Special Theory for Superluminal Particle

Abstract

The OPERA collaboration reported evidence for muonic neutrinos travelling faster than light in vacuum. In this paper, an extended relativity theory is proposed. We think all particles can be divided into three kinds: The first kind of particle is its velocity in the range of $0\leq v < c$, e.g. electron, atom, molecule and so on ($c$ is light velocity, i.e., the limit velocity of the first kind of particle). The second kind of particle is its velocity in the range of $0\leq v < c_{m1}$, e.g. photon ($c_{m1}$ is the limit velocity of the second kind of particle). The third kind of particle is its velocity in the range of $c\leq v < c_{m2}$, e.g. tachyon, and muonic neutrinos ($c_{m2}$ is the limit velocity of the third kind of particle). The first kind of particle is described by the special relativity. With the extended relativity theory, we can describe the second and third kinds particles, and can analysis the OPERA experiment results and calculate the muonic neutrinos mass.