{ "id": "1907.05412", "version": "v1", "published": "2019-07-11T17:56:44.000Z", "updated": "2019-07-11T17:56:44.000Z", "title": "A mathematical objection to the existence of relativistic mechanical systems of several particles", "authors": [ "Jesús Muñoz-Díaz", "Ricardo J. Alonso-Blanco" ], "categories": [ "math-ph", "gr-qc", "math.MP" ], "abstract": "We will prove that, in general, a system formed by several particles moving along relativistic trajectories can not be described by a mechanical system. The contradiction that leads to the previous assertion is due to the fact that a mechanical system defines a second order differential equation and this, in turn, induces an absolute time that will generally be incompatible with the proper times of the different particles.", "revisions": [ { "version": "v1", "updated": "2019-07-11T17:56:44.000Z" } ], "analyses": { "subjects": [ "83Axx" ], "keywords": [ "relativistic mechanical systems", "mathematical objection", "second order differential equation", "mechanical system defines", "relativistic trajectories" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable" } } }