98
DOC. 21 GENERAL RELATIVITY
Doc.
21
On
the
General
Theory
of
Relativity
Plenary
Session of November
4,
1915
[p.
778]
My
efforts in
recent
years
were
directed toward
basing
a
general theory
of
relativity,
[1]
also for nonuniform
motion, upon
the
supposition
of
relativity.
I believed indeed
to
have found the
only
law of
gravitation
that
complies
with
a reasonably
formulated
postulate
of
general relativity;
and
I
tried to demonstrate the truth of
precisely
this
solution in
a paper1
that
appeared
last
year
in
the
Sitzungsberichte.
Renewed criticism showed to
me
that this truth is
absolutely impossible
to show
in the
manner suggested.
That this seemed to be the
case
was
based
upon
a
misjudgment.
The
postulate
of relativity-as
far
as
I
demanded it
there-is
always
satisfied
if
the Hamiltonian
principle
is chosen
as a
basis.
But
in
reality,
it
provides
no
tool
to
establish the Hamiltonian function H of the
gravitational
field.
Indeed,
equation (77)
l.c.
which limits the choice of H
says only
that
H
has
to
be
an
invariant
toward linear
transformations,
a
demand that has
nothing
to do with the
relativity
of
accelerations.
Furthermore,
the choice determined
by equation
(78)
l.c. does not
[3]
determine
equation
(77)
in
any
way.
For these
reasons
I
lost trust in the field
equations
I
derived,
looked for
a
way
to
limit the
possibilities
in
a
natural
manner.
In this
pursuit
I
arrived
at
the demand
of
general
covariance,
a
demand from which
I
parted, though
with
a
heavy
heart,
three
years ago
when
I
worked
together
with
my
friend
Grossmann.
As
a
matter
of
fact,
we were
then
quite
close
to
that solution
of
the
problem,
which will
be
given
in the
following.
Just
as
the
special theory
of
relativity
is
based
upon
the
postulate
that all
equations
have
to
be covariant relative
to
linear
orthogonal
transformations,
so
the
[p.
779] theory developed
here
rests
upon
the
postulate
of the covariance
of
all
systems
of
equations
relative
to
transformations
with
the substitution determinant
1.
Nobody
who
really grasped
it
can
escape
from its
charm,
because it
signifies
a
real
triumph
of
the
general
differential calculus
as
founded
by
Gauss, Riemann,
Christoffel,
Ricci,
and
Levi-Civita.
[2]
1"Die formale
Grundlage
der
Relativitätstheorie," Sitzungsberichte
41
(1914), pp.
1066-1077.
Equations
of
this paper
are
quoted
in
the
following