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.

Significant improvements. One figure and two tables added in order to clarify the paradox. The most fundamental expressions unchanged and fully verified

References in corpus (4)

• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair
• Quantum Trajectories based on the Weak Value
• Can parallel lives provide a solution to Hardy's paradox?