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The Total Time Derivative with Bi-Quaternion Electrodynamics
Abstract
In a recent paper [3] we have shown that the basic equations of electrody-namics can be cast into a bi-quaternion form. In this paper I present an other general way how the set of four equations of the generalised Lorentz force can be derived by introducing a new operator: The bi-quaternion total time derivative operator.
Dual electrodynamics and corresponding Maxwell’s equations (in the presence of monopole only) are revisited from dual symmetry
and accordingly the quaternionic reformulation of field equations and equation of motion is developed in simple, compact and
consistent manner.
The theory of electrodynamics can be cast into biquaternion form. Usually Maxwells’ equations are invariant with respect to a gauge transformation of the potentials and one can choose freely a gauge condition. For instance, the Lorentz gauge condition yields the potential Lorenz inhomogeneous wave equations. It is possible to introduce a scalar field in the Maxwell equations such that the generalized Maxwell theory, expressed in terms of the potentials, automatically satisfy the Lorentz inhomogeneous wave equations, without any gauge condition. This theory of electrodynamics is no longer gauge invariant with respect to a transformation of the potentials: it is electrodynamics with broken gauge symmetry. The appearence of the extra scalar field terms can be described as a conditional current regauge that does not violate the conservation of charge, and it has several consequences: the prediction of a longitudinal electroscalar wave (LES wave) in vacuum; superluminal wave solutions, and possibly classical theory about photon tunneling; a generalized Lorentz force expression that contains an extra scalar term; generalized energy and momentum theorems, with an extra power flow term associated with LES waves. A charge density wave that only induces a scalar field is possible in this theory.
A theorem and proof for the total time derivative of a vector field as seen by a moving point
- Paul Wesley Jean
WESLEY Jean Paul, " A theorem and proof for the total time derivative of a vector field as seen by a
moving point", Apeiron 6 Nr. 3-4 (July-October 1999) 237-238
- C I Mocanu
- Hertzian
- Electrodynamics
- Its
- Mechanics
[1]
MOCANU C.I., " HERTZIAN RELATIVISTIC ELECTRODYNAMICS AND ITS ASSOCIATED MECHANICS ",
HADRONIC PRESS, Palm Harbor, FL, 1 (1991) 34-38
Generalized Total Time Derivatives
- E Phipps Thomas
PHIPPS Thomas E, "Generalized Total Time Derivatives", Apeiron 7 Nr.1-2 (January-April 2000) 107-110
Hertzian Relativistic Electrodynamics and its Associated Mechanics
- C I Mocanu
Mocanu C.I., "Hertzian Relativistic Electrodynamics and its Associated Mechanics", Hadronic Press,
Palm Harbor, FL, 1 (1991) 34-38