Evidence for Special Relativity with de Sitter Space-Time Symmetry

Abstract

I show the formulation of de Sitter Special Relativity (dS-SR) based on Dirac-Lu-Zou-Guo's discussions. dS-SR quantum mechanics is formulated, and the dS-SR Dirac equation for hydrogen is suggested. The equation in the earth-QSO framework reference is solved by means of the adiabatic approach. It's found that the fine-structure "constant" $\alpha$ in dS-SR varies with time. By means of the $t-z$ relation of the $\Lambda$CDM model, $\alpha$'s time-dependency becomes redshift $z$-dependent. The dS-SR's predictions of $\Delta\alpha/\alpha$ agree with data of spectra of 143 quasar absorption systems, the dS-space-time symmetry is SO(3,2) (i.e., anti-dS group) $\;$ and the universal parameter $R$ (de Sitter ratio) in dS-SR is estimated to be $R\simeq 2.73\times 10^{12}ly$. The effects of dS-SR become visible at the cosmic space-time scale (i.e., the distance $\geq 10^9 ly$). At that scale dS-SR is more reliable than Einstein SR. The $\alpha$-variation with time is an evidence of SR with de Sitter symmetry.