[Paper Review] Discussion: Time-Symmetric Quantum Counterfactuals

Lev Vaidman|arXiv (Cornell University)|Jan 24, 2014

Quantum Mechanics and Applications14 references3 citations

TL;DR

This paper defends time-symmetric quantum counterfactuals against claims of triviality by correcting misrepresentations in Kastner's critique. It proposes that counterfactuals in quantum mechanics should be defined by fixing measurement outcomes before and after a time t, not by quantum states, enabling non-trivial, consistent counterfactual reasoning in both pre- and post-selected systems, as demonstrated in spin-1/2 and three-boxes examples.

ABSTRACT

There is a trend to consider counterfactuals as invariably time-asymmetric. Recently, this trend manifested itself in the controversy about validity of counterfactual application of a time-symmetric quantum probability rule. Kastner (2003) analyzed this controversy and concluded that there are time-symmetric quantum counterfactuals which are consistent, but they turn out to be trivial. I correct Kastner's misquotation of my defense of time-symmetric quantum counterfactuals and explain their non-trivial aspects, thus contesting the claim that counterfactuals have to be time-asymmetric.

Motivation & Objective

• To correct Kastner’s misquotation and misinterpretation of the author’s defense of time-symmetric quantum counterfactuals.
• To resolve the apparent contradiction in defining counterfactuals when quantum measurements at time t alter the system’s state.
• To demonstrate that time-symmetric counterfactuals are non-trivial and physically meaningful, not merely tautological.
• To challenge the prevailing trend of viewing counterfactuals as inherently time-asymmetric in quantum foundations.
• To show that fixing measurement results before and after time t, rather than quantum states, enables consistent and non-trivial counterfactual reasoning.

Proposed method

• Re-defines counterfactuals not by quantum states but by the set of results from all measurements performed on a system, both before and after time t.
• Applies this definition to the Aharonov-Bergmann-Lebowitz (ABL) rule, showing that the probability of a measurement outcome at time t depends on both pre- and post-selection.
• Uses the framework of quantum mechanics with pre- and post-selection to construct counterfactuals that are time-symmetric and consistent.
• Analyzes two key examples: a spin-1/2 particle with pre- and post-selected states, and a particle in a superposition of three boxes with specific pre- and post-selection.
• Employs weak measurements and strong interaction models to probe the behavior of systems under time-symmetric counterfactual conditions.
• Applies the many-worlds interpretation to justify the notion of a world defined by measurement outcomes, supporting the consistency of the approach.

Experimental results

Research questions

• RQ1 Can time-symmetric quantum counterfactuals be consistently defined without relying on time-asymmetric assumptions?
• RQ2 Why are Kastner’s claims that time-symmetric counterfactuals are trivial based on a misrepresentation of the author’s original argument?
• RQ3 How can counterfactual reasoning in quantum mechanics be non-trivial when both pre- and post-selection are fixed?
• RQ4 What physical phenomena demonstrate the non-triviality of time-symmetric counterfactuals beyond mere logical consistency?
• RQ5 Does the existence of non-trivial time-symmetric counterfactuals challenge the conventional view that counterfactuals are inherently time-asymmetric?

Key findings

• The author corrects Kastner’s misquotation, showing that the claim that post-selection results cannot be fixed is not a central claim in the original argument.
• The difficulty of state change due to measurement at time t is resolved by defining a world not by its quantum state but by the list of measurement outcomes.
• In the spin-1/2 example, the counterfactual probability for a measurement outcome at time t is non-trivially determined by both pre- and post-selection, yielding a well-defined ABL probability.
• In the three-boxes example, the particle is counterfactually certain to be found in both box A and box B if searched, even though it cannot be in both simultaneously in a classical sense.
• The system exhibits behavior resembling two particles in different boxes when subjected to a superposition of strong measurements, indicating non-trivial time-symmetric behavior.
• The framework supports non-trivial time-symmetric counterfactuals in quantum mechanics, challenging the view that counterfactuals must be time-asymmetric.