DOC. 16 FOUNDATIONS
OF GRAVITATION
197
Since
only
linear substitutions
are
admissible,
certain
one-, two-,
and
three–
dimensional manifolds
are privileged,
which
may
be
designated as straight
lines,
planes,
and linear
spaces.
[13]
The
theory
sketched here
overcomes
an
epistemological
defect that attaches
not
only
to
the
original theory
of
relativity,
but also
to
Galilean
mechanics,
and that
was
especially
stressed
by
E.
Mach. It
is obvious that
one
cannot
ascribe
an
absolute
[14]
meaning
to the
concept
of acceleration of
a
material
point,
no
more so
than
one can
ascribe it
to the
concept
of
velocity.
Acceleration
can
only
be defined
as
relative
acceleration of
a point
with
respect
to other bodies.
This
circumstance makes
it
seem
senseless
to
simply
ascribe to
a
body
a
resistance
to
an
acceleration
(inertial
resistance
of
the
body
in the
sense
of classical
mechanics);
instead,
it will have
to
be
demanded that the
occurrence
of
an
inertial resistance be linked
to
the relative
acceleration
of
the
body
under consideration with
respect
to
other bodies.
It
must be
demanded
that the inertial resistance
of
a
body
could be increased
by having
unaccelerated inertial
masses
arranged
in
its
vicinity;
and this increase
of
the inertial
resistance
must
disappear again
if these
masses
accelerate
along
with the
body.
It
turns
out
that
this behavior of inertial
resistance,
which
we
may
call
relativity
of
inertia, actually
follows from
equations (5).
This circumstance constitutes
one
of the
[15]
strongest pillars
of the
theory
sketched.