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

TL;DR

This paper explores the possibility of particles exceeding the speed of light within a multifractal time framework, deriving modified Lorentz transformations and finite energy at light speed, extending special relativity.

Contribution

It introduces a model with multifractal time, derives modified Lorentz transformations, and shows finite energy at light speed, challenging traditional relativistic constraints.

Findings

Total energy of a body at speed c is finite.

Modified Lorentz transformations are formulated.

The theory reduces to special relativity when time dimension is one.

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.