Implication of Spatial and Temporal Variations of the Fine-Structure Constant

Temporal and spatial variation of fine-structure constant $\alpha\equiv e^2/\hbar c$ in cosmology has been reported in analysis of combination Keck and VLT data. This paper studies this variation based on consideration of basic spacetime symmetry in physics. Both laboratory $\alpha_0$ and distant $\alpha_z$ are deduced from relativistic spectrum equations of atoms (e.g.,hydrogen atom) defined in inertial reference system. When Einstein's $\Lambda\neq 0$, the metric of local inertial reference systems in SM of cosmology is Beltrami metric instead of Minkowski, and the basic spacetime symmetry has to be de Sitter (dS) group. The corresponding special relativity (SR) is dS-SR. A model based on dS-SR is suggested. Comparing the predictions on $\alpha$-varying with the data, the parameters are determined. The best-fit dipole mode in $\alpha$'s spatial varying is reproduced by this dS-SR model. $\alpha$-varyings in whole sky is also studied. The results are generally in agreement with the estimations of observations. The main conclusion is that the phenomenon of $\alpha$-varying cosmologically with dipole mode dominating is due to the de Sitter (or anti de Sitter) spacetime symmetry with a Minkowski point in an extended special relativity called de Sitter invariant special relativity (dS-SR) developed by Dirac-In\"{o}n\"{u}-Wigner-G\"{u}rsey-Lee-Lu-Zou-Guo.