Relativistic Point Dynamics and Einstein Formula as a Property of Localized Solutions of a Nonlinear Klein-Gordon Equation View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2013-09

AUTHORS

Anatoli Babin, Alexander Figotin

ABSTRACT

Einstein’s relation E = Mc2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems which do not accelerate. By contrast, the Newtonian approach to the mass is based on an accelerated motion. We study here a particular neoclassical field model of a particle governed by a nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the nonlinear KG equation and its energy density concentrate at a trajectory, then this trajectory and the energy must satisfy the relativistic version of Newton’s law with the mass satisfying Einstein’s relation. Therefore the internal energy of a localized wave affects its acceleration in an external field as the inertial mass does in Newtonian mechanics. We demonstrate that the “concentration” assumptions hold for a wide class of rectilinear accelerating motions. More... »

PAGES

453-499

References to SciGraph publications

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  • 2012-08. Relativistic Dynamics of Accelerating Particles Derived from Field Equations in FOUNDATIONS OF PHYSICS
  • 2010-03. Wave-Corpuscle Mechanics for Electric Charges in JOURNAL OF STATISTICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/s00220-013-1732-z

    DOI

    http://dx.doi.org/10.1007/s00220-013-1732-z

    DIMENSIONS

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