DOC.
31
ON
THE RELATIVITY PROBLEM
311
By
contrast,
a
theory
of
gravitation recently put
forward
by
Nordström satisfies
both the
relativity principle
and the
requirement
of the
gravitation
of the
energy
of
closed
systems,
with
one
restriction that will be described below. Abraham's
contrary
assertion in the article he
published
in this
journal
is
not
valid. In
fact,
I
do
not
think
that
a
tenable
argument against
Nordström's
theory
can
be drawn from
experience.
According
to
Nordström's
theory,
the
principle
of the
gravitation
of the
energy
of closed
systems
at rest
holds
as a
statistical
law.
The
gravitational
mass
of
a
closed
system
(at
rest
as a
whole)
is
in
general an oscillating quantity,
the time
average
of
which
is
given by
the total
energy
of the
system. Owing
to
the
oscillatory
character
of
mass,
such
a
system
must
constantly
emit
longitudinal
waves
of
gravitation.
But
the
energy
loss
to
be
expected according
to
the
theory
is
so
small that
it must
be
imperceptible
to
us.
After
studying
Nordström's
theory
more
carefully, everyone
will have
to
admit
that,
as
viewed from
an
empirical standpoint,
this
theory provides
for
an
unobjection-
able
integration
of
gravitation
into the schema of the
theory
of
relativity
(in
the
narrower
sense).
If
I
am
nonetheless
of
the
opinion
that
we
must
not content
ourselves with this
solution,
this has
reasons
of
an epistemological
kind,
which will
be discussed
in
what follows.
II. The
Theory
of
Relativity
in
the Broader
Sense
Classical
mechanics,
as
well
as
the
theory
of
relativity
in the
narrower
sense,
which
has been discussed
briefly
in the
foregoing,
suffer from
an
undeniable fundamental
defect that
is
accessible
to
epistemological arguments.
The
weaknesses
of
our
world
picture
to
be discussed here have
already
been uncovered with
perfect clarity by
E.
Mach
in
his
penetrating investigations
into the foundations of Newtonian
mechanics,
so
that
I
cannot
claim that what
I
am
saying
here
in
this
respect
is
new.
I
shall
explain
the
essential
point
of
the
matter
by
means
of
an
example
that
I
have chosen
to be
quite elementary
so as
to
allow what
is
essential
to
emerge.
Two
masses are
floating
in
the universe far
away
from
all
celestial bodies. Let
these
masses
be close
enough
to
each other
to be able to
exert
a
mutual influence. Let
an
observer follow the motions of both bodies
by
constantly sighting
in
the direction
of the line
connecting
the
two
masses
toward the vault of
the
fixed
stars.
He will
observe that the line of
sight
traces
a
closed line
on
the visible vault of the
fixed
are
involved.
According
to Mie,
the fact that the
equality
of inertial and
gravitational mass
is
maintained in radioactive transformations
can only
be
explained by assumptions
about
the
special nature
of
the
energy
inside the
atom.
[16]
[17]
[18]
[19]
[20]
[15]