A New Physical Meaning of Sommerfeld Fine Structure Constant

Identifying physical space or Casimir vacuum as a \textit{compressible} tachyon fluid, Planck compressible ether, leads to stochastic definitions of Planck h $=$ m$_{k}$ \textless $\lambda_{k}$\textgreater c and Boltzmann k $=$ m$_{k}$ \textless $\nu_{k}$\textgreater c constants, finite photon mass m$_{k}=$ (hk/c$^{3})^{1/2}$, amu $=$ m$_{k}$c$^{2}=$ (hkc)$^{1/2}$, and modified Avogadro-Loschmidt number N$_{o}=$ 1/(hkc)$^{1/2}=$ 6.03766 x10$^{23}$ mole$^{-1}$. Thus, Lorentz-FitzGerald contractions now result from compressibility of physical space and become \textit{causal} (Pauli) in accordance with Poincar\'{e}-Lorentz dynamic theory of relativity as opposed to Einstein kinematic theory of relativity. At thermodynamic equilibrium h$_{e}=$ m$_{e}$ \textless $\lambda_{e}$\textgreater v$_{e}=$ h$_{k} = $ m$_{k}$\textless $\lambda_{k}$\textgreater c $=$ h, Compton wavelength can be expressed as $\lambda_{c}=$ h/m$_{e}$c $=$ (v$_{e}$/c)h\textless $\lambda_{e}$\textgreater /(m$_{e}$\textless $\lambda_{e}$\textgreater v$_{e}) \quad =\alpha \lambda_{e}$. Hence, Sommerfeld fine structure constant $\alpha $ is identified as the ratio of electron to photon speeds $\alpha =$ e$^{2}$/(2$\varepsilon_{o}$hc) $=$ v$_{e}$/c $=$ 1/137.036. The mean thermal speed of electron at equilibrium with photon gas is v$_{e}=$ 2.187640x10$^{6}$ m/s and its de Broglie wavelength is $\lambda_{e}=$ 3.3250x10$^{-10}$ m. Also, electron kinetic energy for oscillations in two directions \textless x$+$\textgreater and \textless x-\textgreater or $\varepsilon_{e}=$ h$\nu_{e}=$ m$_{e}$v$_{e}^{2}=$ kT$_{e}$ results in electron temperature T$_{e}=$ 3.15690x10$^{5}$ K.