The Three-Box "Paradox" and Other Reasons to Reject the Counterfactual Usage of the ABL Rule

TL;DR

This paper critiques the use of the ABL rule in quantum paradoxes, showing that apparent contradictions arise from invalid counterfactual reasoning and are resolved by proper interpretation.

Contribution

It demonstrates that the three-box paradox results from misapplying the ABL rule and connects this analysis to the consistent histories approach.

Findings

The paradox is due to invalid counterfactual application of the ABL rule.

Proper interpretation resolves the apparent contradiction.

Critiques recent counterarguments defending the counterfactual use.

Abstract

An apparent paradox proposed by Aharonov and Vaidman in which a single particle can be found with certainty in two (or more) boxes is analyzed by way of a simple thought experiment. It is found that the apparent paradox arises from an invalid counterfactual usage of the Aharonov-Bergmann-Lebowitz (ABL) rule, and effectively attributes conflicting properties not to the same particle but to different particles. A connection is made between the present analysis and the consistent histories formulation of Griffiths. Finally, a critique is given of some recent counterarguments by Vaidman against the rejection of the counterfactual usage of the ABL rule.