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

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Beltrami-de Sitter -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de Sitter/反de Sitter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Robertson-Walker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Beltrami-de Sitter/反de Sitter时空，宇宙学常数恰恰给出惯性运动的起 源. 关键词： 狭义相对性原理 宇宙学原理 de Sitter不变的狭义相对论 Beltrami-de Sitter时空 同时性 Mach原理

Beltrami-de Sitter spacetime and de Sitter invariant special relativity

The puzzle on the relation between principle of special relativ ity and cosmological principle, as well as the Beltrami-de Sitter-Lu puzzle on de Sitter/anti-de Sitter spacetimes in ~Einstein'KG-*6]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 observers 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'KG-*6]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 gives 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'KG-*5]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.