Superluminal Motion in The interacting System of Electrons, Positrons and Photons

Abstract

The coupled system of Boltzman equations for the interacting system of electrons, positrons and photons in high external electric, E, and arbitrary magnetic, H, fields is solved. The consideration is made under the conditions of arbitrary heating and the mutual drag of carriers and photons. The non-stationary and non-uniform distribution function of photons for the all considered cases is obtained. It is shown that the distribution function of photons has the stationary limit for the drift velocities $(\vec{u}\vec{q}/ \hbar ω_q) <1 $ and grows exponentially with time for the drift velocities $(\vec{u}\vec{q}/ \hbar ω_q) \geq 1$. As a result of the analyses of the phenomena of coupling of the mutual drag system of carriers with the photons, we obtained some fundamental results: {\bf a)} the finiteness of the mass of photon (i.e. the rest mass of the photons is not zero); {\bf b)} reality of tachyons as a quasi-particles with a real mass in amplifying system (or regime); {\bf c)} the mechanism of the theory of relativity and that of the Doppler effect which coincides with the renormalization of frequency or mass as a result of the mutual drag of carriers and photons at external field (force) are the same. These conclusions were obtained as a result of the fact that the relativistic factor enters the expressions of the distribution function of photons and other physical expressions in the first order in the form $[1-(u^2/c^2) ]^{-1}$, but not in the form $[1-(u^2/c^2) ]^{-1/2}$ as in Einstein&#39;s theory. Also it is shown that the velocity of light is an average velocity of photons in the ground state.