Beltrami-de Sitter spacetime and de Sitter invariant special relativity
Beltrami-de Sitter spacetime and de Sitter invariant special relativity
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贝尔特拉米-德西特时空和德西特不变狭义相对论
DOI：
10.7498/aps.54.2494
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发表时间：
2005-06
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分析了狭义相对论原理与宇宙学原理之间的关系之谜，以及爱因斯坦相对论框架中de Sitter/反de Sitter时空的Beltrami-de Sitter-Lu之谜。将狭义相对论原理推广到常曲率时空，并用Beltrami度规建立de Sitter/anti de Sitter时空狭义相对论的运动学和粒子动力学是可能的。在这样的Beltrami系统中，Beltrami坐标下的同时性只是一个惯性系统，相应的ob服务器是惯性观测者，惯性定律对测试粒子和光信号是有效的，并且可以很好地定义守恒和满足广义爱因斯坦公式的观测值。除了Beltrami坐标的同时性外，还存在旋转观测的适当时间同时性，从而将Beltrami度规转换为类Robertson-Walker度规，从而给出了一个封闭的三维空间，其与平面度的偏差为宇宙常数的数量级。因此，在这样一种狭义相对论中，相对论原理与“完美”宇宙学原理有着内在的联系，没有任何困惑。此外，根据最近的天文观测，重申了马赫原理，并证明了宇宙常数只是作为Beltrami-de Sitter时空中de Sitter不变狭义相对论中惯性运动的原点。
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.