Minimizers with discontinuous velocities for the electromagnetic variational method
- Departamento de Fisica Rodovia Washington Luis, Universidade Federal de Sao Carlos, km 235 Caixa Postal 676, Sao Carlos, Sao Paulo 13565-905, SP (Brazil)
The electromagnetic two-body problem has neutral differential delay equations of motion that, for generic boundary data, can have solutions with discontinuous derivatives. If one wants to use these neutral differential delay equations with arbitrary boundary data, solutions with discontinuous derivatives must be expected and allowed. Surprisingly, Wheeler-Feynman electrodynamics has a boundary value variational method for which minimizer trajectories with discontinuous derivatives are also expected, as we show here. The variational method defines continuous trajectories with piecewise defined velocities and accelerations, and electromagnetic fields defined by the Euler-Lagrange equations on trajectory points. Here we use the piecewise defined minimizers with the Lienard-Wierchert formulas to define generalized electromagnetic fields almost everywhere (but on sets of points of zero measure where the advanced/retarded velocities and/or accelerations are discontinuous). Along with this generalization we formulate the generalized absorber hypothesis that the far fields vanish asymptotically almost everywhere and show that localized orbits with far fields vanishing almost everywhere must have discontinuous velocities on sewing chains of breaking points. We give the general solution for localized orbits with vanishing far fields by solving a (linear) neutral differential delay equation for these far fields. We discuss the physics of orbits with discontinuous derivatives stressing the differences to the variational methods of classical mechanics and the existence of a spinorial four-current associated with the generalized variational electrodynamics.
- OSTI ID:
- 21464484
- Journal Information:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevE.82.026212; (c) 2010 The American Physical Society; ISSN 1539-3755
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
ACCELERATION
CLASSICAL MECHANICS
ELECTRIC CURRENTS
ELECTRODYNAMICS
ELECTROMAGNETIC FIELDS
EQUATIONS OF MOTION
LAGRANGE EQUATIONS
MATHEMATICAL SOLUTIONS
ORBITS
TRAJECTORIES
TWO-BODY PROBLEM
VARIATIONAL METHODS
CALCULATION METHODS
CURRENTS
DIFFERENTIAL EQUATIONS
EQUATIONS
MANY-BODY PROBLEM
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS