ELECTRODYNAMICS
OF MOVING MEDIA 507
again
defended the Einstein-Laub
expression
with the
help
of
a new
example.[32]
However,
the
expression was soon disputed
in
print.[33]
Controversy
continued
over
this
question,
as
well
as over
the
closely
related
question
of
the
correct
expression
for the stress-momen-
tum-energy
tensor
of
the
electromagnetic
field in
a
material
medium.[34]
In recent
years,
it has been
suggested
that these controversies
arose
from the
failure
to
recognize
that
only
the total force
acting
on
a macroscopic body
is
uniquely
defined. Its
division into two parts-an
electromagnetic (ponderomotive)
force exerted
by
the field
and
a
mechanical force exerted
by ponderable
matter-is
arbitrary
to
a large
extent.
Fur-
thermore, the division
of
the
electromagnetic
force
density
into
components acting respec-
tively on
charge
and conduction current
densities and
on polarization
and
magnetization
densities is also
not
unique.[35]
It
is
possible
to rewrite
Einstein's
and
Laub's
expression
for the total
electromagnetic
force
density
in such
a way
that it
is
consistent
with Min-
kowski's
expression
for the force
density
on a
conduction current
element.[36]
As noted
above,
Lorentz's
equations
for
moving
media differ from Minkowski's
rela-
tivistic
equations.
This
was
considered
puzzling,
since the
underlying equations
of
the
electron
theory,
from which Lorentz derived the
macroscopic
equations,
are
relativisti-
cally
invariant.
Dmitry
Mirimanoff,
a
Privatdozent
in Mathematics at the
University
of
Geneva,
attempted
to show that
Lorentz's
equations can
be
brought
into accord with the
principle
of
relativity by suitably redefining
the transformation
properties
of
some
of
the
field variables under Lorentz transformations.[37] Einstein 1909a
(Doc.
55)
shows
that
this
is
impossible.[38]
Einstein
apparently
had
some difficulty getting
this
paper
accepted by
the
Annalen. In
a
letter
of
19
January
1909,
Wien indicated that he
was once again
returning
the
paper
to
Einstein,
and asked for
a
somewhat
more
detailed
exposition.
Presumably,
Einstein's
revision
of
the
manuscript
satisfied
Wien,
since it
was accepted
three
days
later.
In the last
paragraph
of
his
paper,
Einstein drew attention to
an
electron-theoretical
derivation
of Minkowski's
equations by
Frank.[39]
This
paper
established, for
nonmagnetic
media,
that it
was
Lorentz's
failure to take the Lorentz contraction and time dilation
fully
into account which led to his derivation
of
nonrelativistic
equations.
[32]
See
Einstein
1910b.
[33] See, e.g.,
Gans 1911 and Grammel 1913.
[34]
See
Pauli
1921, pp.
662-668,
for
a
review
of
these discussions
up
to 1921
(see p.
216
of
Pauli
1958 for
a
note
added
to
the
English
edi-
tion).
See
De Groot and
Suttorp
1972,
chap. V,
§
7,
for
a
review that includes
subsequent con-
tributions.
[35] See, e.g.,
De
Groot and
Suttorp 1972,
chap.
V,
§
7,
and Pavlov 1978 for discussions
of
the
nonuniqueness
of
these divisions.
[36]
See, e.g.,
Pavlov
1978,
p.
172.
[37]
See Mirimanoff
1909.
[38]
A letter
of
12
February
1909 from Miri-
manoff
to
Einstein indicates that
they
had
pre-
viously corresponded
about
Mirimanoff's
paper.
[39]
See
Frank
1908. For
a
review
of
electron-
theoretical derivations
of Minkowski's
equa-
tions
up
to 1920,
see
Pauli
1921,
pp.
659-662.