320 DOC. 42 SPECIAL AND GENERAL RELATIVITY
Inertial
and
Gravitational Mass
77
Even
though
it
is
being
accelerated with
respect
to
the "Ga-
lileian
space"
first
considered,
we
can
nevertheless
regard
the
chest
as
being at rest.
We have thus
good grounds
for
extend-
ing
the
principle
of
relativity
to
include
bodies
of reference
which
are
accelerated with
respect to
each
other,
and
as a
result
we
have
gained
a
powerful argument
for
a
generalised
postulate
of
relativity.
We
must note carefully
that the
possibility
of this mode of
interpretation
rests
on
the fundamental
property
of the
grav-
itational
field
of
giving
all
bodies the
same
acceleration,
or,
what
comes
to
the
same
thing,
on
the
law
of the
equality
of
inertial and
gravitational mass.
If
this
natural
law
did
not exist,
the
man
in
the
accelerated
chest would
not
be able
to
inter-
pret
the behaviour
of
the bodies around
him
on
the
supposi-
tion of
a
gravitational field,
and he would
not
be
justified
on
the
grounds
of
experience
in
supposing
his
reference-body to
be
"at
rest."
Suppose
that the
man
in
the chest
fixes
a
rope
to
the inner
side of the
lid,
and that he attaches
a
body to
the free end
of
the
rope.
The
result of this
will
be
to
stretch the
rope
so
that
it
will
hang "vertically"
downwards.
If
we
ask for
an
opinion
of the
cause
of tension
in
the
rope,
the
man
in
the chest
will
say:
"The
suspended body experiences
a
downward
force
in
the
gravitational field,
and this
is
neutralised
by
the tension of
the
rope;
what determines the
magnitude
of the tension of the
rope
is
the
gravitational
mass
of the
suspended body."
On the
other
hand,
an
observer who
is poised freely
in
space
will
interpret
the condition of
things
thus:
"The
rope must per-
force
take
part
in
the accelerated motion of the
chest,
and it