DOC.
9
FORMAL FOUNDATION
OF
RELATIVITY
65
ZbpuvBuv(e)=p(e)dxu+2
(60)
{14}
where
Buv(e),
Buv(m),
Bu
are connected to the sixvector of the field by the following
relations

dx~
q;
=a(m)~g~4;t XE
g~1J
ds
(60a)
J1
dx~
dx~
___ ___
(e)
(m)th~1L
There are also no obstacles
to
carry out an energymomentum summation along
the lines of equation (42a); but the previous deliberations show with sufficient clarity
how one has to proceed with the transformation of already known laws of nature into
generalcovariant ones.
D. The
Differential
Laws
of
the
Gravitational
Field
In
the
previous section
we
considered the
coefficients guv
as
given functions of the
xv.
And these coefficients are to be understood
as
the components of the gravitational
potential. It remains to fmd the differential laws that are satisfied by these quantities.
The epistemological satisfaction of
the
theory that has been developed up to here can
be seen in the fact that this theory complies with the principle of relativity in the
broadest meaning of the word. Seen under
a
formal aspect, this is based upon the
feature that the equation systems are general, i.e., covanant under arbitrary
substitutions
of
the xv.
The demand that the differential laws of
the
guv
must also be generalcovariant
appears therefore appropriate. However, we want
to
show that we have to restrict this
demand if
we
want to satisfy the law of cause and effect. In fact, we shall prove that
the laws that characterize the course of events in
a
gravitational field can impossibly
be covariant in
all
generality.
S12.
Proof
of
a
Necessary Restriction
in
the Choice
of
Coordinates
[p.
1067]
[34]
We consider
a
finite part
E
of the continuum where some material process does not