22 DOC.
5
CONTRIBUTIONS TO
QUANTUM
THEORY
[9]
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1
This
is
Planck's
formula for the
mean energy
of
a
onedimensional
monochromatic
resonator.2
[10]
[p.
823]
The fact that in this
manner
one
arrives
at
Planck's
formula is
noteworthy
in
more
than
one respect.
It
appears,
for
one,
that the
concepts
of
physical
and chemical
change
of
a
molecule lose their
principal
contrast. The
quantumlike change
of
the
physical
state
of
a
molecule
seems
not
to be different in
principle
from the chemical
change.
One
can go
even
further. The laws of
Brownian
movement
have led
to
blurring
the
principal
contrast
between
a
molecule and
an
arbitrarily
extended
physical system;
Debye,
on
the other
hand,
has shown that
arbitrarily
extended
systems can
be described with
great success through quantumtheoretically
different
states.
Even the
quantumlike change
of
state
of
an
extended
system
can
be
understood in
a manner
analogous
to
the chemical
change
of
a
molecule. In this
sense,
equations
1)
and
2) can unhesitatingly
be
applied
to
proper
vibrations
of
arbitrarily
extended
systems.
[12]
Furthermore, imagine
the
component
of
resonator
energy
ea
in the mixture
to
be
separated
from the others. Our derivation is based
upon
the
assumption
that this
is
possible,
in
principle,
without
change
of the resonator
energy.
This
assumption
is
analogous
to the
one
in the
theory
of
chemical
equilibrium,
namely
that
a
chemical
mixture
can
be
separated
into its
simple
constituents without chemical reactions
taking place.
One
can
now imagine changing
the
temperature
of
the isolated
component
while the resonator
energy
ea
stays
constant. How far this is
possible
in
practice depends upon
the "reaction rate" with which the molecules
change
their
e.
The
component
can
be
arbitrarily
cooled without
any
loss of
energy
ea
if
this
rate
is
sufficiently
small. In that
case we
have
a
structure similar
to
a
radioactive
one.
For
a
principal understanding
of the radioactive
phenomena
of
diamagnetism
it
is,
therefore,
not
necessary
to
assume
the existence of
a
zeropoint energy
in the
sense
of
Planck.
It is sufficient to
assume
the existence of
a
quantumlike partitioned
energy
that reaches its thermal
equilibrium sufficiently slowly.
[13]
[11]
2It
has
been
pointed
out to
me
that
Bernoulli
gave
a
similar derivation
of
Planck's
formula
(ZS.
f. Elektrochem.
20, 269, 1941).
But
Bernoulli
based his result
on
two
erroneous
formulas
[4)
and
5)
of
his
paper].