Emergent phenomena in higher-order electrodynamics
Computer Futures, Inc.
Physics Department, Woodbury University
University of Southern New Hampshire
Last modified: April 25, 2006
EMERGENT PHENOMENA IN HIGHER-ORDER ELECTRODYNAMICS
Jonathan Vos Post Christine M. Carmichael
Computer Futures, Inc. Physics Department
3225 N. Marengo Ave. Woodbury University
Altadena, CA 91001 Woodbury University
(626) 398-1673 7500 Glenoaks Blvd.
email@example.com Burbank, CA 91510-7846
[draft 4.0 of 15 Dec 2005, 60 pages, approx. 17,100 words including all appendices]
[completely new Section 5, pp.25-30; graviton discussion with Hockney added to notes]
International Conference on Complex Systems (ICCS)
June 25-30, 2006
Boston, Massachusetts, USA
Host: New England Complex Systems Institute
Conference Chair: Yaneer Bar-Yam
Conference Track: Physical Systems, Quantum and Classical
Conference Sub-tracks/themes: Spatio-temporal patterns in physical systems from subatomic to astrophysical, multiscale structure and dynamics.
In theories of electrodynamics, spatio-temporal patterns in physical systems from subatomic to astrophysical have been analyzed for almost 150 years by Maxwell’s equations, usually in the vectorized version (div, curl) developed by Oliver Heaviside. However, [Weinberg, 2005]: “Maxwell's formulation [of] the field equations contain terms with only a minimum number of spacetime derivatives. Today we know that the equations governing electrodynamics contain terms with any number of spacetime derivatives, but these terms, like the higher-derivative terms in general relativity, have no observable consequences at macroscopic scales.”
As Rochrlich puts it: “Of the four interactions [gravitation, electromagnetic, weak, strong] the electromagnetic one is certainly most thoroughly investigated and best understood. But it is not at all completely understood. Of the electrically charged particles we know most about the electron. The theory of the electron has throughout its history been very closely linked to the theory of fundamental electromagnetic interactions. It has been the model and guide for the understanding of the other interactions. Looking at the electron you will see elementary particle theory at its best. You will also see how poor this ‘best’ really is, and how much still remains to be done.”
We first review these historical facts, which can be interpreted as an overly-strict application of Occam’s razor analogous to a related neglect by Einstein of higher-order terms in General Relativity [Weinberg, 2005]. At this level, our review is aimed at a general audience interested in the Sociology and Philosophy of Science, and the traditional avoidance of complexity science and emergent nonlinear behavior. As Weinberg puts it: “... It seems that scientists are often attracted to beautiful theories in the way that insects are attracted to flowers—not by logical deduction, but by something like a sense of smell.” In addition, a technical level of this paper equationally examines three more general electrodynamic theories.
At microscopic scales, and also in extreme conditions such as relativistic plasmas [Pelletier, 1998], the higher-order terms neglected by James Clerk Maxwell lead to a range of theories with nonlinear emergent phenomena which may be astrophysically significant, and experimentally testable. Such theories include:
(1) Podolsky's higher-order electromagnetism [Accioly, 1977];[3-6] which includes generalization of Maxwell's equations, in the limit of small field strengths; Podolsky's theory leads to results free of infinities usually associated with a point source;
(2) Born-Infeld theory [Ketov, 2001] which is the particular covariant deformation of Maxwell electrodynamics by higher order terms depending upon F only;
(3) Pelletier and Marcowith’s analysis of nonlinear dynamics in the relativistic plasma of
astrophysical high-energy sources which, when in rough equipartition, have generalized Alfvén waves that propagate at velocities close to the velocity of light.
Predictions from these nonstandard electrodynamic theories include:
(1) Podolsky's higher-order field equations define a charactreristic length of approximately 10^-16 cm, characterizing in a phenomenological way a possible modification of QED (Quantum Electrodynamic) at short distances of the order of magnitude of the Compton wavelength of the neutral vector boson Z, which mediates the unified weak and electromagnetic interactions.
(2) Ketov proposed the N = 2 supersymmetric extension of the four-dimensional Born-Infeld action could be interpreted as the Goldstone-Maxwell action associated with spontaneous (partial) breaking of (rigid) N = 4 supersymmetry down to N = 2, and the N = 2 (Abelian) vector supermultiplet of Goldstone fields. The basic idea behind this interpretation was the anticipated equivalence (modulo a non-linear field redefinition) between the N = 2 super-BI action in four dimensions and the gauge-fixed world-volume action of a D3-brane propagating in six dimensions. This equivalence was verified in reference , in the leading and subleading orders only (see also reference ), and Ketov reports progress in obtaining the transformation laws of the hidden non-linearly realized symmetries (including spontaneously broken translations and extra N = 2 supersymmetry) which determine the form of the N = 2 super-BI action and prove its Goldstone nature.
(3) in electron or pair-dominated plasmas as hypothesized the source of high-energy cosmic rays, the origin of the high-energy emission of blazars and microquasars, the synchrotron radiation of jets, and/or the gamma-ray bursts of cosmic fireballs; the energy transfer from the electromagnetic perturbations to the particles depends on the nonlinear dynamics, leading to the possibility of self-modulation instability and soliton formation, and a new kind of collisionless quasi-parallel relativistic shock when a relativistic pair cloud pervades an ambient medium.
Implications to future research and simulations in Complexity Science are discussed, as well as possible astrophysical observations and laboratory experimentation.