Derivation of Relativistic law of Addition of Velocities from Superposition of Eigenfunctions and Discreteness

Abstract

We have defined a slowness, s, as the reciprocal conjugate of velocity, v. s = -ih/v. We have shown that Einstein's postulate (v has an upper limit) implies that s is discrete. A velocity operator is defined as the derivative with respect to s. Superposition of corresponding Eigenfunctions give Galilean law of addition of velocities. We have replaced the differential operator by the corresponding finite difference symmetric operator. We have shown that superposition of corresponding discrete Eigenfunctions give relativistic law of addition of velocities. A reciprocal symmetric number system is developed and with the help of this number system we have shown the relation between superposition and relativistic law of addition of velocities.