Beltrami-de Sitter时空和de Sitter不变的狭义相对论  

Beltrami-de Sitter spacetime and de Sitter invariant special relativity

作　　者：郭汉英[1] 黄超光[1] 田雨[2] 徐湛[3] 周彬[1] 

机构地区：[1]中国科学院高能物理研究所,北京100049 [2]中国科学院理论物理研究所,北京100080 [3]清华大学物理系和高等研究中心,北京100084

出　　处：《物理学报》2005年第6期2494-2504,共11页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:90103004;10175070;10375087;10373003;10347148;90403023)部分资助的课题.~~

摘　　要：分析了在相对论体系中狭义相对性原理和宇宙学原理之间的关系以及BeltramideSitter陆启铿疑难.指出可以把狭义相对性原理推广到非零常曲率时空,在具有Beltrami度规的deSitter反deSitter时空中建立狭义相对论的运动学和粒子动力学.在这类狭义相对论中,相对于Beltrami坐标同时性,Beltrami坐标系就是惯性坐标系,相应的观测者为惯性观测者;对于自由粒子和光讯号,惯性定律成立;可以定义可观测量,它们不但守恒而且还满足推广的爱因斯坦关系.除了Beltrami坐标时同时性之外,对于共动观测,还可以取固有时同时性;此时,Beltrami度规成为RobertsonWalker型的度规,其3维空间是闭的,对于平坦的偏离为宇宙学常数的量级.这表明,在这类狭义相对论中,相对性原理与“完美”宇宙学原理之间存在内在联系,并不存在那些问题.进而,基于最新观测事实,重述了Mach原理;指出对于BeltramideSitter反deSitter时空,宇宙学常数恰恰给出惯性运动的起源.The puzzle on the relation between principle of special relativity and cosmological principle, as well as the Beltrami-de Sitter-Lu puzzle on de Sitter/anti-de Sitter spacetimes in Einstein's framework of relativity are analyzed. It is possible to generalize the principle of special relativity to the spacetimes with constant curvature and to establish the kinematics and particle dynamics for the special relativity in de Sitter/anti-de Sitter spacetimes with Beltrami metric. In such a Beltrami system by the Beltrami coordinate simultaneity is just an inertial system, the corresponding ob servers are inertial observers, the inertial law is valid for test particles and light signals, and observables can be well defined which conserve and satisfy the generalized Einstein's formula. In addition to the Beltrami coordinate simultaneity there is also the proper-time simultaneity for the comoving observations and thus the Beltrami metric is transformed into the Robertson-Walker-like metric which give's a closed 3-dimensional space and its deviation from flatness is of the order of cosmological constant. Therefore, it turns out that in such a kind of special relativity the relativity principle has an intrinsic affiliation with the 'perfect' cosmological principle and without any puzzle. Furthermore, based on the recent astronomical observations, the Mach's principle is restated and it is showed that the cosmological constant acts just as an origin of inertial motions in the de Sitter-invariant special relativity on Beltrami-de Sitter spacetime.

关 键 词：狭义相对性原理 宇宙学 狭义相对论 MACH原理 惯性运动 

分 类 号：O412.1[理学—理论物理]