DOC.
51
329
Doc.
51
ON
THE FUNDAMENTAL ELECTROMAGNETIC
EQUATIONS
FOR
MOVING
BODIES
by
A.
Einstein
and
J.
Laub
[Annalen
der
Physik 26
(1908):
532-540]
In
a
recently
published
study1
Mr. Minkowski
has presented
the funda-
mental equations
for the
electromagnetic
processes
in
moving
bodies.
In view
of
the fact that this
study
makes
rather
great
demands
on
the reader in its
mathematical
aspects,
we
do
not
consider it
superfluous
to
derive here these
important equations
in
an
elementary
way,
which,
is,
by
the
way,
essentially
in
agreement
with that
of Minkowski.
§1.
Derivation
of
the
fundamental equations
for
moving
bodies
The route to
be
taken
is
as
follows:
We
introduce
two
coordinate
systems
K
and K',
both
of which
are
nonaccelerated but
in
relative
motion.
If
the
space
contains
matter at rest
relative
to
K', then the
laws of
the
electrodynamics
of
bodies
at rest,
described
by
the Maxwell-Hertz equations,
will hold with
respect to
K'. If
we
transform these
equations to
the
system
K, we
directly obtain
the
electrodynamic equations
of
moving
bodies for
the
case
that the velocity of
the
matter
is spatially
and temporally
constant.
Obviously,
the
equations
so
obtained hold
at
least in first
approximation
also
in the
case
when
the distribution
of velocity of
the
matter
is arbitrary.
[2]
This
assumption
is also partly justified
by
the fact that the result obtained
in this
way
is strictly valid in the
case
of
a
number
of bodies
moving
with
different uniform velocities that
are
separated
from each
other
by vacuum
interspaces.
When
referred
to
the
system
K',
the
vector
of the electric force will
be
denoted
by
(£', that
of
the
magnetic
force
by
V',
that of the dielectric
displacement
by
©', that
of the
magnetic
induction
by
,
that of
the
1H.
Minkowski, Gottinger
Nachr.
1908
[1]