Can a Particle's Velocity Exceed the Speed of Light in Empty Space?

Abstract

Relative motion in space with multifractal time (fractional dimension of time close to integer $d_{t}=1+\epsilon (r,t), \epsilon \ll 1$) for "almost" inertial frames of reference (time is almost homogeneous and almost isotropic) is considered. Presence in such space of absolute frames of reference and violation of conservation laws (though, small because of the smallness of $\epsilon$) due to the openness of all physical systems and inhomogeneiy of time are shown. The total energy of a body moving with $v=c$ is obtained to be finite and modified Lorentz transformations are formulated. The relation for the total energy (and the whole theory) reduce to the known formula of the special relativity in case of transition to the usual time with dimension equal to one.