Abstract
Common Special Relativity (SR) is invariant under Poincae transformations and its basic space-time metric is Minkowski metric which satisfies the vacuum Einstein equation without cosmologic constant Λ . In this paper it is shown that when Λ ≠ 0 , Poincae invariant SR becomes De Sitter/Anti De Sitter (dS/AdS) Invariant SR. Solving the vacuum Einstein equation with non-zero Λ and considering the inertial moving law for free particle (the first Newton law), it is found that the generic basic metric for SR with Λ ≠ 0 is the Beltrami metric, which was originally suggested by Lu-Zou-Guo in 1974. In this present paper all Killing vectors for Beltrami metric are presented via solving the Killing equations, and that Beltrami space-time has maximum symmetries is shown. Through this way all conservative qualities are found, and dS/AdS invariant SR is formulated. The canonic formalism for dS/AdS SR mechanics has been derived. We find out that the corresponding dispersion relations of positive-version and negative-version Hamiltonian are not symmetric. Comparing with common SR this asymmetry property coming from Λ ≠ 0 is very special. We conjecture that it may leat to reveal the reasons for understanding matter-antimatter asymmetric in the evolutions of the Universe. By using canonic quantization, we formulate dS/AdS SR Quantum Mechanics. The corresponding SR quantum wave equations are given. We briefly introduce and comment the experiments to detect the fine-structure constant ( α ) variations via observing the absorbtion spectrums of atoms (or ions) at z ≈ 1 ~ 3 against quasar’s lines. Such α -change experiment results are against the prediction of that α keeps unchange, which come from the Poincae invariant SR. Considering that α -changes in dS/AdS invariant SR atomic physics have been confirmed in theory, such α -change experiment results could be thought as a support to dS/AdS invariant SR. The physics of dS/AdS-invariant SR is beyond the standard model of physics.
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