504
ELECTRODYNAMICS
OF
MOVING
MEDIA
force.
Assuming
the
presence
of
elastically
bound
charges
in dielectrics, and
of
free
charges
in
conductors,
the electron
theory
aims to derive
the
macroscopic
field
equations
for various material
media, as
well
as
their constitutive
relations,
by suitably averaging
fields,
charges,
and currents
over macroscopic regions
of
each
medium. Lorentz
was
able
to
use
such
microscopic
models
of
matter to
explain a
number
of
electrical, magnetic,
and
optical phenomena
in
material
media.[3]
Hertz's
electrodynamics
of
moving
media
obeys
the
Galileian
relativity
principle,
and
hence is
able to account for
the failure
of
attempts
to detect the motion
of
the earth
by
means
of
optical experiments.
But it
failed
to
explain
other
optical
phenomena,
and
was
soon rejected.[4]
Emil
Cohn
postulated
another set
of
phenomenological equations
that
remedies the defects
of Hertz's
theory
and still
is
able
to
account for the failure
of
attempts
to detect the motion
of
the
earth.[5]
By
1899 Einstein
was a
firm adherent
of
atomism for both matter and
electricity,
and
expressed
himself
in
favor
of
the basic
concepts
of
the electron
theory a
number of
times
thereafter.[6] In his first
paper on
the
theory
of
relativity
he showed that the basic
equations
of Lorentz's
electron
theory are
consistent with relativistic kinematics
if
the
transformation
properties
of
the
quantities entering
the
equations are properly
defined. But he did not
address the
problem
of
formulating a
relativistic
electrodynamics
of
moving
media.
In 1908,
Hermann Minkowski turned
to
this
problem.
He had
recently
discovered
a
four-dimensional
geometrical
reformulation
of
the
theory
of
relativity,
in which Lorentz
transformations
are
interpreted
as
rotations
in
a space
with three real and
one imaginary
coordinate.[7]
He
utilized the four-dimensional formalism to facilitate
investigation
of
the
invariance
of
various
equations
under the Lorentz
group.
In
particular,
he found the elec-
trodynamical
equations
for
a moving
medium
that
follow,
with the
use
of
the
relativity
principle,
from the form
of
the
equations
for
a
medium
at rest.[8] Minkowski showed that
Lorentz's
macroscopic equations
for
moving
media do
not
agree
with the
relativistic
equa-
tions.[9]
He
was working on a
derivation
of
the relativistic
equations
from the electron
theory
at the time
of
his death
in 1909.[10]
Einstein
and Laub
wrote their two
papers
in
1908 as a
response
to
Minkowski's
work.
[3]
See Lorentz
1904c,
§
IV,
"Elektroma-
gnetische Vorgänge
in
ponderablen
Körpern."
[4]
For
a
discussion
of Hertz's
theory
and its
rejection, see
the editorial
note,
"Einstein
on
the
Theory
of
Relativity,"
§
II,
p.
255.
[5]
See Hirosige
1966
for
a
discussion
of
Hertz's
and
Cohn's
theories.
[6]
See Vol.
1,
the editorial
notes,
"Einstein
on
Thermal, Electrical,
and Radiation Phenom-
ena,"
pp.
235-237, and
"Einstein
on
the Elec-
trodynamics
of
Moving
Bodies,"
pp.
223-225.
[7]
His first lecture
on
the
subject (Minkowski
1907b)
was
not
published
until 1915. His first
publication on
the four-dimensional
approach
was
Minkowski 1908. In
a
letter
of
9 October
1907, Minkowski informed Einstein that Ein-
stein
1905r
(Doc. 23)
was
to be discussed in
a
Göttingen
seminar
(see Pyenson 1985,
p.
83),
and
requested
an offprint.
For discussions
of
Minkowski's
work
on special relativity, see
Galison 1979 and
Pyenson
1977.
[8]
See Minkowski 1909.
[9]
See Minkowski
1908,
§
9. In
§
10
Min-
kowski showed
that,
up
to
terms of first order in
the
velocity,
Cohn's
equations
agree
with his
own.
[10]
His work
was completed by
Max Born and
published as
Minkowski 1910.