316 DOC. 71 PRINCETON LECTURES
THE
GENERAL
THEORY
to
the mode
of
thinking
in science
to
conceive of
a
thing
(the space-time continuum)
which
acts itself,
but which
[68]
cannot
be
acted
upon.
This
is
the
reason
why
E.
Mach
was
led to
make the
attempt
to
eliminate
space as an
[69]
active
cause
in
the
system
of mechanics.
According
to
him,
a
material
particle
does
not
move
in
unaccelerated
motion
relatively to
space,
but
relatively to
the
centre
of
all
the other
masses
in
the
universe;
in this
way
the
series
of
causes
of
mechanical
phenomena
was
closed,
in
contrast
to
the mechanics
of
Newton and
Galileo.
In order
to
develop
this
idea within the
limits of the
modern
theory
of
action
through
a
medium,
the
properties
of
the
space-
time continuum which determine inertia
must
be
regarded
as
field
properties
of
space,
analogous to
the
electromagnetic
field.
The
concepts
of classical
mechanics afford
no
way
of
expressing
this. For this
reason
Mach’s
attempt
at
a
solution failed for
the time
being.
We
shall
come
back
to
this
point
of view
later. In
the second
place,
classical
mechanics exhibits
a
deficiency
which
directly
calls for
an
extension
of
the
principle
of
relativity
to
spaces
of
reference which
are
not
in uniform motion
relatively
to
each other. The ratio
of the
masses
of
two
bodies
is
defined
in
mechanics in
two
ways
which differ from each
other
fundamentally;
in
the
first
place,
as
the
reciprocal
ratio
of
the accelerations which the
same
motive
force
imparts to
them
(inert
mass),
and in
the
second
place, as
the ratio
of
the
forces
which
act upon
them
in
the
same
gravitational
field
(gravitational mass).
The
equality
of
these
two
masses,
so
differently
defined,
is
a
fact
which
is
confirmed
by
experiments
of
very
high accuracy
(experi-
ments
of
Eötvös),
and
classical
mechanics
offers
no
explana-
tion for this
equality.
It
is,
however,
clear
that
science
is
fully justified
in
assigning
such
a
numerical
equality only
[56]