Quantum Force and Space-Time Topology*

Zeilinger’s dispersivity theorem predicts the absence of force, while Shelankov and Berry predict the presence of a force for the Aharonov-Bohm effect. An experiment is presented that supports Shelankov and Berry’s prediction, while theory is presented to encompass both predictions thus resolving this confusing problem [1]. Even if we feel that this issue is now resolved others remain [2], In particular, we will present a theoretical argument that questions the idea that one must enclose a magnetic flux to observe the Aharonov-Bohm effect [3]. The idea is offered that spatial topology that is relevant for the Aharonov-Bohm effect is part of a space-time topology that may be used to escape the requirement that one has to enclose a magnetic flux, while still preserving gauge invariance. New experimental thought experiments [4] and the Berry-connection to what this means for other Berry phase examples are presented.

[1] Maria Becker, Giulio Guzzinati, Armand Béché, Johan Verbeeck & Herman Batelaan, Asymmetry and non-dispersivity in the Aharonov-Bohm effect, Nature Comm. 10, 1700 (2019).  

[2] Herman Batelaan and Akira Tonomura, The Aharonov–Bohm effects: Variations on a subtle theme. Physics Today 62, 38 (2009).

[3] Pablo L. Saldanha,  Electrodynamic Aharonov-Bohm effect, Phys. Rev. A 108, 062218, December 2023.

[4] Pablo L. Saldanha and Herman Batelaan, Topological schemes in spacetime for the electrodynamic Aharonov-Bohm effect, submitted to EPL, arXiv:2411.09622.