17,090 research outputs found
Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation
The Lorentz law of force is the fifth pillar of classical electrodynamics,
the other four being Maxwell's macroscopic equations. The Lorentz law is the
universal expression of the force exerted by electromagnetic fields on a volume
containing a distribution of electrical charges and currents. If electric and
magnetic dipoles also happen to be present in a material medium, they are
traditionally treated by expressing the corresponding polarization and
magnetization distributions in terms of bound-charge and bound-current
densities, which are subsequently added to free-charge and free-current
densities, respectively. In this way, Maxwell's macroscopic equations are
reduced to his microscopic equations, and the Lorentz law is expected to
provide a precise expression of the electromagnetic force density on material
bodies at all points in space and time. This paper presents incontrovertible
theoretical evidence of the incompatibility of the Lorentz law with the
fundamental tenets of special relativity. We argue that the Lorentz law must be
abandoned in favor of a more general expression of the electromagnetic force
density, such as the one discovered by A. Einstein and J. Laub in 1908. Not
only is the Einstein-Laub formula consistent with special relativity, it also
solves the long-standing problem of "hidden momentum" in classical
electrodynamics.Comment: 7 pages, 1 figur
How does the electromagnetic field couple to gravity, in particular to metric, nonmetricity, torsion, and curvature?
The coupling of the electromagnetic field to gravity is an age-old problem.
Presently, there is a resurgence of interest in it, mainly for two reasons: (i)
Experimental investigations are under way with ever increasing precision, be it
in the laboratory or by observing outer space. (ii) One desires to test out
alternatives to Einstein's gravitational theory, in particular those of a
gauge-theoretical nature, like Einstein-Cartan theory or metric-affine gravity.
A clean discussion requires a reflection on the foundations of electrodynamics.
If one bases electrodynamics on the conservation laws of electric charge and
magnetic flux, one finds Maxwell's equations expressed in terms of the
excitation H=(D,H) and the field strength F=(E,B) without any intervention of
the metric or the linear connection of spacetime. In other words, there is
still no coupling to gravity. Only the constitutive law H= functional(F)
mediates such a coupling. We discuss the different ways of how metric,
nonmetricity, torsion, and curvature can come into play here. Along the way, we
touch on non-local laws (Mashhoon), non-linear ones (Born-Infeld,
Heisenberg-Euler, Plebanski), linear ones, including the Abelian axion (Ni),
and find a method for deriving the metric from linear electrodynamics (Toupin,
Schoenberg). Finally, we discuss possible non-minimal coupling schemes.Comment: Latex2e, 26 pages. Contribution to "Testing Relativistic Gravity in
Space: Gyroscopes, Clocks, Interferometers ...", Proceedings of the 220th
Heraeus-Seminar, 22 - 27 August 1999 in Bad Honnef, C. Laemmerzahl et al.
(eds.). Springer, Berlin (2000) to be published (Revised version uses
Springer Latex macros; Sec. 6 substantially rewritten; appendices removed;
the list of references updated
Operator Gauge Symmetry in QED
In this paper, operator gauge transformation, first introduced by Kobe, is
applied to Maxwell's equations and continuity equation in QED. The gauge
invariance is satisfied after quantization of electromagnetic fields. Inherent
nonlinearity in Maxwell's equations is obtained as a direct result due to the
nonlinearity of the operator gauge transformations. The operator gauge
invariant Maxwell's equations and corresponding charge conservation are
obtained by defining the generalized derivatives of the first and second kinds.
Conservation laws for the real and virtual charges are obtained too. The
additional terms in the field strength tensor are interpreted as electric and
magnetic polarization of the vacuum.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
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