Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
; Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China
; Tsing Hua Univ, Dept Phys, Beijing 100084, Peoples R China
; Tsing Hua Univ, Ctr Adv Study, Beijing 100084, Peoples R China
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.