DOC.
25 SOLVAY
DISCUSSION REMARKS
395
quantum hypothesis plausible. According
to
Lorentz, however,
Nernst's
decomposition
of
an elliptic
oscillation
into
three
mutually perpendicular
circular oscillations
is
"artificial" and does
not
correspond
to
a decomposition
of
the
energy
into
three
additive
components.
No.
149
(Nernst
et
al.
1914,
pp.
235-236;
Nernst
et al.
1912,
p.
239)
7)
It
has
been
pointed
out several times
that the
application
of the
quantum
hypothesis
to structures with
more
than
one
degree
of freedom
meets with difficulties
of
a
conceptual
formal
kind,
irrespective
of whether
one
views
the
quanta
as energy
quanta or as
indivisible
elementary regions
of the
q-p-manifold.
If
one
modifies
the
equation
for the
mean
energy
E of
a
three-dimensional
oscillator that
is yielded
by
statistical
mechanics,
E
fE~e~dE
•1 -
_______
1-I
£
fFYe~"dE
by
introducing
sums
instead of
integrals,
which
one
does
by giving
to
E
in
sequence
the
values 0,
hv,
2hv
etc., one
does not
thus arrive
at
three
times
of
the
energy
of
the
linear
Planck oscillator.
Thus,
the
quantum theory
in its current form leads to
contradictions
as soon as one
seeks to
apply
it to structures with several
degrees
of freedom.
In his second
comment,
Einstein
attempted
to
explain
the
temperature
independence
of
what he
interpreted
as
the
damping
of
ionic oscillations within
a crystal, referring to
observations
of
residual
rays
reported
in
the
preceding
comment
by
Rubens. Einstein's
comment is
related
to
an
extended
controversy among
himself,
Rubens,
and Nernst about
the
interpretation
of
the
experiments on
residual
rays performed by
Rubens and his
group.
Nernst in his lecture and Rubens in his
comment
argued
that the
results of these
experiments are
in
conflict with Einstein's
interpretation
of the
Nernst-Lindemann formula for
specific
heats
as
being
the
consequence
of
a strong damping
of
the
elementary
oscillators
constituting
the
solid
body (see
Einstein
1911g
[Doc.
21],
p.
679).
Rubens
argued
that the
results of his
measurements
can
be
interpreted
by assuming
two
proper
frequencies
of
the solid
body, an
interpretation
that
Einstein did
not
accept.
No.
156
(Nernst
et al.
1914, p. 238;
Nernst
et al.
1912,
pp.
295-296)
8)
The
fact
that the
damping
of
optically
discernible ionic
oscillations
is
independent
of the
temperature
had
to
be
expected
based
on
conventional
mechanics.
For
if
one
assumes that,
in
the
solid
state,
atoms
are
bound
to each
other
by
elastic
forces,
then
according
to mechanics
the
equations
of
motion
become linear
homogeneous
differential
equations,
so
that
from
one
solution of the latter
one
obtains
another
one by
merely
multiplying
the
amplitudes
by a
constant,
without
otherwise
having
to
change
the
time
functions.
From
this it follows
that the
degree
to which individual
oscillating
structures
deviate from
monochromatic behavior
does not
depend
on
the
temperature.
-
It
is
odd