208
DOC.
5
LOCALIZATION OF ELECTROMAGNETIC ENERGY
this
latter view
should be
adopted.2
The
considerations
on
which I
based
myself
rest
on
a
principle
of
Boltzmann's,
according
to which
the
entropy
S
and the
statistical
probability
W
of
a
state
of
an
isolated
system
are
connected
by
the relation
S
=
-log
W,
N
s
where
R
is
the
gas
constant
for
a
perfect
gas
and
N
the number
of
molecules in
one
gram-molecule.
If
a
complete
molecular
picture
of the
system
considered
is
given, one
can
calculate
the
statistical
probability
W
for
each state
of the
system,
and
from this
one
can
calculate S with
the
aid
of the
formula.
If,
conversely,
the
system
is
known
thermodynamically,
then
one
will know
S,
and from this
one
will be able to derive
the
statistical
probability
of each
state
of the
system.
To be
sure, one
cannot establish
an
elementary theory
(e.g.,
a
molecular
theory)
of the
system
from
W in
a
unique
and
well-defined
fashion; but, still, any
theory
giving
the
wrong
values
of
W
for
any
of the
states
can
be
considered
unacceptable.
One
can
then
find
the
entropy
of radiation
in
empty
space by means
of
thermodynamics,
using
the
law
of
black-body
radiation,
and
solve
the
following
problem:
consider
two
spaces
enclosed
within
impermeable
walls
and
connected
by a
tube that
can
be
closed;
let
V
be the
volume
of
one
of the
spaces
and
V0
the total
volume;
assume
that these
spaces are
filled with
a
radiation whose
frequency
lies
between
v
and
v +
dv,
and
whose
total
energy
is
E0.
We seek
to calculate
the
entropy
S
of the
system
for
every possible
distribution of the
energy
E0
between the
two
spaces.
From the
entropy S
of
each
of these
possible
distributions,
one can
deduce
the
statistical
probability corresponding
to each
of
them.
In
this
way one
finds for
a
sufficiently
dilute
radiation the
following expression
for the
probability
that
at
a given
moment all
of the
energy
E0
is
contained
in
the volume
V:
W
=
V
K
\e,
[7]
It
can easily
be
shown
that
this
expression
is not compatible
with
the
principle
of
superposition.
As
regards
the distribution between the
two
spaces,
the radiation
behaves
as
if its
energy
were
localized in
E0/hv
points
moving
independently
of each other.
From
this it
follows-unless
one
wants to
admit that the
use
of
impermeable
walls in
these considerations
is inadmissible-that,
regarding
the
localization
of
its
energy,
the
radiation
must
itself
have
a
structure not
given by
the
ordinary
theory.
In
conclusion,
let
me say
that the
commonly
accepted
localization
of
energy
(just
like
the
momentum in
the
electromagnetic
field)
is
by no means a necessary
consequence
of
the
Maxwell-Lorentz
equations.
Furthermore,
one
can
give,
for
example,
a
distribution
compatible
with
the mentioned
equations that,
for
static and
stationary states,
coincides
[8]
completely
with
the
one
given by
the old
theory
of
action
at
a
distance.
[6]
2A.
Einstein,
Ann.
d.
Phys.,
4,
17
(1905):
139ff.
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