The Fundamental Constants if $c$ is Changing: A New Mass Constant and its Connection with the Electron

When special relativity is extended to expanding hyperbolic position space [1], $c$ decreases as $t^{-1/2}$ and there is a new expansion constant, $\sigma =c_0 ^2H_0 ^{-1}=3.89\times 10^{34}$ m$^2$s^{-1}$. Many fundamental constants become time-dependent and must be corrected by a small power of $c$. The corrected electrical permittivity of space is $\bar {\varepsilon }_{o} =\varepsilon_o c$, and $\alpha $ remains constant. The corrected gravitation constant is $\bar {G}=G/c$. A new fundamental mass constant of gravitation and cosmology occurs, $m_\ast =\left( {\hbar ^2/\bar {G}\sigma } \right)^{1/3}=\left( {\hbar ^2H_0 /G_0 c_0 } \right)^{1/3}$, with the value $1.087\left( {\pm 0.010} \right)\times 10^{-28}\mbox{ kg}$. Its product $\alpha m_\ast $ with $\alpha $ accounts for 87{\%} of the observed inertial mass $m_e $ of the electron. This establishes a new phenomenological relationship between the constants of electromagnetism and the electron on the one hand and those of gravitation and cosmology on the other. \newline [1] F. T. Smith, Ann. Fond. L. de Broglie, \textbf{30}, 179 (2005); ); http://www.ensmp.fr/aflb/AFLB-302/table302.htm