Tuesday, June 5, 2012

1206.0337 (Anatoli Babin et al.)

Relativistic point dynamics and Einstein formula as a property of
localized solutions of a nonlinear Klein-Gordon equation

Anatoli Babin, Alexander Figotin
Einstein's relation E=Mc^2 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, 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.
View original: http://arxiv.org/abs/1206.0337

No comments:

Post a Comment