Path integrals, the ABL rule and the three-box paradox

Abstract

The three-box problem is analysed in terms of virtual pathways, interference between which is destroyed by a number of intermediate measurements. The Aharonov-Bergmann-Lebowitz (ABL) rule is shown to be a particular case of Feynman's recipe for assigning probabilities to exclusive alternatives. The 'paradoxical' features of the three box case arise in an attempt to attribute, in contradiction to the uncertainty principle, properties pertaining to different ensembles produced by different intermediate measurements to the same particle. The effect can be mimicked by a classical system, provided an observation is made to perturb the system in a non-local manner.

References in corpus (5)

• The Three-Box Paradox Revisited
• Classical Three-Box "paradox"
• Logical Pre- and Post-Selection paradoxes, measurement-disturbance and contextuality
• Feynman-path analysis of Hardy's paradox: measurements and the uncertainty principle
• Reply to "The three-box paradox revisited" by Ravon and Vaidman

Cited by in corpus (7)

• The meaning of "anomalous weak values" in quantum and classical theories
• Weak measurements measure probability amplitudes (and very little else)
• Three-box paradox and "Cheshire cat grin": the case of spin-1 atoms
• Path probabilities for consecutive measurements, and certain "quantum paradoxes"
• Speakable and unspeakable in quantum measurements
• No contextual advantage in non-paradoxical scenarios of two state vector formalism
• Why physical understanding should precede the mathematical formalism - conditional quantum probabilities as a case-study