DOC.
17
PROBLEM OF GRAVITATION
201
energy.
The
gravitating mass
is
determined
by
its total
energy, including
its
gravitational energy.
Finally, postulate
4
probably
cannot
be
grounded on
experience.
Its
only
justification
lies in
our
confidence in the
simplicity
of
the
laws of
nature,
and
we
may
not
rely
on
its
correctness
with
as
much
right
as
in the
case
of
the
other three axioms.
I
am
well
aware
of the fact that
postulates
2-4
better resemble
a
scientific
declaration
of
faith than
a
firm foundation.
I
am
also far from
claiming
that the
two
generalizations
of
Newton's
theory
to
be described in the
following
are
the
only
ones
possible;
but
I
dare
say
that
at
the
present
state
of
our
knowledge they are
the
most
natural
ones.
§3.
Nordström's
Theory
of
Gravitation
[13]
According
to
the familiar
theory
of
relativity conjoined
with the
theory
of
gravitation,
an
isolated material
point moves
uniformly
in
a straight
line
according
to Hamilton's
equation
«(M
-
0,
(1)
where,
in the usual
manner,
we
have
set
I
9
2 dr
=
sj-dxl
-
dx2
-
dx
dx42 =
\Jc2dt2
-
dx2
-
dy2
-
dz
=
dt\Jc2
Q
Equation
(1) can
also be
written in the form
(2)
8
{|Hdtj =
0,
where
H
=
-m
dr
fc~22
-
=
-mv"
dt -
q
(1a)
is
the
Lagrangian
of the
moving point
and
m
is
a
constant
characteristic of
it,
its
"mass." From
this-as
Planck has
shown-one
obtains
immediately
the momentum
(Ix,
Iy,
Iz)
and the
energy
E of the
point
follow
directly
in the familiar
way.2
[14]
I
- _
x
I
-
-=r-
-
m
* dx
\Jc2
-
q-2
2These
expressions
differ from the
customary
ones
only
by
the
constant factor
1/c.