Electromagnetic gauge as an integration condition: De Broglie's argument revisited and expanded
Einstein's mass-energy equivalence law, argues de Broglie, by fixing the zero of the potential energy of a system,ipso facto selects a gauge in electromagnetism. We examine how this works in electrostatics and in magnetostatics and bring in, as a “trump card,” the familiar, but highly peculiar, system consisting of a toroidal magnet m and a current coil c, where none of the mutual energy W resides in the vacuum. We propose the principle of a crucial test for measuring the fractions of W residing in m and in c; if the latter is nonzero, the (fieldless) vector potential has physicality. Also, using induction for transferring energy from the magnet to a superconducting current, we prove that W is equipartitioned between m and c.
KeywordsPotential Energy Electromagnetism Vector Potential Integration Condition Current Coil
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- 1.L. de Broglie,Une Nouvelle Conception de la Lumière (Hermann, Paris, 1934);Nouvelles Recherches sur la Lumière (Hermann, Paris, 1936).Google Scholar
- 2.L. de Broglie,Compt. Rend. Acad. Sci. 225, 163 (1947).Google Scholar
- 3.O. Costa de Beauregard,Ann. Fond. Louis de Broglie, in press.Google Scholar
- 4.L. de Broglie,Portugaliae Physica 3, 1–19 (1949); see p. 11.Google Scholar
- 5.M. Jouguet,Cours de Physiqe, Vol. 2. Electricité (Eyrolles, Paris, 1962), p. 224.Google Scholar
- 6.W. Shockley and R. P. James,Phys. Rev. Lett. 18, 876 (1967).Google Scholar
- 7.H. Haus and P. Penfield,Phys. Rev. Lett. A 26, 412 (1968).Google Scholar
- 8.O. Costa de Beauregard,Phys. Rev. Lett. A 24, 177 (1967).Google Scholar
- 9.S. Coleman and J. H. Van Vleck,Phys. Rev. 171, 1370 (1968).Google Scholar
- 10.O. Costa de Beauregard,Phys. Lett. 28A, 365 (1968).Google Scholar