We discuss the seminal article by Le Bellac and Lévy-Leblond in which they identified two Galilean limits (called “electric” and “magnetic” limits) of electromagnetism and their implications. Recent work has shed new light on the choice of gauge conditions in classical electromagnetism. We show that the recourse to potentials is compelling in order to demonstrate the existence of both (electric and magnetic) limits. We revisit some nonrelativistic systems and related experiments, in the light of these limits, in quantum mechanics, superconductivity, and the electrodynamics of continuous media. Much of the current technology where waves are not taken into account can be described in a coherent fashion by the two limits of Galilean electromagnetism instead of an inconsistent mixture of these limits.
REFERENCES
1.
M.
Le Bellac
and J. M.
Lévy-Leblond
, “Galilean electromagnetism
,” Nuovo Cimento Soc. Ital. Fis., A
14
, 217
–233
(1973
).2.
J. M.
Lévy-Leblond
, “Nonrelativistic particles and wave equations
,” Commun. Math. Phys.
6
, 286
–311
(1967
).3.
M.
de Montigny
and G.
Rousseaux
, “On the electrodynamics of moving bodies at low velocities
,” Eur. J. Phys.
27
, 755
–768
(2006
).4.
H. K.
Dirks
, “Quasi-stationary fields for microelectronic applications
,” Electr. Eng.
79
, 145
–155
(1996
).5.
U.
van Rienen
, J.
Flehr
, U.
Schreiber
, and V.
Motrescu
, “Modeling and simulation of electro-quasistatic fields
,” in Birkhauser Verlag (Basel, Switzerland), International Series of Numerical Mathematics
146
, 17
–31
(2003
);U.
Schreiber
, J.
Flehr
, V.
Motrescu
, and U.
van Rienen
, “The electro-quasistatic model in different applications
,” in Scientific Computing in Electrical Engineering Proc. 4th Conference on Scientific Computing in Electrical Engineering
, W. H. A.
Schilders
, E. Jan W.
ter Maten
, and S. H. M. J.
Houben
, eds., SCEE Springer-Verlag Berlin Mathematics in Industry 4
, 356
–363
(2004
);U.
van Rienen
, J.
Flehr
, U.
Schreiber
, S.
Schulze
, U.
Gimsa
, W.
Baumann
, D. G.
Weiss
, J.
Gimsa
, R.
Benecke
, and H. W.
Pau
, “Electro-quasistatic simulations in bio-systems engineering and medical engineering advances
,” Radio Sci.
3
, 39
–49
(2005
).6.
J.
Larsson
, “Electromagnetics from a quasistatic perspective
,” Am. J. Phys.
75
, 230
–239
(2007
).7.
8.
J. M.
Lévy-Leblond
, “Une nouvelle limite non-relativiste du groupe de Poincaré
,” Ann. Inst. Henri Poincare, Sect. A
3
, 1
–12
(1965
).9.
A.
O’Rahilly
, Electromagnetic Theory: A Critical Examination of Fundamentals
(Dover
, New York
, 1965
).10.
C. C.
Su
, “Explicit definitions of electric and magnetic fields in potentials and derivation of Maxwell’s equations
,” Eur. J. Phys.
22
, L5
–L8
(2001
).11.
V. P.
Yakubov
, “Special theory of relativity in electrodynamics
,” Russ. Phys. J.
47
, 726
–738
(2004
).12.
O. D.
Jefimenko
, “Presenting electromagnetic theory in accordance with the principle of causality
,” Eur. J. Phys.
25
, 287
–296
(2004
).13.
G.
Rousseaux
, “Lorenz or Coulomb in Galilean electromagnetism
?” Europhys. Lett.
71
, 15
–20
(2005
).14.
G.
Rousseaux
, “On the physical meaning of the gauge conditions of classical electromagnetism: The hydrodynamics analogue viewpoint
,” Ann. Fond. Louis Broglie
28
, 261
–269
(2003
), ⟨arxiv.org/abs/physics/0511047⟩.15.
J. Clerk
Maxwell
, A Treatise on Electricity and Magnetism
(Dover
, New York
, 1954
), Vols. I
and II
; originally published in 1873.16.
Y.
Pierseaux
and G.
Rousseaux
, “Les structures fines de l’ électromagnétisme classique et de la relativité restreinte
,” ⟨arxiv.org/abs/physics/0601023⟩.17.
J.
Earman
, World Enough and Space-Time, Absolute versus Relational Theories of Space and Time
(MIT Press
, Cambridge, MA
, 1989
).18.
R.
Rynasiewicz
, “Field unification in the Maxwell–Lorentz theory with absolute space
,” Philos. Sci.
70
, 1063
–1072
(2003
) or ⟨philsci-archive.pitt.edu/archive/00001096⟩.19.
F. J.
Dyson
, “Feynman’s proof of the Maxwell equations
,” Am. J. Phys.
58
, 209
–211
(1990
).20.
H. R.
Brown
and P. R.
Holland
, “The Galilean covariance of quantum mechanics in the case of external fields
,” Am. J. Phys.
67
, 204
–214
(1999
).21.
A.
Vaidya
and C.
Farina
, “Can Galilean mechanics and full Maxwell equations coexist peacefully
?” Phys. Lett. A
153
, 265
–267
(1991
).22.
H. R.
Brown
and P. R.
Holland
, “The non-relativistic limit of the Maxwell and Dirac equations: The role of Galilean and gauge invariance
,” Stud. Hist. Philos. Mod. Phys.
34
, 161
–87
(2003
).23.
24.
M.
Greiter
, “Is electromagnetic gauge invariance spontaneously violated in superconductors
?” Ann. Phys. (N.Y.)
319
, 217
–249
(2005
).25.
H. A.
Lorentz
, “Remarque au sujet de l’induction unipolaire
,” Archives néerlandaises des sciences exacts et naturelles
9
, 380
(1904
).26.
H.
Minkowski
, “Die Grundgleichungen für die elektromagnetischen Vorgange in bewegten Körpern
,” Nachr. Ges. Wiss. Gottingen, pp. 53
–111
(1908
);H.
Arzeliès
, Milieux Conducteurs ou Polarisables en Mouvement, Etudes Relativistes
(Gauthier-Villars
, Paris
, 1959
).27.
A.
Einstein
and J.
Laub
, “Über die elektromagnetischen Grundgleichungen für bewegte Körper
,” Ann. Phys.
26
, 532
–539
(1908
).28.
W. K. H.
Panofsky
and M.
Phillips
, Classical Electricity and Magnetism
(Addison-Wesley
, New York
, 1955
).29.
W. C.
Roentgen
, “Über die durch Bewegung eines im homogenen elektrischen Felde befindlichen Dielectricums hervorgerufene elektrodynamische Kraft
,” Ann. Phys.
35
, 264
–270
(1888
).30.
A.
Eichenwald
, “Über die magnetischen Wirkungen bewegter Körper im elektrostatischen Felde
,” Ann. Phys.
11
, 1
–30
(1903
).31.
H. A.
Wilson
, “On the electric effect of rotating a dielectric in a magnetic field
,” Philos. Trans. R. Soc. London
204
, 121
–137
(1904
).32.
M.
Wilson
and H. A.
Wilson
, “On the electric effect of rotating a magnetic insulator in a magnetic field
,” Philos. Trans. R. Soc. London, Ser. A
89
, 99
–106
(1913
).33.
J. B.
Hertzberg
, S. R.
Bickman
, M. T.
Hummon
, D.
Krause
, S. K.
Peck
, and L. R.
Hunter
, “Measurement of the relativistic potential difference across a rotating dielectric cylinder
,” Am. J. Phys.
69
, 648
–654
(2001
).34.
F. T.
Trouton
, “The results of an electrical experiment involving the relative motion of the earth and ether
,” Trans. Royal Dublin Soc.
7
, 379
–384
(1902
).35.
F. T.
Trouton
and H. R.
Noble
, “The mechanical forces acting on a charged electric condenser moving through space
,” Philos. Trans. R. Soc. London
202
, 165
–181
(1903
).36.
H. C.
Hayden
, “High sensitivity Trouton–Noble experiment
,” Rev. Sci. Instrum.
65
, 788
–792
(1994
).37.
O. D.
Jefimenko
, “The Trouton–Noble paradox
,” J. Phys. A
32
, 3755
–3762
(1999
).38.
E.
Carvallo
, “L’électromagnétisme et le principe de relativité
,” Compt. Rend.
173
, 1155
–1157
(1921
);E.
Carvallo
, “Le problème de la relativité dans les diélectriques
,” Compt. Rend.
173
, 1461
–1463
(1921
).39.
A.
Einstein
, “Ether and the Theory of Relativity: An Address delivered on 5 May 1920, in the University of Leyden
,” in Sidelights on Relativity
(Dover
, New York
, 1922
).40.
O.
Darrigol
, “The electrodynamics of moving bodies from Faraday to Hertz
,” Centaurus
36
, 245
–360
(1993
);O.
Darrigol
, “Emil Cohn’s electrodynamics of moving bodies
,” Am. J. Phys.
63
, 908
–915
(1995
).41.
42.
A.
Einstein
, “Zür Elektrodynamik bewegter Körper
,” Ann. Phys.
17
, 891
–921
(1905
);A. I.
Miller
, Albert Einstein’s Special Theory of Relativity
(Addison-Wesley
, New York
, 1981
).43.
Einstein used the Heaviside–Hertz formulation, whereas Poincaré used the Riemann–Lorenz formulation in his relativity article (Ref. 16 of this article).
44.
J. D.
Norton
, “Einstein’s investigation of Galilean covariant electrodynamics prior to 1905
,” Arch. Hist. Exact Sci.
59
, 45
–105
(2004
);G.
Hon
and B. R.
Goldstein
, “How Einstein made asymmetry disappear: symmetry and relativity in 1905
,” Arch. Hist. Exact Sci.
59
, 437
–544
(2005
).45.
46.
G. H.
Keswani
and C. W.
Kilmister
, “Intimations of relativity: Relativity before Einstein
,” Br. J. Philos. Sci.
34
, 343
–354
(1983
).47.
J. Clerk
Maxwell
, “On the induction of electric currents in an infinite plane sheet of uniform conductivity
,” in The Scientific Papers of James Clerk Maxwell
(Dover Phoenix Editions
, 2003
), Vol. II
, pp. 286
–296
.© 2007 American Association of Physics Teachers.
2007
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