Abstract

Historically, electrodynamics began when Gauss and Weber generalized Coulomb law for the case of moving charges. In the framework of this approach interaction force between two charges depends on their velocities difference, i.e. on their relative movement. Some authors (for instance [1]) show that this approach has not been exhausted yet. Spencer and her colleagues [2] have generalized this approach and shown that some experiments that cannot be explained within the framework of present-day electrodynamics may be naturally explained in terms of relative movement. These and other papers began a rebirth period for Gauss-Weber ideas. In particular Bernstein [3] shows that Weber?s formula has already covered all ?relativistic? effects. Historically, the Gauss-Weber approach was eclipsed by the field Maxwell approach, and forgotten by the end of 19th century. For instance, Einstein apparently didn?t know Weber?s papers. At any rate, he never mentioned Gauss and Weber, although the resemblance between the consequences of the two theories is surprising. Maxwell theory investigates the problem, not of charges interaction, but of the ?field? created by a moving charge in the surrounding space. In order to come to interaction force, an additional postulate is introduced. It is usually called Lorentz force formula. This formula describes interaction of the fields created by a moving charge with another charge called ?test charge?. This test charge is supposed not to create fields of its own but external fields created by the first charge are supposed to directly act on this test charge. Although Lorentz force formula predicts results of many experiments its effect in today form looks completely unsatisfactory. Many authors (for instance [2]) shows that Lorentz force formula isn?t able to explain a lot of experimental facts. Lorentz force asymmetry also leads to many theoretical and aesthetic problems. If it is considered exhaustive we come to contradiction to the third Newtonian law: it allows situations when one charge acts on the other and this other doesn?t act on the first one. In addition if we don?t accept either concept, then the very idea of ?absolute velocity? which appears in Lorentz force formula turns to be suspended. Actually dissatisfaction with this side of the formula stimulated Einstein with his Relativity Theory. In other terms Lorentz force formula in its present-day form is asymmetric and not universal. Ampere [4] and Whittaker [5] proposed formulas of their own to describe charge interaction force. They did this in terms of ?differential currents?. When paraphrased in terms of moving charges these formulas could expand and symmetries Lorentz force formula. But their ?field sense?, i.e., their connection with Maxwell equations, was not clear until recently. This paper?s author proposed certain generalization as Maxwell equation as Lorentz force formula [6], [7]. The generalized formula implies Lorentz, Ampere, Whittaker, Weber and Spenser formulas. It also includes some additional items not known previously. For instance it predicts cluster effect, Bohm-Aharonov effect and electro-weak interaction. The Weber formula has the same invalidity as the Lorentz one: it is asymmetric and not universal. The generalized formula includes items which make Weber formula symmetric and coordinate it to the whole set of experiments. The generalized formula for charge interaction is naturally modernized to describe photons interaction [8]. And this explains some quantum paradoxes.

References

1. Andre K.T. Assis, Relational Mechanics (Apeiron, Montreal, 1999).
2. D.E. Spencer, G. Coutu, W.W. Bowley, U.Y. Shama, P.J. Mann, "The Experimental Verification of the New Gaussian Equation for the Force between Moving Charges: Overhead Welding", International Conference on Space, Time and Motion., September 23-29, 1996, St. Petersburg, Russia.
3. V.M. Bernstein, " Electrodynamics and Gravitation Based on Trends Preceeding Maxwell and Einstein", Galilean Electrodynamics 11, (5) 91 (2000).
4. A.M. Ampere, Theorie mathematique des phenomenes electrodynamiques uniquement deduite de l?experience (Blanchard, Paris, 1958).
5. E.T. Whittaker, A History of the Theories of Aether & Electricity, p 91 (Longman, Green and Co, London, 1910).
6. J.G. Klyushin, " A Field Generation for the Lorentz Force Formula", Galilean Electrodynamics 11, (5), 83 (200).
7. J.G. Klyushin, " Generalised Electrodynamics and Lorentz Force Formula", NPA conference proceeding, Storrs, Connecticut, 2003.
8. J.G. Klyushin, " Wave Solution and Quantum Mechanics - Part 1", Galilean -Electrodynamics 15, Special Issues 2, GED ? East, Fall (2004).