THE SOLUTION TO THE HARDY’S PARADOX

Abstract

BY USING BOTH, THE WEAK-VALUE FORMULATION AS WELL AS THE STANDARD PROBABILISTIC APPROACH, WE ANALYZE THE HARDY'S EXPERIMENT INTRODUCING A COMPLEX AND DIMENSIONLESS PARAMETER ($EPSILON$) 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 $EPSILON=1$||HOWEVER, EVEN IN THIS CASE WE CAN INTERPRET THIS RESULT AS A NATURAL CONSEQUENCE OF THE FACT THAT THE PARTICLES CAN CROSS THE POINT $P$, BUT AT DIFFERENT TIMES DUE TO A NATURAL CONSEQUENCE OF THE ENERGY-TIME UNCERTAINTY PRINCIPLE.