[Paper Review] The Hardy Experiment in the Transactional Interpretation

Ruth E. Kastner|arXiv (Cornell University)|Jun 25, 2010

Quantum Mechanics and Applications11 references3 citations

TL;DR

This paper applies the possibilist transactional interpretation (PTI) to the Hardy experiment, resolving its apparent paradox by rejecting the notion that state vector components correspond to actual particles in spacetime regions. PTI provides a consistent, non-local account of quantum correlations through advanced and retarded waves, showing that the paradox dissolves when non-actualized possibilities are properly accounted for.

ABSTRACT

The Hardy experiment is analyzed from the standpoint of the Transactional Interpretation (TI) in its possibilist variant, PTI. It is argued that PTI provides a natural and illuminating account of the associated phenomena, resolving the apparent paradox which arises from the mistaken notion that components of the state vector labeled by spacetime regions imply the actual presence of a corpuscle in that region.

Motivation & Objective

• To resolve the conceptual paradox in the Hardy experiment using the possibilist transactional interpretation (PTI).
• To challenge the interpretation that state vector components imply actual particle presence in specific spacetime regions.
• To provide a coherent account of non-local quantum correlations without retrocausality or collapse.
• To clarify the role of possible transactions in quantum measurement processes.

Proposed method

• Applying the possibilist transactional interpretation (PTI), which treats quantum processes as transactions between advanced and retarded waves.
• Modeling the Hardy experiment using PTI's framework of offer and confirmation waves to describe quantum events.
• Analyzing the interference and non-local correlations in the experiment through the lens of possible transactions rather than actual particle trajectories.
• Using the transactional process to explain why the joint probability of certain outcomes is zero, resolving the apparent contradiction.
• Emphasizing that state vector components do not imply actual particles in spacetime regions, countering a common misinterpretation.
• Reframing the measurement process as a selection of a specific transaction from a set of possibilities, avoiding the need for wavefunction collapse.

Experimental results

Research questions

• RQ1 How does the possibilist transactional interpretation (PTI) account for the correlations observed in the Hardy experiment?
• RQ2 Why does the standard interpretation lead to a paradox in the Hardy experiment, and how does PTI resolve it?
• RQ3 What is the physical meaning of state vector components in spacetime regions according to PTI?
• RQ4 Can non-local quantum correlations be explained without invoking retrocausality or particle localization?
• RQ5 How does PTI differ from standard interpretations in describing the measurement process in the Hardy experiment?

Key findings

• The apparent paradox in the Hardy experiment arises from the mistaken belief that components of the state vector correspond to actual particles in spacetime regions.
• PTI resolves the paradox by showing that the joint outcome with zero probability results from the absence of a valid transaction, not from a contradiction in quantum mechanics.
• The transactional process in PTI naturally accounts for non-local correlations through the exchange of advanced and retarded waves.
• The interpretation avoids the need for wavefunction collapse or retrocausal signaling, providing a consistent ontological framework.
• The analysis demonstrates that the state vector describes a set of possibilities, not actualities, and that only a completed transaction corresponds to a physical outcome.
• The paper concludes that the Hardy experiment is fully consistent within PTI, with no violation of relativity or causality.