342 DOC.
71
PRINCETON LECTURES
THE GENERAL
THEORY
inertia and
gravitation
is formally expressed by
the
fact
that the
whole
left-hand
side of
(90)
has
the character
of
a
tensor
(with
respect to any
transformation
of
co-ordinates),
but
the
two terms
taken
separately
do
not
have
tensor
character.
In
analogy
with
Newton’s
equations,
the
first
term
would be
regarded
as
the
expression
for
inertia,
and the
second
as
the
expression
for
the
gravitational
force.
We
must next
attempt
to
find
the laws of
the
gravita-
tional
field.
For
this
purpose,
Poisson’s
equation,
Af =
4rKp
of
the Newtonian
theory must
serve as a
model. This
equation
has
its
foundation
in
the idea that
the
gravita-
tional
field arises from
the
density
p
of
ponderable matter.
It
must
also be
so
in
the
general
theory
of
relativity.
But
our investigations
of the
special
theory
of
relativity
have
shown
that
in
place
of
the
scalar
density
of
matter
we
have
the
tensor
of
energy per
unit
volume.
In the latter
is
included
not only
the
tensor
of the
energy
of
ponderable
matter,
but
also
that
of
the
electromagnetic
energy.
We
have
seen,
indeed,
that
in
a
more
complete
analysis
the
energy tensor
can
be
regarded only
as a provisional
means
of
representing matter.
In
reality,
matter
consists of
electrically charged particles,
and
is to
be
regarded
itself
as a
part,
in
fact,
the
principal part,
of the
electromagnetic
[99]
field.
It
is
only
the circumstance that
we
have
no
suffi-
cient
knowledge
of the
electromagnetic
field of
concentrated
charges
that
compels us, provisionally,
to
leave
undeter-
mined in
presenting
the
theory,
the
true
form of this
tensor.
From
this
point
of view it
is at present appropriate to
introduce
a
tensor
Tuv
of the second
rank
of
as
yet
unknown
structure,
which
provisionally
combines the
energy
density
of
the
electromagnetic
field
and that
of
ponderable
matter;
[82]