Axiomatization of Special Relativity in First Order LogicSupported by the National Science Foundation of China under Grant Nos. 11235003 and 11475023, National Social Sciences Foundation of China under Grant No. 14BZX078 and the Research Fund for the Doctoral Program of Higher Education of China, and the Undergraduate Training Program of Beijing

• Published in: Communications in theoretical physics Vol. 66; no. 1; pp. 19 - 28
• Main Authors: Luo, Yi-Chen, Chen, Lei, He, Wan-Ting, Ma, Yong-Ge, Zhang, Xin-Yu
• Format: Journal Article
• Language: English
• Published: Chinese Physical Society and IOP Publishing 01.07.2016
• Subjects: axiomatization; first-order logic; special relativity
• ISSN: 0253-6102
• DOI: 10.1088/0253-6102/66/1/019

The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecRel for special relativity proposed recently by Andréka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional space-time perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecRel+. Then we introduce an axiom of mass (AxMass) and take four-momentum conservation as an axiom (AxCFM) in SpecRel+. It turns out that the twin paradox and energy-mass relation can be derived from SpecRel+ logically. Hence, as an extension of SpecRel, SpecRel+ is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity.