Axiomatization of Special Relativity in First Order Logic

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 p...

Full description

Saved in:
Bibliographic Details
Published in理论物理通讯：英文版 Vol. 65; no. 7; pp. 19 - 28
Main Author 罗懿晨 陈磊 何宛亭 马永革 张昕禹
Format Journal Article
LanguageEnglish
Published 2016
Subjects
一阶逻辑
公理化
双生子佯谬
四维时空
物理理论
狭义相对论
相对论动力学
系统图像
Online AccessGet full text
ISSN0253-6102

Cover

More Information
Summary: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.
Bibliography:special relativity first-order logic axiomatization
11-2592/O3
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.
Yi-Chen Luo , Lei Chen , Wan-Ting He , Yong-Ge Ma , Xin-Yu Zhang （1Department of Physics, Beijing Normal University, Beijing 100875, China; 2Research Center for Value and Culture, School of Philosophy, Beijing Normal University, Beijing 100875, China）
ISSN:0253-6102