DOC.
5
CONTRIBUTIONS TO QUANTUM THEORY
39
Published in
Deutsche
Physikalische Gesellschaft. Verhandlungen 16 (1914):
820-828. Lec-
ture
held
on
24
July 1914.
Published
30 August 1914.
[1]See
Nernst
1906 for the
first formulation of the heat
theorem and
Planck 1912a for
Planck's views
on
it.
[2]On many
earlier occasions Einstein had made extensive and
important
use
of Boltz-
mann's
principle (see, e.g.,
Einstein
1909b,
1909c
[Vol. 2,
Docs.
56 and
60]).
The discussion
in
this
paper
of
an
approach
that avoids its
use
stands
in
striking
contrast.
[3]In discussion remarks
at the
first
Solvay Congress
in 1911
as
well
as
at
the second
one
in
1913,
Einstein had
criticized
Walther Nernst's
thermodynamic proofs
of
his
heat theorem
(see,
respectively,
Nernst
et
al.
1912, p.
302,
or
Nernst
et
al.
1914,
p.
243
[Vol. 3,
Doc.
25,
sec.
VII];
and
Grüneisen
et
al.
1921,
pp.
293-298,
or
Vol.
4,
Doc.
22,
sec.
IV).
In
1912
Einstein
wrote
a
paper
criticizing Nernst,
which
he first
submitted
to
the
Physikalische Zeitschrift
but later
retracted.
See
Einstein
to Ludwig Hopf,
after
20 February 1912
(Vol. 5,
Doc. 364), note 6,
for
more
details and
references
to
Einstein's
contemporary
correspondence on
this topic.
[4]Einstein's
offer
was
taken
up
by
Michael
Polanyi,
which
led
to
an
exchange
of letters
between him
and
Einstein and
a
paper,
Polanyi
1915
(see
Einstein
to
Michael
Polanyi,
13
December
1914,
30
December
1914, 10
February
1915, 8
May
1915, 18
June
1915,
and
6 July
1915;
see
also
Polanyi
1915,
p.
351,
for mention of Einstein's
offer).
[5]The
inclusion of
the
last
term
makes
the
entropy
extensive.
See
also
Doc.
26, note
11,
for
further discussion of this
point.
[6]"Ev"
should
be
"EO."
[7]The plus sign
in the
second
term
on
the
left-hand side should be
a
minus
sign.
[8]This is
actually
a
refinement of Planck's formulation of Nernst's theorem
(see
the
Preface
of Planck
1913).
[9]"Eo"
in the exponential in
the third
expression
should be
"Eö."
[10]This
derivation
was
first
given
by
Einstein in Einstein 1907a.
[11]Bernoulli 1914.
See
also Einstein's earlier
negative
evaluation of Bernoulli's abilities
in
Einstein
to
Fritz
Fichter-Bernoulli,
17
January 1912
(Vol. 5,
Doc.
338),
and Einstein
to
Hein-
rich
Zangger, 20
May
1912
(Vol. 5,
Doc. 398).
Einstein
was
asked
his
opinion
of Bernoulli
in
connection with
the
latter's
candidacy
for
a
chair
at
the
University
of Basel.
His
advice
was
ignored,
and
Bernoulli
was
appointed
Extraordinary
Professor of
Physical Chemistry.
[12]See
Debye
1910,
1912.
[13]In
his revised
quantum
theory
of
1911
Planck
had
introduced
a
zero-point energy
(see
Planck
1911a,
1911b).
The
possible physical
consequences
discussed
by
Planck included the
speculation
that random
"quantum
emission"
might
somehow
account
for
radioactivity
(see
Planck
1911a,
p.
148).
See
also Einstein's
comments
on
the
connection between
diamagnetism
and
the
existence of
a
zero-point energy
in
his
papers
on
Ampere's
molecular
currents
(see,
e.g.,
Einstein and
De
Haas 1915a
[Doc. 13], p. 153); see
also Vol.
4,
the
editorial
note,
"Ein-
stein and Stern
on
Zero-Point
Energy,"
pp.
270-273,
for Einstein's earlier interest
in
zero-
point energy.
[14]"3)"
should
be "1a)."
[15]In
his later
papers
on
the
quantum
theory
of
radiation,
Einstein
1916j
(Doc.
34)
and
Ein-
stein 1916n
(Doc. 38),
Einstein
carefully
allowed for the
possible degeneracy
of
energy states.
[16]See Debye
1912 and
especially
Debye
1910.
James
Jeans,
following
Lord
Rayleigh,
had
treated
the
radiation
in
an
enclosure
as a
physical system to
which
one
could
apply
statistical
mechanics
(see Rayleigh
1900
and
Jeans
1905a, 1905b,
1905c).
[17]"3b)"
should
be
"1b)."
[18]See
Ehrenfest 1913. Although
Ehrenfest
did
not publish
a
general
treatment
of
the
adia-
batic
theorem until
1916 (Ehrenfest
1916),
he
certainly
discussed
the
topic
earlier with Ein-
stein.
In Ehrenfest
1916,
Ehrenfest
even
ascribes the
name
"adiabatic
hypothesis" to
Einstein.
[19]This
conclusion
was
later criticized
by
Ehrenfest. For Einstein's admission three
years
later that
he
was
wrong, and
for
a
modified
argument
to prove
the
general validity
of
equation
4a),
see
Einstein
to
Paul
Ehrenfest,
12
November
1917.