ua nt - p h / 98 07 03 7 v 3 1 0 Fe b 19 99 The Three - Box “ Paradox ” and other Reasons to Reject the Counterfactual Usage of the ABL Rule

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. The Aharonov-Bergmann-Lebowitz (ABL) rule is a well-known formula for calculating the probabilities of the possible outcomes of observables measured at an intermediate time t 1 between pre-and post-selection measurements at