DOC.
16
FOUNDATIONS OF GRAVITATION
193
of terrestrial
light
sources,
namely,
a
shift of about
two
millionths
of
the
wavelength.
A
further
consequence
of
this
equivalence
hypothesis
is the
bending
of
light rays
in
[4]
a
gravitational field,
which amounts to 0.84 seconds
of
arc
for
a light ray passing
near
the
sun
and is thus
not
inaccessible
to
experimental
test.
This
bending
of
light
[5]
rays
implies
that
the
velocity
of
light
is
not constant,
but
depends,
instead,
on
the
location. This forces
us
to
generalize
the
theory
of
space
and
time,
known
as
the
theory
of
relativity,
since the latter
was
based
on
the
assumption
of the
constancy
of
the
velocity
of
light.
According
to
the familiar
theory
of
relativity, an
isolated material
point moves
rectilinearly
and
uniformly according
to
the
equation
8(fds)
=
0,
where
ds2
=
-dx2
-
dy2
-
dz2
+
c2dt2,
and
c
denotes the
(constant)
velocity
of
light.
The
equivalence hypothesis permits
the
conclusion that in
a
static
gravitational
field
(of special kind)
a
material
point
moves
according
to
the above
equation,
in which
now, however,
c
is
a
function
of
location
and
is
determined
by
the
gravitational potential.
From this
special
case
of the
gravitational
field,
one can
arrive
at
a general
case by
passing
to
moving
coordinate
systems by
means
of coordinate transformation.2 In this
way
one
recognizes
that the
[6]
only sufficiently
encompassing
invariant-theoretical
generalization
of the
indicated
law
of
motion consists in
assuming
that the "line
element ds" has the form
=
£
Sit***Ak' (i'k
=
1,2,3,4)
ik
where the
gik
are
functions of
x1,
x2,
x3,
and
x4,
while the first three coordinates
characterize the
position,
and
the last
one
the
time,
and the
equation
of
motion
is
again
to
have the form
S(fds)
=
0.
If
one
considers that in
this
view,
instead
of
the
customary
line element
of
the
original theory
of
relativity,
ds2
=
£
dxi2
i
one
has the
more general
2We
postulate
that
we
arrive at
an
equally
justified
description
of
the
process
if
we
refer it to
an appropriately
moving
coordinate
system;
in
that
way we
abide
by
the basic
idea
of
the
theory
of
relativity.
Previous Page Next Page