Andréka, Hajnal; Madarász, Judit X.; Németi, István; Székely, Gergely Axiomatizing relativistic dynamics without conservation postulates. (English) Zbl 1148.03028 Stud. Log. 89, No. 2, 163-186 (2008). Summary: A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous \(E = mc^{2}\). The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated. Cited in 2 ReviewsCited in 13 Documents MSC: 03B80 Other applications of logic 70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics 83A05 Special relativity 83C40 Gravitational energy and conservation laws; groups of motions Keywords:axiomatization; relativistic dynamics; first-order logic; equivalence of mass and energy; foundation of relativity PDFBibTeX XMLCite \textit{H. Andréka} et al., Stud. Log. 89, No. 2, 163--186 (2008; Zbl 1148.03028) Full Text: DOI arXiv References: [1] Andréka H., Burmeister P. and Németi I. (1981). ’Quasivarieties of partial algebras–a unifying approach towards a two-valued model theory for partial algebras’. Studia Sci. Math. Hungar. 16: 325–372 · Zbl 0537.08004 [2] Andréka, H., J.X. Madarász, and I. Németi, ’Logical axiomatizations of spacetime; samples from the literature’, in A. Prékopa and E. 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