
at
a
distance
h
from each
other,4
in such
a way
that
the
gravitational
potential
in
S2
is
greater
by
y
.
h
than that
in
S1.
Suppose
that
S2
has sent
off
a
certain
amount
of
energy
E
toward
S1
in
the form of
radiation. Let the
energies
in S1
and
S2
be measured
with sets
of
apparatus
that
are
completely
identical
when
brought
to
the
same
place
in
the
system
z
and
there
compared
with each
other.
Nothing
can
be asserted
a
priori
about the
process
of
this
energy
transfer,
because
we
do not know how
the
gravitational
field influences
the
radiation
and
the
measuring
instruments
in
S1
and
S2.
But in
accordance
with
our assumption
of
equivalence
of K
and
K',
we can
replace
the
system
K,
which
is
situated
in
a
homogeneous
gravitational
field,
by
the
gravitation-free
system
K', which
moves
with
uniform acceleration
in
the direction of
the
positive
z-axis,
and
to
whose z-axis
the material
systems
S1
and
S2
are rigidly
bound.
We
will
evaluate the
process
of
energy
transfer
by
radiation from
S2
to S2 from
a
nonaccelerated
system
K0.
At the
moment when
the radiation
energy
E2
has
been emitted
from
S2
toward
S1,
the
velocity
of K'
with
respect
to
K0
will
be
zero.
The radiation
will arrive at
S1
after
a
time
h/c has
elapsed (to
a
first
approximation).
But
at
that
moment
the
velocity
of
S1
with
respect
to
K0
will be
y
•
h/c
=
v.
Hence,
according
to
the
ordinary theory
of
relativity,
the radiation
arriving
in
S1
will not
possess
the
energy
E2,
but the
greater energy
E1,
which
is
related
to
E2,
to
a
first
approximation,
by
the
equation5
(1)
Fig. 1.
^
=E2
ra
ii
TT
+
V
1
+
t.
9
L
cj
[5]
4
S1
and
S2
are
considered
infinitely
small
compared
with h.
5 A. Einstein, Ann.
d.
Phys.
17
(1905): 913,
914.