DOC.
17
PROBLEM OF
GRAVITATION 219
d_
x 1
..
dx
(1c')
m
dt
gs44 -
9*
2
^44
"
92
£9.
On
the
Relativity
of
Inertia
It
follows from
(1c')
that the
momentum
I and the
energy
E of
a mass
point moving
slowly
in the Newtonian
gravitational
field is
given by
the
equations
and
/.
n"dv
t
w ^
n~dv
1
E
=
mc 1
-
etc.
(12)
Thus,
even
though,
as
the first
term
of
the
expression
for E
shows,
the
energy
of
a mass
point
at rest
decreases with the
cumulation
of
masses
in
its
vicinity,
the
same
cumulation effects
an
increase in the inertia of the
mass
point
in
question.
This result
is
of
great
theoretical
interest. Because
if
the inertia of
a
body
can
increase due
to
cumulation of
masses
in
its
vicinity,
then
we
have
no
choice but
to
view the inertia
of
a point
as
being
caused
by
the existence of the other
masses. Thus,
inertia
appears
to
be caused
by a
sort of interaction between the
mass
point
to
be accelerated and all
of the other
mass
points.
This result
seems
quite
satisfactory
if
one
considers the
following.
It does
not
make
sense
to
speak
of the
motion,
and hence also of the
acceleration,
of
a
body
A
by
itself.
One
can
only speak
of the motion
or
acceleration
of
a
body A
relative
to
other bodies
B, C,
etc. Whatever holds
true
kinematically
for acceleration would also
have
to hold
true
for the inertial resistance with which bodies
oppose
acceleration;
it
is to
be
expected a priori,
even
if
not
exactly
necessarily,14
that inertial resistance
is
nothing
else
but
a
resistance of the considered
body A
to relative acceleration with
respect
to
the
totality
of all of the other
bodies
B,
C,
etc.
It is well known that this
standpoint
was
first defended with
perfect rigor
and
lucidity by
E.
Mach in his
history
of
mechanics,
so
that
I
can
simply
refer
to
his
arguments
here. Let
me
also
make
14One
usually dodges
the
consequences
of
such
arguments by introducing
reference
systems
with
respect
to which
freely moving mass points carry
out
a
rectilinear uniform
motion
(inertial
systems).
What is
unsatisfactory
is
that it remains
unexplained
how the
inertial
systems can
be
privileged
with
respect
to
other
systems.
[56]
[57]