528 DOC. 52
PONDEROMOTIVE FORCES
550
A. Einstein
u.
J.
Laub.
Ponderomotorische
Kräfte.
Entsprechende Gleichungen
gelten
für
die beiden anderen
Komponenten
der
ponderomotorischen
Kraft.
Integriert
man
(12)
über
den unendlichen Raum,
so
erhält
man,
falls im
Unendlichen
die
Feldvektoren
verschwinden,
die
Gleichung:
[12] (14)
ƒ*.*-
Sie
sagt
aus,
daB
unsere ponderomotorischen
Kräfte
bei Ein-
fuhrung
der
elektromagnetischen Bewegungsgröße
dem
Satz
von
der
Gleichheit
von
actio und reactio
genügen.
Bern,
7.
Mai 1908.
(Eingegangen
13. Mai
1908.)
Published
in Annalen
der
Physik
26
(1908):
541-550. Dated
Bern,
7
May 1908,
received
13
May
1908, published
7
July
1908.
[1]
Minkowski 1908.
[2]
For
Minkowski’s
expression
for the
pon-
deromotive
force, see
Minkowski
1908,
p.
97.
[3]
In the units used in Einstein
and
Laub
1908a
(Doc. 51)
and later in this
paper
(see
p.
545),
the last two
terms
in this
equation
should
be divided
by c.
[4]
For
contemporary expositions
of
the elec-
tron
theory,
see
Lorentz
1904c,
Bucherer
1904.
[5]
For discussions
of
this duality,
also
called
the Heaviside-Hertz
analogy, see
Lorentz
1904b, p.
99; Föppl 1894,
pp.
121-122;
and
Abraham/Föppl 1904,
p.
211.
[6]
See,
e.g., Lorentz
1904c, pp.
151-155.
[7]
Abraham 1905. This reference
was
added
at Wien’s
suggestion (see
Jakob Laub to
Ein-
stein, 18
May
1908).
[8]
For
a
discussion
of
criticisms
of
Einstein’s
and Laub’s
expression
for
the
ponderomotive
force,
see
the editorial
note,
“Einstein
and Laub
on
the
Electrodynamics
of
Moving
Media,”
pp.
506-507.
[9]
“Curl
E”
should be
preceded by a
minus
sign.
[10]
As
a consequence
of
the
difference be-
tween the
Einstein-Laub and the Minkowski
expressions
for
the
ponderomotive
force den-
sity,
Einstein’s and Laub’s
expressions
for the
components
of
the
electromagnetic
stress tensor,
to which the force
density
is related
by eq.
(12),
also
differ
from Minkowski’s
expressions
for the
spatial components
of
the four-dimensional
stress-energy-momentum
tensor
(see
Minkowski
1908,
pp.
92-93). For
a
discussion
of
controver-
sies about the
electromagnetic stress-energy–
momentum tensor,
see
the
editorial
note,
“Einstein
and Laub
on
the
Electrodynamics
of
Moving
Media,”
p.
507.
[11]
Lorentz 1904c. Lorentz’s
expressions
for
Xx,
Xy,
Xz
differ somewhat from Einstein’s and
Laub’s. For
an
account
of
Wien’s
comments to
Laub, indicating
Wien did not
accept
the Ein-
stein-Laub definition
of
the
ponderomotive
force
density, see
Jakob Laub to Einstein,
18 May
1908.
[12]
The total time derivative should
precede
the
integral sign.