Relativistic linear restoring force
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Publication:4919737
DOI10.1088/0143-0807/33/5/1041zbMATH Open1263.70025arXiv1205.5299OpenAlexW3103621040MaRDI QIDQ4919737
Author name not available (Why is that?)
Publication date: 15 May 2013
Published in: European Journal of Physics (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1205.5299
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