314 DOC.
31
ON THE RELATIVITY PROBLEM
=
E
/XV
which
is
an
invariant, i.e.,
a
quantity independent
of the choice of the reference
system
(i.e.,
of the choice of the four
space-time
coordinates).
The
quantities
guv are
functions
of
x1
..
x4
and
serve
to
represent
the
gravitational
field.
With the
help
of
the
absolute differential
calculus,
which
was
developed by
Ricci
[23]
and Levi-Civita
on
the basis of Christoffel's mathematical
investigations,
it
is
possible,
based
on
the existence of the above
invariant, to
replace
the familiar
systems
of
equations
of theoretical
physics by
such
equivalent systems (in
the
case
of
constancy
of all of the
guv)
that hold
totally independently
of the choice of the
space-time
coordinates
xv.
All such
systems
of
equations
contain the
quantities guv,
i.e.,
the
quantities
that determine the
gravitational
field. The latter therefore have
an
influence
on
all
physical processes.
Conversely,
the
physical processes
must
also determine the
gravitational field,
i.e.,
the
quantities guv.
One arrives
at
the differential
equations
that determine these
[24] quantities by means
of the
hypothesis
that the
momentum and
energy
conservation
[25]
laws
must
hold for the material
processes
and the
gravitational
field taken
together.
[26]
This
hypothesis
also
restricts,
after the
fact,
the choice of the
space-time
variables
x,
[27]
without, however,
arousing again
the
epistemological
doubts
analyzed
earlier.
Because
according
to
this
generalized
theory
of
relativity,
physical properties peculiar
to
privileged spaces
no
longer
exist.
The
course
of all
processes
is
governed by
the
quantities guv,
which
are
in
turn
determined
by
the
physical happenings
in
all
of the
rest
of the universe.
The
principle
of the inertia and the
gravitation
of
energy
is
completely
satisfied
in this
theory.
Further,
the laws of motion of
gravitational
masses are
such that
it is
not
absolute acceleration
(acceleration
with
respect
to
"space")
that
appears
as
that
which
is
decisive for the
occurrence
of inertial
resistance,
but
instead-as
must
be
demanded
on
the basis of
the
above
considerations-acceleration
with
respect
to other
[28]
bodies.
The
theory
of
relativity
in the broader
sense
does
not
signify
the abandonment
of the earlier
theory
of
relativity,
but rather
a
further
development
of the latter that
seems
to
me
necessary
for the
epistemological
reasons I
pointed
out.
Zurich, Polytechnic.
A.
Einstein