The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecR el for special relativity proposed recently by Andr′eka et al. is not enough to explain all the main r...The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecR el for special relativity proposed recently by Andr′eka 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 spacetime perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecR el^+. Then we introduce an axiom of mass(Ax Mass) and take four-momentum conservation as an axiom(Ax CFM)in SpecR el^+. It turns out that the twin paradox and energy-mass relation can be derived from SpecR el+logically. Hence,as an extension of SpecR el, SpecR el^+is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity.展开更多
基金Supported by the National Science Foundation of China under Grant Nos.11235003 and 11475023National Social Sciences Foundation of China under Grant No.14BZX078+1 种基金the Research Fund for the Doctoral Program of Higher Education of Chinathe Undergraduate Training Program of Beijing
文摘The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecR el for special relativity proposed recently by Andr′eka 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 spacetime perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecR el^+. Then we introduce an axiom of mass(Ax Mass) and take four-momentum conservation as an axiom(Ax CFM)in SpecR el^+. It turns out that the twin paradox and energy-mass relation can be derived from SpecR el+logically. Hence,as an extension of SpecR el, SpecR el^+is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity.
