DOC.
21
MOLECULAR MOTION IN
SOLIDS
369
when
c
denotes the
velocity
of
light
in
vacuum,
v0
the
proper frequency
of the
oscillator,
and
u0
the radiation
density
for the
frequency
v0.
[6]
Let the oscillator considered
be
an
ion bound
to
an equilibrium position
by
quasi-elastic
forces.
Suppose
the radiation
space
also
contains
gas
molecules,
which
are
in statistical
(thermal) equilibrium
with
the
radiation,
and
which
may experience
collisions
with
the
ion
constituting our
oscillator. On
the
average,
no
energy
may
be
transferred
to
the
oscillator
through
these
collisions; for, otherwise,
the oscillator
would
disturb the
thermodynamic
equilibrium
between the
gas
and the
radiation.
Hence
one
must conclude
that the
mean energy
that the
gas
molecules alone
would
impart
to
our
oscillator
is
exactly
equal
to
the
mean energy imparted
to
the oscillator
by
the radiation
alone,
which
is to
say
that it
is equal
to E.
Further,
since it
is,
in
principle,
irrelevant for the
[7]
molecular
collisions
whether the
structure in
question
carries
an
electric
charge
or
not,
the
above
relation
holds
for
every
structure
that
oscillates
approximately
monochromati-
cally.
Its
mean
energy is
related
to
the
mean density u
of the radiation of
the
same
frequency
at
the
temperature
considered.
Hence,
if
one
conceives
of
the atoms
of
solids
as
nearly monochromatically
oscillating
structures,
then
one
obtains
directly
from
the
radiation formula the formula for
specific
heat, whose value should be
N(dE/dT) per
gram-molecule.
We
see
that
this
argument,
the result of
which, as we know,
does not
agree
with
the
results of
statistical
mechanics,
is
independent
of the
quantum
theory,
as
well
as
of
any
particular theory
of radiation
whatsoever.
It
is
based
solely on
1.
the
empirically
established
law
of
radiation,
2.
Planck's
analysis
of
resonators,
which
is based,
in
turn,
on
Maxwell's
electrody-
namics
and
mechanics,
3.
the
assumption
that atomic
oscillations
are
sinusoidal to
a
great degree
of
accuracy.
Regarding
(2),
it
should be
expressly
noted that the
oscillation
equation
for
the
oscillator
employed
by
Planck cannot
be derived
rigorously
without mechanics.
For
when
solving
problems
of
motion,
electrodynamics
makes
use
of the
assumption
that the
sum
of the
electrodynamic
and other
forces
acting
on
the framework of
an
electron
is
always
zero,
or-if
one
ascribes
a
ponderable
mass
to
the structure-that the
sum
of the
electrodynamic
and
other
forces
equals
the
mass
times
the
acceleration.
Thus, one
has
a
priori
a
good reason
to
doubt the
correctness
of the result of
Planck's
analysis, seeing
that
the
application
of the fundamental
postulates
of
our
mechanics to
rapid periodical
processes
leads to
results that
are
in conflict with
experience,4
and
that, therefore,
the
application
of these fundamental
postulates
must
raise doubts here
too. Nevertheless,
4
That
is
to
say
that
our
mechanics
is not
able to
explain
the
small
specific
heats of
solids
at
very
low
temperatures.