Axiomatizing Relativistic Dynamics without Conservation Postulates

Abstract

Abstract. A part of relativistic dynamics (or mechanics) 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.

A note on ‘Einstein's special relativity beyond the speed of light by James M. Hill and Barry J. Cox’

“…This is done in Madarász & Székely [7], relying on Andréka et al [8]. We get formula (3.1) in relativistic units, by introducing an observer-independent quantity for FTL particle b as…”

Comparing Relativistic and Newtonian Dynamics in First-Order Logic

“…The reason for this fact is that the simultaneities of observers moving relative to each other in SpecRelKin differ from each other, and this implies that the proportions involved in AxCen − change, too. See Prop.4.1 and Fig.3 in [6]. The next axiom states that the relativistic mass of a body depends at most on its rest mass and its speed.…”

“…However, as far as we know, our co-authored paper [6] is the only one which deals with the FOL axiomatization of relativistic dynamics, too. Newtonian and relativistic kinematics are compared in the level of axioms in [5, §4.1].…”

Axiomatic derivation of the Doppler factor and related relativistic laws

“…Some recent papers dealing with the axiomatization of special relativity concepts are Andréka et al [2][3][4] and Moriconi [9]. In the first three papers, the axiomatization is based on a logical analysis, while in the last one, it is grounded in physical principles.…”