400
DOC.
25
SOLVAY DISCUSSION REMARKS
No. 224
(Sommerfeld
et al.
1914, pp.
308-310;
Sommerfeld
et al.
1912, pp.
382-383)
17)
The
objection
touches
upon
a
sensitive
point
of
the
conception. According
to
the
quantum theory
in its
original
formulation,
the
way
it
is applied
in
the consideration
just
presented,
one
would
have
to
imagine
that
always only one
quantum
of
a
specific
frequency
at
a
time
is
emitted
in
a
collision, so
that the result of
our integration
would
be
correct
only as an average
value
over many
collisions. But this
conception is artificial;
rather,
the consideration
reveals
clearly a
weak
point
of the
conception
characterized
by
monochromatic
energy
quanta.
19)
According
to
Sommerfeld's
conception,
the
frequencies
v- are
not
emitted
h
in
a
collision
of
an
electron because the
collision
is
not sudden.
According
to this
conception,
the
higher terms
of
the
Fourier
expansion
do
not
appear
in
the emitted
field
because
they already
do
not
appear
in
the Fourier
expansion
of the accelerations
occurring
in
the
collision. This
conception
has
the
great
advantage
that
one can
adhere
to Maxwell's
equations
when
calculating
the emitted
field.
Unfortunately, however,
this
conception
also
brings
with it
a
serious
difficulty,
which must not
be left unmentioned.
If
a
radiation
space
contains
a
gas
with
electrically
charged
atoms,
then these
atoms
emit
and
absorb radiation
energy
when
they
collide,
and it would have to be
possible
to
derive
the radiation formula
by a
statistical
investigation
of
such
a system.
The
fact
that
one
arrives
here
at
Rayleigh's
formula,
if
one
starts
off
from classical mechanics
and
Maxwell's
electrodynamics,
can
be taken
as
indisputably
proved.
To reach
agreement
with
experience, one
has to
modify
the theoretical foundations
in such
a way that,
at
a
emission coefficient
given
temperature
of the
gas,
the
quotient
- for the
gas
becomes
absorption
coefficient
exceedingly
small
for
large
v.
Thus,
for
large v,
the
emission coefficient
must
become
exceedingly
small relative to
the
absorption
coeff. Is this
likely
to
be
achieved
by
Sommerfeld's
collision law?
Basically,
the latter
amounts
to the
assumption
that the
higher
terms
are
missing
in
the Fourier
expansion
of
the collision
acceleration of
the individual
charged mass
points.
From
this it follows
directly
that the
corresponding
terms
are
missing
in
the
emission.
But
it
seems
that the
absence
of these
terms in
the Fourier
expansion
of the
collision
acceleration
also excludes
an
absorption
of
those
frequencies,
so
that
in
essence
the
above
quotient
should
not be at all
influenced
by
Sommerfeld's
hypothesis.
No. 233
(Sommerfeld
et
al.
1914,
p.
310;
Sommerfeld
et
al.
1912,
p.
384)
18)
It
may
nevertheless
be difficult to
maintain the
view
that radiation of
a given
frequency
can
be emitted
only
in
quanta
of
magnitude
hv
by
monochromatic
oscillators,
but
in
arbitrarily
small
portions
by colliding
electrons.
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