[Paper Review] The analysis of Hardy's experiment revisited

Lev Vaidman|ArXiv.org|Mar 12, 1997

Musicology and Musical Analysis3 citations

TL;DR

This paper reaffirms Lev Vaidman's original analysis of Hardy's paradox, countering Cohen and Hiley's criticism by defending the role of the 'product rule' failure in pre- and post-selected quantum systems. It demonstrates that the contradiction in Hardy's gedanken experiment arises not from quantum mechanics' inconsistency, but from the invalid application of classical reasoning to quantum elements of reality, reinforcing the non-classical nature of quantum theory in weak measurement contexts.

ABSTRACT

Cohen and Hiley [Phys. Rev. A 52, 76 (1995)] have criticized the analysis of Hardy's gedanken experiment according to which the contradiction with quantum theory in Hardy's experiment arises due the failure of the "product rule" for the elements of reality of pre- and post-selected systems. It is argued that the criticism of Cohen and Hiley is not sound.

Motivation & Objective

• To respond to Cohen and Hiley's criticism of the original analysis of Hardy's gedanken experiment.
• To reaffirm that the contradiction in Hardy's experiment stems from the failure of the product rule for elements of reality in pre- and post-selected systems.
• To clarify the conceptual foundations of quantum mechanics in weak measurement and retrodiction contexts.
• To reinforce the non-classical nature of quantum reality by showing that classical reasoning leads to inconsistency in quantum predictions.
• To establish that the inconsistency in Hardy's paradox is not a flaw in quantum theory, but a consequence of applying classical logic to quantum elements of reality.

Proposed method

• Analyzes the logical structure of Hardy's gedanken experiment using the framework of pre- and post-selected quantum systems.
• Applies the product rule for elements of reality, which classically states that if A and B are real, then AB is real.
• Identifies that in Hardy's setup, the product rule fails due to quantum interference effects in the joint state.
• Uses the formalism of weak measurements and retrodiction to assess the reality of joint outcomes in entangled systems.
• Compares the predictions of quantum mechanics with classical expectations to expose the inconsistency arising from classical reasoning.
• Demonstrates that the contradiction in Hardy's paradox is not a failure of quantum mechanics but a consequence of assuming classical elements of reality.

Experimental results

Research questions

• RQ1 Why does Hardy's gedanken experiment appear to contradict quantum mechanics?
• RQ2 What is the role of the product rule in determining the reality of joint outcomes in pre- and post-selected systems?
• RQ3 How does Cohen and Hiley's criticism of the original analysis hold up under scrutiny?
• RQ4 Can the contradiction in Hardy's paradox be explained without rejecting quantum mechanics?
• RQ5 In what way does quantum mechanics violate classical reasoning about elements of reality?

Key findings

• The contradiction in Hardy's paradox arises not from quantum mechanics being inconsistent, but from the failure of the product rule when applied to elements of reality in pre- and post-selected systems.
• Cohen and Hiley's criticism is shown to be unsound, as their argument misrepresents the assumptions and logical structure of the original analysis.
• The failure of the product rule is a direct consequence of quantum interference and nonlocality, not a flaw in the formalism.
• Quantum mechanics remains consistent when applied to pre- and post-selected systems, even when classical reasoning leads to paradoxical conclusions.
• The analysis confirms that quantum theory does not allow for a consistent classical description of joint properties in entangled systems, reinforcing the non-classical nature of quantum reality.
• The results support the view that quantum mechanics cannot be completed by adding elements of reality that obey classical logic.