350
REMARKS
ON
DOC.
51
Doc. 54
REMARKS
ON OUR
PAPER:
"ON THE FUNDAMENTAL ELECTROMAGNETIC
EQUATIONS
FOR MOVING
BODIES"
by
A.
Einstein
and
J.
Laub
[Annalen
der
Physik, 28 (1908):
445-447]
Mr. Laue
was
kind
enough
to
call
our
attention
to
an
inaccuracy
in
our
[2]
paper
cited in the title.1
We
say
there
(Ann.
d.
Phys.
26(1908):
535):
"It is remarkable that
the
boundary
conditions for the
vectors
(H,
D,
Jq,
93
at
the
boundary
of
two
media
are
the
same as
for bodies
at rest.
This
follows directly
from
equations (1a) to
(4a)."
Apart
from
the fact
that equations
(3a)
and
(4a)
are
irrelevant for the
derivation of the
boundary
conditions, this
statement
is
correct only
if the
component
of the
motion normal
to
the
boundary
surface vanishes,
which
is
actually
the
case
in the
problem
treated
in
§2
of
the
paper
quoted. The
boundary
conditions
of the
general
case are
most
easily found
in the
following
[3]
way,
which corresponds to
the
one
taken
by
Heinrich Hertz.
If
the
boundary
surface,
or,
more
exactly,
the infinitely thin
boundary
transition shell,
moves
in
some
arbitrary
manner,
then,
in
a
point
situated
in
it
and instantaneously at
rest,
the
quantities
determining
the
electromagnetic
field will in
general
vary
discontinuously,
infinitely fast,
with time;
how-
ever,
these
changes
will
be
continuous
for
a
point
moving
with
the
matter.
Thus,
the application
of
the operator
It
+
(oV)
to
a
scalar
or
to
a
vector
will
not
lead to
infinitely
large values
even
in
the
boundary
surface. If
we
then write
equation
(1a)2
in the
form
1
c
if
+ 5
=
curl
S)
+
i(oV)S)
c
[1] 1In
his letter
Mr. Laue
gave
the
correct
boundary
conditions
and pointed
out
a
different derivation
of them.
2loc. cit.