DOC.
1
MANUSCRIPT ON SPECIAL RELATIVITY
9
connection,
H. A. Lorentz
conceives
of
electricity
as
being
bound to
corpuscles
of
molecular dimensions
(electrons
in the broader
sense),
a conception
whose
validity
is
hardly
doubted
today.[19]
But
complications
are
thereby
created for the
theory,
in
that
one
is
dealing
here with field
quantities
that
vary rapidly
with location and that
are
to
be
replaced, then, by
suitable
mean
values.[20]
One
can
avoid these
complica-
tions without
doing any
essential
damage
if
one
proceeds
in the
following way.
According to
the
picture
that Lorentz's
conception gives,
we
have
to
conceive
an
electrically polarizable body
in the
following way.
In
every
unit volume
of
a
body
in
an
electrically
neutral state there
are present
at
least
two
approximately
evenly
distributed kinds of electrons
of
zero
total
charge.
But these
are
not
freely
movable;
instead,
they are
linked
to matter
by
elastic forces
(in
the
simplest case).
An electric
field
displaces
the
positive
and
negative
electrons
from
their
equilibrium position by
means
of
oppositely
directed forces. In
this
process,
the
electromagnetic
field varies
extremely rapidly
with location. We avoid this
by
conceiving
of
the
positive as
well
as
the
negative
electrons of the
same
kind
as being
combined
into
continua.
In
the
simplest case,
we
have
to
picture
an
inertia-free electrical continuum of
positive
density and,
in
the
case
of
an
electrically
unexcited
body,
one
of
equally great
negative density,
linked
elastically
to
the
matter.
If
we
also wish
to
represent
the
conductivity
of the
body,
we
introduce,
in
addition,
two further
electrically opposite
density-continua
that
can
move
relative
to
the
body by overcoming
a
kind
of
friction.
There
is
nothing
strange
in the introduction of several continua
at
the
same
location
if
one
realizes that this
is
only
an
idealization aimed
at
avoiding
mathematical
complications.
In
this
way
we
make it
possible
for the field
strengths
e
and
h
to
retain their
simple meaning.
Likewise,
equations
(I)
retain their
general validity,
the
only
difference
being
that in the first
of
these
equations we
have
to
put
E
np
in
place
of
np,
where the
sum
is to
be extended
over
all
continua; likewise,
in
the
second
equation
p
has
to
be
replaced by
E
p.
Polarization. Let
pv
be the
density
of
an
electrical continuum bound
to matter
(polarization density).
Let the
continuum be
displaced infinitesimally
relative
to
the
matter.
Let the
vector
of
this
displacement
be
nv'.
In that
case,
pvnv'
is also
a
vector,
and
we
will
designate
the
sum
E
Pvnv',
which also has the character
of
a
vector,
as
the
vector
p
of the electrical
polarization.
Then
px
is the
sum
of the electrical
quantities
that
traverse,
per
unit
surface,
a
surface
perpendicular
to
the
X-axis, per
[p. 7]
unit surface
during
the
establishment of "electrical
polarization";
the
projection
pn
on
the normal
to
an arbitrarily
oriented
surface has
an
analogous meaning.
If
a
dielectric borders
on
a
vacuum,
and if
n
denotes the normal
to
the surface
of
the
latter directed
toward the
latter,
then pn-taken
on
the
surface-therefore
measures
an
electrical surface
density
(surface
density
of
the
bound
electricity)
that is
produced
by
the
polarization
densities
on
the surface of the
dielectric.