狭义相对论数学基础的探讨  

Discussion to Mathematical Foundation of Special Relativity

作　　者：高云娥[1] 于学刚[1] 

机构地区：[1]天津商业大学理学院,天津300134

出　　处：《数学的实践与认识》2014年第3期211-216,共6页Mathematics in Practice and Theory

摘　　要：狭义相对论的变革点就是相对时空观,而相对论时空与非欧几何学有着密切的联系.在介绍了传统的Minkowski空间后,引入双曲虚单位,其所构造的双曲复数对应双曲Minkowski复空间.利用双曲Minkowski空间复数运算规则,可以使高速运动客体的物理规律与复数的性质结合起来,为解决狭义相对论的普遍形式提供新的数学工具.The innovation point of special relativity is the relativistic space-time concept,which is closely related with geometry.In this paper,we first introduce the traditional Minkowski space,then give the hyperbolic complex number constructed by hyperbolic imag inary unit,which is corresponding to hyperbolic Minkowski space.By use of the complex operational rules of hyperbolic Minkowski space,we can make the physical laws of high-speed moving object combine with properties of complex numbers.It will provide new mathematical foundation for the general form of special relativity.

关 键 词：相对论时空 双曲Minkowski空间 LORENTZ变换 

分 类 号：O412.1-0[理学—理论物理]