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Theories reducing to Coulombian electrodynamics, relativistic electrodynamics doesn't
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; electrodynamics theory; electrodynamics; electrodynamics; dual electrodynamics; and action-at-a-distance theory.
This Research report shows that (i) the assertion that relativistic field electrodynamics reduces to the theory of 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.
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 . 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.
We believe that this Research report starts a new era in our understanding of the physics of interactions, beyond the profound cultural divide between the field and the many-body physics' community in dealing with spacetime. It is a shock for classical field theoreticians, plasma physicists, and others who believed that our understanding of classical electrodynamics was already complete. It is also a strong shock for particle physicists, because quantum field theory is deeply rooted into the classical theory of fields —which is quantized using standard procedures—. It turns into a historical curiosity the premature claims about the end of science advanced on that famous book —with the same apocalyptic title— by .
Physicists as will find satisfactory that this Research report confirms that the non-field approach to electromagnetism works better, letting us to advance in the task of unification of interactions. The mathematician —who was the first to prove in recent years the mathematical incompatibility between field electrodynamics and the electrodynamics developed by — has praised even the abstract of this Research report: El Abstract es muy claro y interesante
. Similar writings were sent by the expert in radiation reaction and renormalization : judged from the ABSTRACT, your review must be designing and interesting
. His three page-long analysis is reproduced in the section 14.2 of this Research report.
We only can speculate that this Research report would fascinate even to —two of the most celebrated promoters of a non-field approach to electrodynamics—, because we can go beyond the limits of their own electrodynamics without fields.
At the other hand, field theoreticians find repugnant the idea that field theory is not a complete theory of electrodynamics and that cannot reproduce the formulae developed by more than one hundred and ninety years ago! In one sense, this is not different from the position of the 20th century physicists who strongly rejected the development of quantum mechanics and its revolutionary change of picture.
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2010, March 12 at 08:10:29
Prof. L. P. Horwitz sent us the next note (after the report was published):
«I should note that the Stueckelberg et al theory does have electromagnetic interaction as well as action at a distance possibilities, and there we find self-interaction, but a little more complicated than Abraham-Lorentz-Dirac. See, for example, me, N. Katz and O.Oron, Discrete Dynamics in Nature and Society vol. 2004, no. 1, p. 179-204 (2004).»
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