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Canonical science report 20093

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Theories reducing to Coulombian electrodynamics, relativistic electrodynamics doesn't

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Kind of report: Research.

Draft version: 2009 Nov 02. First version: 2009 Dec 10. Last version: 2009 Dec 10, 11:59 UTC.

Figures

This Research report includes one high-resolution figure in color.

Above, compatibility of action-at-a-distance theory with cosmological distribution of masses (stars, planets...); asymptotic distances describing the waited behavior of potential energy do not imply instantaneous distances for the actual distribution of matter. Below, asymptotic distances in general relativity and other theories as field theory of gravity imply an asymptotic vacuum that is in contradiction with the actual distribution of matter

Electromagnetic interactions in post-relativity and relativistic field theory. The direct-particle-action of post-relativity correctly accounts for the topology of the binary interactions in a system of point charges, even after a local limit is applied. As a consequence, the local approximation to post-relativity is not the standard relativistic theory of fields but an improved version without divergent self-interactions. In the standard relativistic theory, the emphasis in geometrical requirements of spacetime symmetry introduces unphysical elements in the description of interactions. Click on the image for a zoom.

Abstract

Scientific knowledge is accumulative. Theoretical and fundamental scientists require a single comprehensive theory applying to all physical phenomena. Coulombian electrodynamics is used for a broad range of electromagnetic phenomena. This implies that any theory of electromagnetism, to be taken seriously, would reduce to Coulombian electrodynamics in some limit.

This Research report studies the Coulombian limit of six theories, presenting the difficulties and inconsistencies found when rigorously revised. The theories considered are: relativistic field electrodynamics; Stefanovich electrodynamics theory; Weber electrodynamics; Wheeler & Feynman electrodynamics; Chubykalo & Smirnov-Rueda dual electrodynamics; and Stückelberg, Horwitz, & Piron action-at-a-distance theory.

This Research report shows that (i) the assertion that relativistic field electrodynamics reduces to the theory of Coulomb as well as (ii) the assertion that the static-field-low-velocity relativistic equation of motion is identical to the Coulombian equation of motion do not hold up on close inspection. For instance, the Coulombian potential ϕ = ϕ\(R\(t\)\) cannot be reproduced by the field potential (\ab ^)ϕ = (\ab ^)ϕ \( (\ab ^) x‚(\ab ^) t \) of relativistic electrodynamics in any limit. This is in agreement with earlier results showed in Phys. Rev. E (1997, 53, 5373; 1998, 57, 3683). It is also demonstrated that some observational difficulties of relativistic theories of electromagnetism —such as the unphysical self-interactions— are related to their lack of compatibility with Coulombian electrodynamics.

Among the six theories cited above, only the theories of Weber, of Chubykalo & Smirnov-Rueda, and of Stückelberg, Horwitz, & Piron reduce to Coulombian electrodynamics.

One of the main findings of this Research report is that all the current theories of electromagnetism revised belong to one of two incompatible classes, extending and generalizing the incompatibility between quantum electrodynamics and quantum mechanics denounced by Dirac. The main pros and cons for each kind are presented.

Finally, this Research report introduces the new post-relativity theory and discusses its possibilities and advantages over current theories.

Citation of last version

  • Theories reducing to Coulombian electrodynamics, relativistic electrodynamics doesn't 2009: Can. Sci. Rep. 20093v1. González-Álvarez, Juan R.

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