On a New Position Space Doubly Special Relativity Theory

Abstract

The general consensus feeling amongst researchers is that it is generally difficult to obtain a position space Lorentz invariant Doubly Special Relativity (DSR) theory. In this reading, we propose such a theory. The Lorentz transformations are modified such that the resultant theory has not one, but two invariants -- the speed of light c = 2.99792458x10⁸ms^-1, and a minimum length l_p. Actually, we achieve our desire by infusing Heisenberg's quantum mechanical uncertainty principle into the fabric of Minkowiski spacetime.  It should be stated that this theory has been developed more as a mathematical exercise to obtain a physically reasonable as is possible a position space DSR theory that is Lorentz invariant.  In the low energy regime, the theory gives the same predictions as Einstein's Special Theory of Relativity (STR).