DOC.
71
PRINCETON LECTURES 339
THE
GENERAL THEORY
OF RELATIVITY
(Continued)
[97]
WE
are now
in
possession
of the
mathematical
apparatus
which
is necessary
to
formulate the
laws
of
the
general
theory
of
relativity.
No
attempt
will be
made
in this
presentation
at systematic
completeness,
but
single
results
and
possibilities
will be
developed
progressively
from
what
is
known and
from
the
results
obtained. Such
a
presenta-
tion
is
most
suited
to
the
present provisional state
of
our
knowledge.
A
material
particle upon
which
no
force
acts moves,
according
to
the
principle
of
inertia,
uniformly
in
a
straight
line.
In the four-dimensional continuum of the
special
theory
of
relativity (with
real time
co-ordinate)
this
is
a
real
straight
line.
The
natural,
that
is,
the
simplest,
generalization
of the
straight
line
which
is meaningful
in
the
system
of
concepts
of
the
general
(Riemannian)
theory
of
invariants
is
that
of
the
straightest,
or
geodesic,
line. We
shall
accordingly
have
to assume,
in the
sense
of the
principle
of
equivalence,
that the motion
of
a
material
particle,
under the action
only
of
inertia and
gravitation, is
described
by
the
equation,
(90)
d2x"
ds2
+
r
M
dX"
dXB
_
r.
In
fact,
this
equation
reduces
to
that
of
a
straight
line if
all
the
components,
Tuav,
of
the
gravitational
field
vanish.
[79]