Feynman-path analysis of Hardy's paradox: measurements and the uncertainty principle

TL;DR

This paper analyzes Hardy's paradox using Feynman's path integral approach, revealing how different measurements alter pathways and lead to contradictions, while also exploring the origin of strange weak values.

Contribution

It introduces a Feynman-path framework to clarify Hardy's paradox and the nature of weak values in quantum mechanics.

Findings

Different measurements change the set of real pathways.

Contradictions arise when applying the same ensemble to different measurement contexts.

Weak values are explained within the path integral formulation.

Abstract

Hardy's paradox is analysed within Feynman's formulation of quantum mechanics. A transition amplitude is represented as a sum over virtual paths which different intermediate measurements convert into different sets of real pathways. Contradictory statements emerge when applying to the same statistical ensemble. The "strange" weak values result is also investigated in this context.