{"paper":{"title":"Relativistic Linear Restoring Force","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"D. Clark, J. Franklin, N. Mann","submitted_at":"2012-05-23T22:03:25Z","abstract_excerpt":"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 correcti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5299","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}