DOC.
30
FOUNDATION
OF GENERAL RELATIVITY 187
or,
in
view of
(56),
+
&
-
o
•
(57)
Comparison
with
(41b)
shows
that with the
choice
of
system
of co-ordinates which
we
have
made,
this
equation
predicates nothing
more or
less
than the
vanishing of
di-
vergence
of
the
material
energy-tensor. Physically,
the
occurrence
of
the
second term
on
the left-hand
side
shows
that
laws
of
conservation
of momentum
and
energy
do not
apply
in
the strict
sense
for matter
alone,
or
else
that
they
apply only
when the
guv
are
constant, i.e.
when the
field
in-
tensities
of gravitation
vanish.
This
second term
is
an ex-
pression
for momentum, and for
energy,
as
transferred
per
unit of
volume
and time from the
gravitational field
to matter.
This
is brought
out still
more
clearly by
re-writing
(57)
in the
sense
of
(41) as
_
- A
aeTa
.
(57a)
The
right
side
expresses
the
energetic
effect
of
the
gravita-
tional
field
on
matter.
Thus the
field
equations
of
gravitation
contain
four
con-
ditions which
govern
the
course
of
material
phenomena.
They
give
the
equations
of
material
phenomena
completely,
if
the latter
is
capable
of being
characterized
by
four
differ-
ential
equations independent
of
one
another.*
D.
Material Phenomena
The mathematical
aids
developed
in
part
B
enable
us
forthwith
to
generalize
the
physical
laws of
matter
(hydro-
dynamics,
Maxwell's
electrodynamics),
as
they
are
formulated
in
the
special
theory
of
relativity,
so
that
they
will fit in
with
the
general
theory
of
relativity.
When this
is
done,
the
general
principle
of
relativity
does not indeed afford
us a
further limitation
of
possibilities;
but it
makes
us
acquainted
with the
influence of
the
gravitational
field
on
all
processes,
*On this
question
cf.
H.
Hilbert,
Nachr. d. K.
Gesellsch.
d.
Wiss.
zu
Gottingen, Math.-phys.
Klasse,
1915,
p.
3.
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