16
DOC.
1
MANUSCRIPT ON SPECIAL RELATIVITY
of
the electrical densities of
matter.
But, second,
electrical
polarization brings
about
pressure
forces
due
to
the
circumstance that the
(infinitesimally
small)
elastically
displaced
electrical continua of
polarization
exert
forces,
whose
nature
we
cannot,
in
general,
characterize
more
precisely, on
the material
particles
connected with them.
Obviously,
these forces
depend only on
the
polarization
and the dielectric
constant
but
not
on
the field
strength.
From the
physical standpoint
it is
natural, therefore,
to
decompose
the Maxwell
pressure
forces into
components
in the
following way
[p. 12]
Pa
"Pa*
Pa
*
Pa'
*
»'•
* p» etc., P
xy
Pxy rxy rxy
where
Pxx =
«2
i*
C +
I)
t
-
if
X X
Pxy
^x^y
etc.
fxx
1
(
p
e-12
fxy
1
£
-
1
PxPy
etc.
p(m)
=
rxx
1
m
n
-
1(
2
p(m
=
rxy
1
II
~
1
mxmy
etc.
(10a)
As is
shown
in
§2,
the first
system
(pxx
etc.)
of
pressure
forces is valid
for
arbitrary
dynamic problems.
For the second and the third
system
(pxx(e)
etc.
and
pxx(m)
etc.),
this
general validity
follows from the circumstance that the elastic forces
of
polarization
do
not
depend
on
whether the deformations that make
up
the
polarization
are
temporally
invariant
or
not.
From this
it
follows that the Maxwell
pressure
forces
retain their
meaning
in
the
case
of
dynamical problems
as
well.
As
a
glance
at
equations
(7)
shows,
in order
to
obtain the forces exerted
by
the
electromagnetic
field
on
the
matter
in bodies
at
rest,
all
that
we
need
know,
in
addition,
is the
momentum
of the
electromagnetic
field. In order for the
momentum
conservation law
not to
be violated
by electrodynamics,
those forces
must
be
determined
by equations
of the form
of
equations
(7).
But
just
as
in
nonpolarizable
media,
the
momentum
of the
field in
polarized
media will be determined
by
the field
strengths
e
and
h
alone. For it is
impossible
to
see
why
momentum
and
energy
flux
should
correspond
to
the elastic
forces
of
polarization.
Therefore,
if
one
again sets[28]
sx
=
c[e, h],
then-at
least within the
range
of
validity
of
equations
(8)-one
has
to
set
fx-
-
dp'XX dp'
xy
_
dp'XZ
1
ÖS
dx
dy
dz
2
dt
etc.
...(11)
If
one
inserts the
expressions
for
p'xx
etc.
from
(10)
or
(10a)
into this
formula,
and
transforms
by
means
of
equations (Ia),
one
therefore obtains for the
ponderomotive