112
DOC.
153 MAY 1909
opening
of the
objective;
and this
requires
(since
the
quanta
may
be
displaced laterally
with
respect
to
each other
(cf.
Fig. 2))
that the lateral
extension
of each
quantum must
be
considerably larger
than the
opening
of the
objective.
If
this
has
a
radius of
50
cm,
then the lateral extension of
a
light
quantum must
indeed
be
put at
no
less
than
5,000
cm2.
An
even
higher
number
is
obtained
if
one
takes
into
account
that,
e.g.,
the
new
reflecting telescope
of
Prof.
Hale
(Mount Wilson,
California),[14]
with its
opening
of
150 cm,
furnishes
images
of
a
sharpness
that
corresponds
to this
opening,
and
since it
is
not to be
expected
that
our
instruments
have
openings
that
by
pure
chance
happen to
correspond
to
the actual extension of
the
light
quanta,
the lateral extension of the latter
may
well be
even
considerably greater.
From the
above it
follows,
further,
that
the
objective
never
absorbs
a
whole
light
quantum,
and
that
a
very
extensive
splitting
of
light
quanta
must
take
place
when
the
naked
eye
is
directed
toward
a
star.
For
due
to
the
smallnes
of the
pupil surface,
perhaps
only
one
10,000th part
of each
light
quantum
will
enter
the
eye,
and
a
visual
impression
can
be
formed
only
when the
fragments
of
a
large
number of
quanta entering
the
organ
of
vision
merge
with
each other
simultaneously.
The
individuality
of each
single light
quantum
would be out
of the
question.
One should
also
note the
following.
If each
light
quantum
has
a
certain extension
in
the direction of
propagation,
then
one
would have
to
think
that
an
absorbing particle
is
able
to
absorb
light only
when
enough
waves
follow
one
another
so
that
in
the end the
particle is
able
to
get
a
whole
quantum.
But
(to put
it
vividly)
how
can
the
particle
know
at
the time when the
first
waves
arrive
whether
a
sufficient
number of additional
waves
will follow?
In order
to
overcome
this
difficulty,
one
would have to
imagine
that the
particle
holds
on
to
the
energy
of
the first
waves provisionally,
and
only
does
so
definitively
after the
amount
accumulated
has
reached
the
magnitude
of
a light
quantum.
It
is
a
real
pity
that the
light
quantum
hypothesis
encounters such
serious
difficulties,
because
otherwise
the
hypothesis
is
very pretty,
and
many
of the
applications
that
you
and
Stark
have
made
of
it
are
very enticing.
But
the doubts that
have
been raised
carry
so
much
weight
with
me
that
I
want to confine
myself
to
the
statement:
"If
we
have
a
ponderable
body
in
a
space
enclosed
by
reflecting
walls and filled with ether,
then
the
distribution of the
energy
between the
body
and the ether
proceeds
as
if
each
degree
of
freedom of the ether
could
take
up
or give
off
energy only
in
portions
of the
magnitude
hv."
As
you see,
not much
is
gained therby;
the
"as
if"
would have
to
be
elucidated
through
further
analysis.
The
problem
still
remains
extremely
difficult.
To
be
sure,
one
idea,
even
though
a
rather
desperate
one,
did
occur
to
me.
The
simplest
explanation
one
could
offer for
the
fact that the ether
in
the
closed
space
under consideration
does
not
contain the
amount
of
energy
that
corresponds
to
Jeans's
equation
consists in
the
assumption
that
not all
of
the
degrees
of freedom that
are possible according
to
the
customary
calculation
are
actually
at work.
One
could
imagine
that
all the
degrees
of freedom
are
divided into