XlVi
INTRODUCTION
TO
VOLUME
8
Einstein’s
challenge triggered
a
correspondence
with Michael
Polányi, starting
in December 1914. In
an
earlier
proof
of
the
heat theorem
Polányi
had tried
to
show
thermodynamically
that
at
absolute
zero
reversible isothermic
changes are
isen-
tropic-an alternative formulation
of
the heat theorem. A
crucial
ingredient
in the
proof
was
the
vanishing
of
the
specific
heat at absolute
zero,
for
which both theo-
retical and
experimental
indications existed.
Polányi’s
proof is
based
on a thought-
experiment,
in which the
temperature
of
a system
is
systematically
lowered
by
a
succession
of
adiabatic
expansions
and isothermal
compressions.
He claims
that
as
one comes
closer
and closer to
absolute
zero,
the isothermal
compressions
would
eventually
become
isentropic.
Einstein directed his
criticism
at this
claim, pointing
out
that the
proof
is
only
valid
if
it takes
infinitely many steps
to
reach absolute
zero.
If,
on
the
contrary, a
finite
number
of
steps
suffices,
the
proof
fails. Einstein
also
gives a counterexample,
worked
out
in various
ways,
to show that
systems
might
exist
for
which isothermal
compressions
at
zero
temperature
would not be
isentropic.
In
response
to Einstein’s fundamental
criticism,
Polányi
tried
to
modify
his
proof,
but at the end he had to
admit
that it had
at
best
a
limited
validity.
Another
correspondent
who
was
concerned with the
validity
of
the
heat theorem
was
Einstein’s
former
collaborator,
Otto Stern. He had also
published a
thermody-
namic
proof
of
the theorem.
From
his
proof
it
followed that the
entropy
of
mixed
crystals
or
solid solutions
vanishes at
absolute
zero,
if
these
systems
have
a
single
microstate with
an
energy
lower than that of
all
others. In
an
exchange
in the
spring
of
1916,
Einstein
stressed
once again
his conviction
that
the heat theorem could
only
be valid
for
single crystals.
The
discussion then
focused
on
the
question
whether
mixed
crystals
could exist at absolute
zero, and,
if
so,
what their
entropy
would be. Both
parties put
forward
clever
and instructive
arguments
and models to
support
them. The debate ends in
a
stalemate,
with
neither of
the
correspondents
prepared
to
give up
his
point
of
view.
These
two
exchanges on
the heat
theorem
are
not
just interesting
because
of
the
importance
of
the
issues involved.
They are
also
typical
in
showing
Einstein’s
con-
cern
with
fundamental
physical questions
and his
talent of
getting
directly
to the
heart
of
the
matter, illustrating
his
arguments
with
simple
but
illuminating
analo-
gies
or
models and
always aiming
at
conceptual
clarification.
VI
Most
of Einstein’s
scientific
activity during
the
years
covered
by
this volume
was
focused
on
the
development
of
the
general
theory
of
relativity.
In the fall
of
1913,
when Einstein
presented
his lecture
on
the
current state
of
the
problem
of
gravita-
tion in
Vienna,[15]
the
early
version
of
his
theory,
the so-called “Entwurf”
theory,[16]