340 DOC.
71
PRINCETON LECTURES
THE
GENERAL THEORY
How
are
these
equations
connected with
Newton’s
equations
of
motion?
According to
the
special
theory
of
relativity,
the
guv
as
well
as
the
guv,
have the
values,
with
respect to
an
inertial
system
(with
real time co-ordinate
and suitable
choice
of the
sign
of
ds2),
(91)
-1
0 0 0
0
-1
0 0
0 0
-1
0
0 0 0
1
The
equations
of motion then become
d2xu
ds2
=
0.
We
shall call this
the “first
approximation”
to
the
guv-
field.
In
considering approximations
it
is
often
useful,
as
in the
special
theory
of
relativity, to
use an
imaginary
x4-co-ordinate,
as
then the
guv,
to
the
first
approximation,
assume
the values
(91a)
-1
0 0 0
0
-1
0 0
0 0
-1
0
0 0 0
-1
These values
may
be collected
in
the relation
{2} guv
=
-Svu.
To the second
approximation
we
must
then
put
(92)
guv
=
-S.+y",
where the
yuv
are
to
be
regarded
as
small
of the
first
order.
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