THE SOLUTION TO HARDY’S PARADOX

Abstract

BY USING BOTH THE WEAK-VALUE FORMULATION AS WELL AS THE STANDARD PROBABILISTIC APPROACH, WE ANALYZE HARDY’S EXPERIMENT INTRODUCING A COMPLEX AND DIMENSIONLESS PARAMETER (ϵ), WHICH ELIMINATES THE ASSUMPTION OF COMPLETE ANNIHILATION WHEN BOTH THE ELECTRON AND THE POSITRON DEPARTING FROM A COMMON ORIGIN CROSS THE INTERSECTION POINT P. WE THEN FIND THAT THE PARADOX DOES NOT EXIST FOR ALL THE POSSIBLE VALUES TAKEN BY THE PARAMETER. THE APPARENT PARADOX ONLY APPEARS WHEN ϵ=1, WHICH IS JUST A SINGULAR VALUE. IN THIS PAPER WE DEMONSTRATE THAT THIS PARTICULAR VALUE IS FORBIDDEN INSIDE THE SCENARIO PROPOSED BY THE EXPERIMENT.