Time-Symmetrized Quantum Theory, Counterfactuals, and `Advanced Action'

TL;DR

This paper examines the objections to the counterfactual interpretation of the time-symmetrized quantum theory (TSQT), analyzes Vaidman's proposed solutions, and explores the connection to Price's concept of 'advanced action' to clarify the theory's validity.

Contribution

The paper distinguishes between counterfactual and non-counterfactual readings of the ABL rule and critically evaluates Vaidman's new definitions of time-symmetrized counterfactuals.

Findings

Vaidman's definitions do not fully resolve the objections.

The special case by Cohen and Hiley remains valid.

A link between TSQT and Price's 'advanced action' is established.

Abstract

Recent authors have raised objections to the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz (ABL) rule of time symmetrized quantum theory (TSQT). I distinguish between two different readings of the ABL rule, counterfactual and non-counterfactual, and confirm that TSQT advocate L. Vaidman is employing the counterfactual reading to which these authors object. Vaidman has responded to the objections by proposing a new kind of time-symmetrized counterfactual, which he has defined in two different ways. It is argued that neither definition succeeds in overcoming the objections, except in a special case previously noted by Cohen and Hiley. In addition, a connection is made between TSQT and Price's concept of `advanced action', which further supports the special case discussed.