110
DOC. 4
THEORY OF STATIC GRAVITATIONAL
FIELD
[10]
(1a)
UP
+
df
=
rot
(c£),
0
=
div§
,
^
=-rot(cg),
p
=
div@.
The
physical meaning
of the
quantities
appearing
in these
equations
is
a
perfectly
determinate
one. x, y, z are
measured
by
measuring
rods laid
along
the
rigid system
K. t
is the time in
system
K
as
measured
by variously
constituted clocks
arranged
at
rest at
the
points
of the
system K;
t is
defined
by
the
stipulation
that the
velocity
of
light
in K shall
not
depend
on
the time
or
the direction. b
is
the
velocity
of
electricity
measured in
terms
of the time
t.
p
is the
density
of
electricity
measured in units
of
the
following
kind:
In
a
nonaccelerated
system
two
such
units
shall
exert
on
each
other the force
1
at
a
distance of
1
cm
between
them,
where force
1
is the force that
imparts
the acceleration
1
to
one
gram
if
one
chooses
as
the unit of time the time
needed
by light
to
travel
1
cm (light
time).
The field
vector
s
has the
following
meaning.
If
one
has
a
spring
balance
graduated
in such
a
way
that it
measures
the
force in the
noncoaccelerated1
system
E, based
on
the
light-time
unit,
and
if
one
affixes the unit of
electricity
to
the
point
of
contact
of
this
spring
balance,
then this
balance
measures
directly
the field
intensity
|s|.
$
is
defined in
an analogous way.
According
to
the
principle
of
equivalence,
the
equations (1a)
are
to
be viewed
as
the fundamental
electromagnetic equations
in
a
static
gravitational
field.
They
are
to
be
viewed
as
exact
insofar
as
they
hold
to
the
same
degree
of
approximation
no
matter
how much the
gravitational potential may vary
with the location. On
the other
hand,
they
could be inexact for the
reason
that the
electromagnetic
field
might
influence the
gravitational
field in such
a
way
that the latter
is
no
longer
a
static field.
Furthermore,
even
in the
cases
in which
they
are
strictly
valid
they
do
not
allow the
calculation of the
influence exerted
by
the
electromagnetic
field
on
the
gravitational
field
(c).
1I
have,
of
course,
in mind that
system
E which
possesses no
relative
velocity
with
respect
to
K
at
the relevant
moment.