108
DOC. 22 ADDENDUM TO DOC.
21
[p.
799]
[p. 800]
Doc. 22
On the General
Theory
of
Relativity
(Addendum)
by
A. Einstein
In
a
recent
investigation1
I have shown how
Riemann’s
theory
of
covariants
in
multidimensional manifolds
can
be utilized
as a
basis for
a theory
of
the
gravitational
field. I
now
want to show here that
an even more
concise and
logical
structure of the
theory can
be achieved
by introducing an admittedly
bold additional
hypothesis on
the
structure
of
matter.
The
hypothesis
whose
justification we
want
to
consider relates to the
following
topic.
The
energy
tensor
of
"matter"
Tyu
has
a
scalar
^
Tff,
whose
vanishing
for
the
electromagnetic
field is well known. In
contrast,
it
seems
to
differ from
zero
for
matter
proper.
Because,
if
we
consider the
most
simple special
case,
that
of
an
"incoherent" continuous fluid
(with pressure
neglected),
then
we are
used to
writing
.-
dx" dxv
T•"
=
\f~gPo~7^
~7~",ds
ds
and
we
have
£
K
=
£sMVr-
=
Po^-
n
Iiv.
The scalar
of
the
energy
tensor
does
not
vanish in this
approach.
One
now
has to remember that
by our knowledge
"matter" is not to be
perceived
as
something primitively given or physically plain.
There
even
are
those,
and
not
just
a
few,
who
hope
to
reduce
matter
to
purely electrodynamic processes,
which
of
course
would have to be done
in
a
theory more completed
than
Maxwell’s
electrodynamics.
Now
let
us just assume
that
in such
completed electrodynamics
the
scalar
of
the
energy
tensor also would vanish! Would the
result,
shown
above, prove
that matter cannot be constructed in this
theory?
I
think I
can answer
this
question
in the
negative,
because it
might very
well be that in
"matter,"
to which the
previous
expression relates, gravitational
fields
do
form
an
important
constituent.
In
that
case,
^
TMM
can appear positive
for the entire structure while in
reality only
£
(Tj¡
+
t¡f)
is
positive
and
]jT
T£
vanishes
everywhere.
In the
following we assume
the
conditions
^7Tmm
=
0
really to
be
generally true.
1These
Sitzungsberichte, p.
778.