Special relativity and theory of gravity via maximum symmetry and localization

Like Euclid, Riemann and Lobachevski geometries are on an almost equal footing, based on the principle of relativity of maximum symmetry proposed by Professor Lu Qikeng and the postulate on invariant universal constants c and R, the de Sitter/anti-de Sitter (dS/AdS) special relativity on dS/AdS-space with radius R can be set up on an almost equal footing with Einstein’s special relativity on the Minkowski-space in the case of R→∞. Thus the dS-space is coin-like: a law of inertia in Beltrami atlas with Beltrami time simultaneity for the principle of relativity on one side, and the proper-time simultaneity and a Robertson-Walker-like dS-space with entropy and an accelerated expanding S ³ fitting the cosmological principle on another side. If our universe is asymptotic to the Robertson-Walker-like dS-space of R ≃ (3/Λ)1/2, it should be slightly closed in O(Λ) with entropy bound S ≃ 3πc ³ k _B /ΛGħ. Contrarily, via its asymptotic behavior, it can fix on Beltrami inertial frames without ‘an argument in a circle’ and acts as the origin of inertia. There is a triality of conformal extensions of three kinds of special relativity and their null physics on the projective boundary of a 5-d AdS-space, a null cone modulo projective equivalence ] ≅ ∂ _P (AdS ⁵). Thus there should be a dS-space on the boundary of S ⁵ × AdS ⁵ as a vacuum of supergravity. In the light of Einstein’s ‘Galilean regions’, gravity should be based on the localized principle of relativity of full maximum symmetry with a gauge-like dynamics. Thus, this may lead to the theory of gravity of corresponding local symmetry. A simple model of dS-gravity characterized by a dimensionless constant g ≃(ΛGħ/3c ³)^1/2 ∼ 10⁻⁶¹ shows the features on umbilical manifolds of local dS-invariance. Some gravitational effects out of general relativity may play a role as dark matter. The dark universe and its asymptotic behavior may already indicate that the dS special relativity and dS-gravity be the foundation of large scale physics. This work was partially supported by the National Natural Science Foundation of China (Grant No. 90503002)