DOC.
25
FOUNDATIONS OF GENERAL THEORY 287
because
Mie
uses only
the covariance-theoretical
demands
of the
customary theory
of
relativity as a
heuristic
tool,
which is
to
say
that he introduces the
a
priori
privileged
reference
systems.
Viewed in
that
way,
the
theory
advocated
by
me
has
[17]
really very
little
right
to exist!
But
I hope
that with the
help
of
the
arguments
presented
here I
have
suceeded
in
clarifying
my way
of
conceiving things.
11.
Finally,
I return
once
again
to
the law of the
identity
of
inertial and
gravitational
mass
and
to
the connection between
mass
and
energy. [18]
The
momentum
of
a
material
point
(taken
with
a negative sign)
forms
together
with its
energy
a
covariant four-vector with the
components
mE
g0,1,
dxv
as
Likewise,4
the
momentum
with
a
negative sign, together
with the
energy
of
a
complete physical system,
forms the covariant four-vector
f
($04 + to4)dV.
From this it follows
at
once
that the inertial
properties
of
a
closed
system
are
the
same as
those of
a
material
point,
and that the
system
(as a
whole)
can
be thus
replaced by
a
material
point.
In
order
to
represent
the total
mass
of
the
closed
system
in
a
simple
manner,
we
build the
components
of these
two
four-vectors for the
case
when the reference
system
is
chosen in
such
a
way
that the material
point
is
at rest
relative
to
it and that the values of the
guv
at
infinity
are
the
same as
in the
customary theory
of
relativity.
If
the reference
system
is chosen in this
way,
then the
two
vectors
that
are
to be set
equal
to
each other have the
components
-2
ö cr
ti
V
rixv
mc
ds
S(X"4 +
to4,dF
/(tu
+ tuW
J* I -4-24 ~+"
*24
!'
S
34
+
hi)
J
I S
'
^44
~f" *44
,l
'
From this it is
evident that the
mass
of
the
system
is
equal
to
the total
energy
of
the
system
so
measured,
divided
by
c.
Here
c
is
the
velocity
of
light
in
vacuum
at
infinity
(c
=
y/g44),
which,
by
the
way,
can
be taken
to
be
arbitrary,
since
it
depends
on
the
choice
of
the reference
system,
insofar
as
the latter has
not
yet
been fixed in
the
foregoing.
The fact that the
gravitational
mass
of
a
closed
system
is
also,
in the
sense
indicated,
equal
to
the
energy
of
the
system
if the
system
is
stationary
becomes
4This
journal,
15
(1914): 108.
[19]