148 EARLY WORK ON
QUANTUM
HYPOTHESIS
that
light propagating through empty space
consists
of
electromagnetic
fields
behaving
as
"independent
structures"
("selbständige
Gebilde").[101] Moreover,
"according to this
theory
[of
relativity],
light
has the characteristic in
common
with
corpuscular
theory
of
transferring
inertial
mass
from the
emitting
to the
absorbing
body"
("hat nach
dieser
Theorie mit einer
Korpuskulartheorie
des Lichtes das Merkmal
gemeinsam,
träge
Masse
vom
emittierenden
zum
absorbierenden
Körper zu
übertragen").[102]
In view
of
the
pres-
ence
of
both
wave
and
corpuscular
terms in fluctuations
of
black-body
radiation
(see
sec-
tion
V),
he
argued
that
a new
"mathematical
theory
of radiation"
("mathematische
Theo-
rie
der
Strahlung") is needed,
which
"can
be considered
as a
sort
of
fusion
of
the
wave
and the
emission
theory
of
light" ("sich
als eine Art
Verschmelzung von
Undulations–
und Emissionstheorie des Lichtes auffassen
läßt").[103]
Einstein
1909b
(Doc. 56)
and Einstein 1909c
(Doc. 60), together
with
Einstein's
con-
temporary correspondence, report some
of
Einstein's
intense,
but unsuccessful,
efforts
to
find
an appropriate theory
that would
serve as
such
a
"fusion."[104]
Rather
than
maintain-
ing
his
earlier
inclination toward
a
corpuscular
theory,
Einstein
now suggested
that
per-
haps some
nonlinear modification
of
the Maxwell field
equations
would
yield
not
only
the
quantum
of
electric
charge e as a consequence,
rather than
an assumption
of
the
theory,
but also the
quantum
structure
of
radiation. He
suggested
that the
linear, homogeneous
optical wave equation
should be
replaced by a
nonlinear
or inhomogeneous wave
equation
containing e as a
coefficient.[105]
In
a lengthy
letter
to
Einstein,
Lorentz criticized
Einstein's
search for
a
modification
of
electrodynamics
that would
encompass
both electrons and
quanta,
remaining
unconvinced
of
the existence
of
independent
light
quanta.[106]
In his
reply,[107]
and in his
Salzburg
lec-
ture, Einstein described further
efforts
to
find
a
suitable modification.
By
the
time
of the
Salzburg meeting
he had
hit
upon an
idea
that
allowed
for
both
interference
and
individu-
ality:
in
analogy
to the electrostatic field
surrounding an electron, a light
quantum
could
be treated
as a
mathematical
singularity
surrounded
by an
extended
vector field,
all
of
the
energy
of
the field
being
concentrated in
such
singularities.[108]
He
suggested
that,
if
many
singularities
lie close
together,
their
fields
overlap
to
produce
the effect of
a
continuous
wave
field.
By
this
example
Einstein
attempted
to show that the
wave
and
quantum
aspects
of
radiation,
which he
firmly
believed to be inherent in
Planck's
law, are
not
necessarily
incompatible.
The
problem
of
finding
the correct relation between these two
aspects
of
radiation dominated his
subsequent
work
on
the
quantum hypothesis.
[101]
Ibid.,
p.
487.
[102]
Ibid.,
p.
490.
[103]
Ibid.,
pp.
499 and 483.
[104]
In addition
to
the
papers cited, see,
in
par-
ticular: Einstein to Arnold
Sommerfeld, 19
Jan-
uary
1910;
Hendrik Lorentz
to Einstein,
6
May
1909;
Einstein
to
Jakob
Laub, 19
May
1909;
Einstein to Hendrik
Lorentz,
23
May
1909;
Ein-
stein
to
Johannes
Stark, 31
July
1909;
Einstein
to
Michele Besso,
31
December 1909. For dis-
cussions
of Einstein's
efforts, see
McCormmach
1970a and Klein 1967.
[105]
See Einstein 1909b
(Doc. 56),
p.
192.
[106]
See Hendrik Lorentz
to Einstein,
6
May
1909.
[107]
See Einstein to Hendrik
Lorentz,
23
May
1909.
[108]
See
Einstein
1909c
(Doc. 60),
pp.
499-
500,
and
Einstein
et
al.
1909c
(Doc. 61).
A
year
later,
Lorentz still
expressed
doubts about
light
quanta,
primarily
because
of
the interference
of
very
weak radiation
(Lorentz 1910,
pp.
1249-
1250).