108
DOC. 153 MAY 1909
One
could
argue
that the
conclusions
referring
to
black
radiation
in
the ether remain
valid
no
matter
how small
the material
mass
of
electrons, and
that
they
can
therefore
probably
also
be
applied
to
the
limiting
case
where
this
mass
is
zero.
However,
this
involves
a
rather
objectionable
passage
to
the
limit.
For that
reason
I
have
taken
up
the
question
again,
and
even
when
taking
into account the circumstance
pointed
out
by van
der
Waals,
I
succeeded
in
arriving
at
a
Gibbsian
ensemble
and at
my
earlier
conclusions
(Jeans's formula)
once
I
assumed that
it
is
permissible
to
neglect
the
terms with
q22,
q2q2[7]
and
q2q3
(in
this
case
the
above
equations serve
for
the determination of
the
coordinates
q2,
expressed
in
terms
of the
q1
and the
q3).
This
is
permitted
if
the
amplitude
of the
oscillations
of
the
electrons
(or
the radius of
curvature
of the
curved
parts
of their
trajectories) is
very
small
compared
with
the
wavelengths
under
consideration.
Thus,
basically
I
introduce
the
same
simplifying
assumption
that
is
often
used
to keep
the
equations
linear. To
be
sure,
the motions of
electrons
may
indeed
show
small
deviations
from
the formulas obtained
in this
way,
but,
when all
is
said
and
done,
one can
state
that
a
direct
and
simple
derivation of
the
radiation formulas
from the
electron
theory
in its
customary
form
is
very unlikely.
The
small
deviations
(related
to
the
magnitudes
of
second
order
with
respect to
the
q),
which
were
just
mentioned,
could
modify
a
radiation formula
a
little,
but
one can hardly expect
that
they
would
bring
about
a
complete change
in
the
form of the
formula
(from
Jeans's
to Planck's). Thus, just
like
you,[8]
I
come
to
the
conclusion
again
that
we
must resort to
considerations of the
kind
used
by
Planck.
For the
most
part,
I
completely
agree
with
your
discourse
on
this
matter
in
your
last
article,[9]
as,
for
example,
with
your
calculation
of the deviations
from the
mean
values
(most probable
values),
be
it
in the
energy
distribution
or
in
the radiation
pressure.
However,
I
would like
to
add
some
further remarks.
I perceive
it
as a
problem
in
Planck's
theory
that
the
state
of
the
radiation
in the
ether
turns out
differently
in it
depending
on
whether
the
energy
exchange
between
ponderable
matter
and
ether
is
mediated
by
"resonators"
or
"free electrons." With the
latter, whose
existence in
metals
can hardly
be
denied,
there
can
be
no
question
of
a
definite
frequency v,
and
thus
an
energy
element hv
also does
not
make
sense.
I
cannot arrive
at
any
conclusion
other than that
black
radiation
must correspond
to
Jeans's
equation
if
the
energy exchange
is
mediated
by
free
electrons. And
so we
would have the
peculiar
result that
if free
electrons
and Planck resonators
were
present
simultaneously,
the ether
would be
placed
into
one
state
by
the
energy
transmitters of
the
one
kind,
and
into
another,
different
state
by
the transmitters of the other
kind. This
does
not
seem very
plausible;
it
would also
contradict the
general thermodynamic law, according
to
which
the
equilibrium
between
two
phases A
and B
is independent
of the
nature
of
a
third
phase
that
we
interpose,
or
also
the notion that
the
expression
for
the
entropy
of
a
system
contains
(apart
from
the
universal
constants
like
the
gas
constant)
only
constants
related
to
the
properties
of the
system. According
to
this
latter
way
of
viewing
the
matter, it
is
unlikely
that
the h
that
appears
in the
entropy
of the ether
would