DOC.
28
NORDSTRÖM'S THEORY OF GRAVITATION
293
Doc.
28
Nordström's
Theory
of Gravitation from the Point of View
of the Absolute Differential Calculus
by
A.
Einstein and
A. D.
Fokker
[Annalen
der
Physik
44
(1914):
321-328]
[1]
In all
previous presentations
of
Nordström's
theory
of
gravitation1
Minkowski's
theory
of
covariants
was
the
only
invariant-theoretical tool
employed, i.e.,
all that
was
required
of
the
equations
of the
theory
was
that
they
be covariant with
respect
to
linear
orthogonal space-time
transformations. But when this condition
is
imposed a
priori
on
the
equations
it does
not
restrict the theoretical
possibilities
to
such
an
extent
that
one
could
arrive in
an
unforced
way
at
the fundamental
equations
of
the
theory,
without
recourse
to
special physical assumptions.
We will show in what
follows that it is
possible
to
arrive
at
a
perfectly
complete
and
satisfying representa-
tion
of
the
theory
if-as
had
already
been done in the Einstein-Grossmann
theory-one
uses
the
invariant-theoretical tool
given
to
us
in the absolute differential
calculus. Since
nature does
not
present
us
with reference
systems
to
which
we
could
refer
things,
we
at
first refer the
four-dimensional manifold
to
totally arbitrary
coordinates
(corresponding
to
Gaussian coordinates in the
theory
of
surfaces),
and
[3]
restrict the
choice
of
the
reference
system only
when the
problem being
treated itself
induces
us
to
do
so.
It
turns out
that
one
arrives
at
Nordström's
theory,
rather than
at
the Einstein-
Grossmann
theory,
if
one
makes the
single assumption
that it is
possible
to
choose
privileged
reference
systems
in
such
a
way
that the
principle
of
the
constancy
of
the
velocity
of
light
will be
preserved.
§1.
The Characteristics of
the
Gravitational Field.
The
Influence
of the
Gravitational Field
on
Physical
Processes
[4]
We assume2
that
a point moving
in
a
gravitational
field
obeys
a
law of motion
whose Hamiltonian form
is
1Cf. G.
Nordström,
Ann.
d.
Phys.
42
(1913): 533;
A.
Einstein,
Phys.
Zeitschr. 14
(1913):
1251.
2Cf.
A.
Einstein,
"Entwurf einer
verallgemeinerten
Relativitätstheorie
un
einer Theorie
der Gravitation"
["Outline
of
a
Generalized
Theory
of
Relativity
and
of
a Theory
of
Gravitation"].
Zeitschr.
f.
Math. und
Phys.
62
(1913):
6.
[2]
[5]