DOC.
42 SPECIAL AND GENERAL RELATIVITY 411
172
Relativity
what
extent
these
doubts
are overcome
by
the
general
the-
ory
of
relativity.
The
Concept
of
Space
in
the
General
Theory
of
Relativity
This
theory
arose
primarily
from
the endeavour
to
under-
stand the
equality
of inertial and
gravitational
mass.
We
start
out
from
an
inertial
system
S1,
whose
space
is,
from
the
physical
point
of
view,
empty.
In other
words,
there exists
in
the
part
of
space contemplated
neither
matter (in
the usual
sense)
nor
a
field
(in
the
sense
of the
special theory
of
relativity).
With ref-
erence
to
S1
let there
be
a
second
system
of reference
S2
in
uniform acceleration.
Then
S2
is
thus
not
an
inertial
system.
With
respect
to
S2
every
test
mass
would
move
with
an
accel-
eration,
which
is independent
of
its
physical
and chemical
na-
ture.
Relative
to
S2,
therefore,
there exists
a
state
which, at
least
to
a
first
approximation, cannot
be
distinguished
from
a
grav-
itational
field.
The
following concept
is
thus
compatible
with
the observable
facts:
S2
is also
equivalent to
an
"inertial
sys-
tem";
but
with
respect
to
S2
a
(homogeneous)
gravitational
field
is
present
(about
the
origin
of which
one
does
not
worry
in
this
connection).
Thus
when the
gravitational
field
is
in-
cluded
in
the framework of the
consideration,
the inertial
sys-
tem
loses
its
objective significance, assuming
that
this
"principle
of
equivalence"
can
be
extended
to any
relative
mo-
tion whatsoever of the
systems
of reference. If
it
is
possible
to
base
a
consistent
theory
on
these fundamental
ideas,
it
will
sat-
isfy
of itself the fact of
the
equality
of inertial and
gravitational
mass,
which
is strongly
confirmed
empirically.