DOC.
153
MAY 1909
113
groups,
such
that those
belonging
to
one
and the
same
group
are firmly
coupled together
and
thus
count
only
as one
degree
of freedom.
Similarly,
one can assume
(in
the
theory
of
specific
heats)
that the
two atoms
of
an
oxygen
molecule,
for
example, are
coupled
very
firmly
to
each other
to form into
a
rotating
body.
Of
course,
with this
train of
thought,
and
maintaining
the
principle
of
equipartition
of
energy,
one can
obtain
any
radiation formula that
one might
desire,
as long
as one
chooses
the
bounds of
the above
groups
in
an
appropriate
way.
But
I
was
far
from successful in
my
attempt
to
develop
this
idea
in
a way
that
is
at
least somewhat
plausible.
It
would be
good
if
something
could be
done
in this
way so
that
one
would
not
have
to
change anything
in Maxwell's
equations
if
one
used the
assumption
of the
above
couplings.
It
seems
to
me
that
it
is
also not
wrong
in
principle
if,
in
order
to arrive at the correct
radiation
formula,
one
were
to
draw the
bounds
of the
groups
more narrowly,
the
larger
the
ether-filled
volume
and the
greater
the
energy
density. Similarly, one can
well
imagine
that
the
freedom
of
motion of the ether increases
with
the increase of
the volume
that
it
occupies,
and
that
the
existing
bonds
or couplings
dissolve when the motions increase.
This last
consideration
shows
that the
conception
of
these
couplings
is
basically
not
so very
different
from the
hypothesis
of
energy
elements.
Suppose
there
are
two
degrees
of
freedom,
A
and
B,
that
are
at first
firmly coupled
with
each
other. Then
they
count
as
only
one
degree
of freedom, and thus receive the amount
of
energy
e
that
accrues
to
each such
degree
of freedom
according
to
the
equipartition
principle.
One
can now
imagine
that
the
coupling
between
A and B will be dissolved
as soon
as, owing
to
an
increase in
the
temperature,
the
quantity
e
reaches
a
certain
value
e0.
Then
A
and
B
together
receive
2e0,
and
this,
in
effect,
amounts
more or
less to
the
same as
B
having
received
either
nothing
at all
or
e0.
One
can
also
try
to
change
the
fundamental
equations
for
the
ether in
an
appropriate
manner,
as
you
have discussed.
What
I
have
tried
to do in this
direction
has
had
a very
unsatisfactory result;
as soon as one
makes
even
the
slightest change
in
Maxwell's
equations,
one
is
faced,
I
believe,
with the
greatest
difficulties.
It
is
true
that
I
wanted
to keep
the
equations
linear.
Perhaps
one
could achieve
more
if
one
gave up
this
requirement.
Is
that
your
opinion
too? To
be
sure,
one
would
then
have
to
assume
that
in all
experiments
in which
propagation
velocities
(refractive
indices) were
measured
or
the
principle
of
superposition
was
confirmed,
the
intensity
of the
light
was so
small
that
the second-order
terms
did
not
come
into
consideration.
The
assumption
of
higher-order
terms has
some
similarities with the
assumption
of
couplings
that
dissolve
as
the
motion
intensifies,
in
that
in
both
cases
the
way
in which
the
phenomena
evolve
is
made
dependent
on
the
intensity.
I cannot
declare
myself
in
agreement
with
your
opinion
that
h is
probably
related
to
e
(the charge
of
the
electron);[15]
in
any case,
I
have
great
doubts.
For
the
three
missing
decimals
are no
small matter;
I
can
imagine
that 4v
or
something
on
that order
comes
in
as
a
factor,
but
900
seems
much too much.
I
also find
it
unsatisfactory
for
a