[Paper Review] Decoherence and the Transactional Interpretation

Ruth E. Kastner|arXiv (Cornell University)|Apr 1, 2020

Quantum Mechanics and Applications22 references4 citations

TL;DR

This paper integrates decoherence into the Transactional Interpretation (TI) of quantum mechanics by showing that TI's objective, non-unitary reduction naturally produces the same decoherence function as standard quantum theory. Unlike unitary-only approaches, TI allows the reduced density operator to represent an actual measurement outcome, resolving the measurement problem with physical realism and consistent dynamics.

ABSTRACT

This paper presents an analysis of decoherence resulting from the physically real non-unitarity, or 'objective reduction,' that occurs in the Transactional Interpretation (TI). Two distinct aspects of the decoherence process are identified and disambiguated; specifically, (i) the resolution of the basic measurement interaction with respect to the observable under study, and (ii) the effect on the measured system of repetition of the measurement interaction. It is shown that the measurement interaction as described in TI leads naturally to the same quantitative expression for the decoherence function as in the standard unitary-only account. However, unlike in the unitary-only approach, under TI, the reduced density operator for the measured system can legitimately be interpreted as representing the occurrence of an actual measurement result.

Motivation & Objective

• To reconcile decoherence with the Transactional Interpretation (TI), which posits physically real, non-unitary reductions.
• To clarify the distinction between two aspects of decoherence: measurement interaction resolution and repeated interaction effects.
• To demonstrate that TI yields the same quantitative decoherence function as standard quantum mechanics.
• To show that in TI, the reduced density operator represents an actual measurement result, not just a statistical ensemble.
• To provide a physically realist foundation for decoherence without relying on unitary evolution alone.

Proposed method

• Analyzes the transactional process as a handshake between retarded and advanced waves, leading to a physically real transaction.
• Identifies two components of decoherence: (i) the resolution of the measurement interaction for a specific observable, and (ii) the cumulative effect of repeated interactions.
• Derives the decoherence function in TI and shows it matches the standard unitary expression.
• Uses the transactional framework to interpret the reduced density operator as representing an actualized outcome, not just a statistical mixture.
• Applies the formalism to a two-level system to demonstrate consistency with standard decoherence results.
• Establishes that objective reduction in TI avoids the measurement problem by collapsing the state non-unitarily.

Experimental results

Research questions

• RQ1 How does the Transactional Interpretation reproduce the standard decoherence function without relying on unitary evolution?
• RQ2 What is the physical meaning of the reduced density operator in TI, and how does it differ from the standard interpretation?
• RQ3 How do the two distinct aspects of decoherence—measurement interaction resolution and repeated interaction effects—manifest in TI?
• RQ4 Can TI provide a physically realist account of decoherence that avoids the measurement problem?
• RQ5 Does the inclusion of objective reduction in TI lead to consistent predictions with standard quantum mechanics?

Key findings

• The decoherence function derived in the Transactional Interpretation matches the standard unitary expression exactly, ensuring consistency with experimental predictions.
• The reduced density operator in TI represents an actualized measurement outcome, not just a statistical ensemble, due to objective reduction.
• The transactional process naturally accounts for both aspects of decoherence: the resolution of a single measurement and the cumulative effect of repeated interactions.
• Objective reduction in TI provides a physically realist mechanism for wave function collapse, resolving the measurement problem.
• The framework maintains unitary dynamics for the total system while allowing for non-unitary, physically real reduction in the subsystem, consistent with empirical decoherence.