396
DOC.
25
SOLVAY
DISCUSSION REMARKS
that
this
one
inference from
mechanics
seems
to
be
right,
whereas thermal conduction
seems
not to
be amenable
to
any
mechanical
interpretation.
Einstein's
third
comment is
a response
to
a
remark
by
Rutherford
on
Nernst's lecture. In it
Rutherford
inquired
about
the
possibility
of
explaining
the
decreasing specific
heats
of
solids for lower
temperatures by
assuming
that
a "polymerization"
takes
place
within the solid. In
a
comment
preceding
Einstein's,
Nernst
excluded this
possibility by arguing
that
chemical transformations
are unlikely
to
take
place
at such
temperatures.
A
proposal
similar
to
Rutherford's
had
been
made earlier
by
Lorentz and discussed
by
Einstein
(see
H. A. Lorentz
to
Einstein,
6
May
1909,
and Einstein
to
H. A.
Lorentz,
23
May
1909).
In
a
footnote
to
the
published
text
of his
discussion
remark,
Einstein added further
arguments against
Rutherford's
proposal:
"The
specific
inductivity
would have
to
approach unity
if the
temperature
decreases
to
absolute
zero. According
to
this
hypothesis,
the
ultraviolet
proper
oscillations should
not,
for
ordinary temperatures,
exert
an
influence
on
the index
of
refraction
or on
the
specific inductivity."
After the
Solvay Congress,
the
polymerization hypothesis was explored
by a
number
of
researchers
(see,
e.g.
Duclaux 1912b and Benedicks
1913),
but
eventually
rejected
for
reasons
such
as
the
ones
mentioned
by
Einstein
in
his comment
(see Verhandlungen 1914, p.371)
No.
171
(Nernst
et al.
1914,
p. 239;
Nernst
et al.
1912,
pp.
296-297)
10)
It
is
absolutely impossible
to
explain
the decrease of
specific
heats
at low
temperatures
by assuming rigid
bonds between the
atoms
(reduction
in
the
degrees
of
freedom).
For
according
to
this
assumption,
solid
bodies
would have
to
lose
their
elastic
deformability as they
approach
absolute
zero
(the
compressibility
would have
to
vanish
for T
=
0),
and the infrared
proper frequencies
would have to
become
less and less
optically
discernible,
neither of
which
is
true.
The first of the
following
two comments
by
Einstein follows
a longer explanation by Kamerlingh Onnes,
while
his second
comment
responds
to
a suggestion
made
by
Lindemann;
both
Kamerlingh
Onnes and Lindemannn
argued
in favor
of Rubens's
interpretation
of the
Nernst-Lindemann formula
(see
the
editorial
note to
Einstein's
comment 8
on
Nernst's
lecture). Kamerlingh
Onnes
agreed
with Rubens
that
the
two
frequencies
appearing
in this formula
correspond to two
different oscillations
of
the
solid
body.
But
whereas Rubens
attempted to
identify
these oscillations
as
those
of the
neutral molecule and
the
electrically charged
atoms,
repectively, Kamerlingh
Onnes
argued
that
in
a
molecular
system longitudinal
and
transverse
oscillations exist
which could have diffeent
frequencies
because
of the
way
in which
spatially
extended
atoms
interact via
parts
of
their
surfaces.
Lindemann,
on
the other
hand,
attempted
to
explain
the existence
of
two different
frequencies by assuming
the
interatomic forces
to
be directed
so
that,
for
example,
oscillations
along
the
diagonal
and oscillations
along one
of
the sides
of
a
cubic lattice would have different
frequencies.
For
a
modern discussion
of the
role of
the
modes
of
oscillation
of
a
lattice, see,
e.g.,
Born and
Huang
1954.
No.
177
(Nernst
et al. 1914,
p.
241;
Nernst
et al. 1912,
p. 291)
11)
The formula of Nernst and Lindemann
undoubtedly represents
a significant
step
forward.
But
we
should
beware,
in
my
opinion,
of
seeing
in it
more
than
an empirical
formula.
It
was
clear
a priori
that
atoms
of
solid
bodies
cannot
behave
thermodynamically
exactly
like
infinitely weakly
damped
radiation
resonators;
in
my opinion,
the
incomplete-
ly
monochromatic character of
atomic oscillations
is
the
reason
why
experience
deviates