In 1956 Mark Kac proposed a process related to the telegrapher equation where the particle travels at constant speed (say the speed of light c) and randomly inverts its velocity. This process had important applications concerning the path-integral solution and the probabilis- tic interpretation of the 1+1 dimensions Dirac equation. The extension to 3+1 dimensions requires that the particle only moves at light-speed, which implies that velocity can be rep- resented as a point on the surface of a sphere of radius c. The realizations of the process for the velocity only may connect these points, and, by strict analogy with the Kac model, it can be assumed that the velocity jumps from one value to another. In this paper we follow a new and different strategy assuming that the velocity performs continuous trajectories (velocity changes direction in a continuous way) which are the realization of a Wiener process on the surface. The processes which emerge transform one in the other by Lorentz boost. The associate Forward Kolmogorov Equation for the joint probability density of position and velocity, which is the (3+1) dimensional analogous of the telegrapher equation, is examined and a simplification is performed by means of variables separation.
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