Relativistic Linear Restoring Force
Abstract
We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right of the relativistic expressions: dp/dt or dp/dtau . Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we introduce a form of retardation appropriate for the description of a linear (in displacement) force arising from the interaction of a pair of particles with a relativistic field. The procedure is akin to replacing Coulomb's law in E&M with a retarded form (the first correction in the full relativistic case). This retardation leads to the expected oscillation, but with amplitude growth in both its relativistic and non-relativistic incarnations.
Cite
@article{arxiv.1205.5299,
title = {Relativistic Linear Restoring Force},
author = {D. Clark and J. Franklin and N. Mann},
journal= {arXiv preprint arXiv:1205.5299},
year = {2015}
}
Comments
To appear EJP