416
DOC.
42
SPECIAL AND GENERAL RELATIVITY
Relativity
and
the Problem of
Space
177
Thus
Descartes
was
not
so
far
from
the truth
when he
believed he
must
exclude the existence
of
an
empty space.
The
notion indeed
appears
absurd,
as long
as
physical
reality
is
seen
exclusively
in
ponderable
bodies.
It
requires
the
idea
of
the
field
as
the
representative
of
reality,
in combination
with the
general principle
of
relativity,
to
show the
true
kernel
of Descartes'
idea;
there
exists
no
space
"empty
of field."
Generalised
Theory
of
Gravitation
The
theory
of
the
pure
gravitational
field
on
the
basis
of
the
general theory
of
relativity
is
therefore
readily
obtainable,
be-
cause we
may
be confident
that the
"field-free" Minkowski
space
with its metric in
conformity
with
(1) must satisfy
the
general
laws
of
field.
From this
special
case
the
law
of
gravi-
tation
follows
by
a
generalisation
which
is practically
free from
arbitrariness.
The
further
development
of
the
theory
is
not
so
unequivocally
determined
by
the
general principle
of
relativ-
ity;
it has been
attempted
in
various directions
during
the
last
few decades. It
is
common
to
all
these
attempts, to
conceive
physical reality
as a
field,
and
moreover,
one
which
is
a
gen-
eralisation
of
the
gravitational
field,
and in which the field
law
is
a
generalisation
of
the
law for
the
pure gravitational
field.
After
long probing
I
believe
that
I
have
now
found1
the
most
1
The
generalisation
can
be characterised
in
the
following way.
In accordance with its derivation
from
empty
"Minkowski
space,"
the
pure gravitational
field
of the functions
gik
has the
property
of
symmetry given by
gik = gki (g12 =
g21,
etc.).
The
generalised field
is
of
the
same
kind, but
without this
property
of
symmetry.
The
derivation
of
the
field
law
is completely analogous
to
that
of the
special case
of
pure gravitation.