DOC.
18
DISCUSSION OF DOC.
16
229
Born:
I
would like
to
address
a
question
to Mr. Einstein, namely,
how fast does
[22]
the effect
of
gravitation propagate according
to
your
theory.
It is not obvious
to
me
that this would
happen
with
the
velocity
of
light;
this
must
be
a
very complicated
relationship.
Einstein: It is
extraordinarily simple
to
write down the
equations
for the
case
where the disturbances
one
places
into the field
are
infinitesimal. In that
case
the
g
differ
only infinitesimally
from those that would be
present
without that
disturbance;
disturbances
propagate
then with the
same
velocity
as light.
Born: But
things are surely very complicated
in the
case
of
great
disturbances?
Einstein:
Yes,
this
is
a
mathematically complicated problem.
In
general,
it
is
difficult
to
find
exact
solutions
of
the
equations,
since the
equations are
not
linear.
Jäger: Einstein should tell
us
how
he
envisions
the execution of the crucial
gas.
A
gas, or perhaps
bettter,
a liquid
under the influence
of
volume
forces, like,
e.g.,
gravity, can
reach
a
state
of
equilibrium only
because
an
equation
of
state holds between
the volume and the
pressure.
Thus,
an equation
of
state is
probably
also
necessary
in
empty space, say
between the
gradients
of
the
velocity
of
light
and certain
stresses
to be fabricated
according
to
Maxwell's
procedure.
For
example,
in the
case
of
centrally symmetric
fields such
a
condition
amounts
to
an equation
of
state
between the
energy density
and stresses in
empty space.
Following
the
analogy
of
Maxwell's
system
for
electrodynamic
stresses,
Mr. M.
Abraham has worked
out
roughly
how
one
must conceive this in
terms
of formulas
(International Congress
of
Mathematicians.
Cambridge. Aug.
1912).
I
have
only one [20]
criticism,
and this takes
us straight
to the heart
of
my question.
For in Abraham's
representation,
the volume forces associated with the field
energy
density
of
a space
free
of
ponderable mass go
to
zero,
and this
may
not
be
if
every
form
of
energy possesses mass
and thus also
gravity,
which claim
Mr. Einstein has made the
centerpiece
of
his
system
of
gravitation.
Has Mr. Einstein
replaced
Abraham's above-mentioned
system
of
stresses
by
another
one,
in which
even
the field
energy density
of
empty space
is
affected
by gravitational
forces that achieve
equilibrium
with
stresses
of
the
Maxwellian kind
by
the latter's
opposing
a
deformation
of
the
field,
e.g., a change
in the
energy density?
In this
way
the field
energy
of
empty space acquires
certain elastic
properties!
Furthermore,
the
gravitational
forces
of
empty space
differ from those
of
matter by
virtue
of
the fact
that,
in the static
case,
the former
always
achieve
equilibrium
with the
quasi-Maxwellian stresses, even
without the aid
of
momentum
or energy
flux,
while the
gravitational
forces
of
discrete bodies reach
equilibrium
without the
production
of
momentum
or
other external forces. From what other
equation
of
state
connecting
the
velocity
of
light
with stresses within matter must this result?
Were Mr.
Einstein to take
a position on
this
question,
it
would
surely provide
welcome
enlightenment
for
many
other
readers
of his
works.
[21]
H.
Reißner.