Nonlocality of the Aharonov-Bohm effect

Abstract

Although the Aharonov-Bohm and related effects are familiar in solid-state and high-energy physics, the nonlocality of these effects has been questioned. Here we show that the Aharonov-Bohm effect has two very different aspects. One aspect is instantaneous and nonlocal; the other aspect, which depends on entanglement, unfolds continuously over time. While local, gauge-invariant variables may occasionally suffice for explaining the continuous aspect, we argue that they cannot explain the instantaneous aspect. Thus the Aharonov-Bohm effect is, in general, nonlocal.

Anomalous weak values and the violation of a multiple-measurement Leggett-Garg inequality

“…Postselection procedures are expected to be mostly harmless in classical statistics, although the subject is vigorously debated [38][39][40][41][42][43]; in this context, postselection carried out in the weak-measurement regime can lead to anomalous values, in that they fall outside the range allowed for standard values [44,45]. When one allows for such a weak measurement to be performed in a Leggett-Garg test, then a direct connection can be established between the violation of macrorealism and the emergence of anomalous postselected values [16,35,46], like it was demonstrated for quantum contextuality [47,48].…”

Comment on “Role of potentials in the Aharonov-Bohm effect”

“…Thus the electromagnetic potentials are, in general, indispensable. In a separate work [8], we further elaborate on the inherently nonlocal features of quantum mechanics. We show how any topological effect comprises two components: a continuous effect that fits Vaidman's approach, and a sudden effect that has no local explanation.…”

Understanding Weak Values Without New Probability Theory

“…Li et al [4,5] challenged Vaidman's claim and insisted that the weak trace could be understood without any unusual probability theory if the disturbances of the weak measurements are considered. However, they agreed with Vaidman with regard to the physical meaning of the weak values.Moreover, Ferrie and Combes [6,7] argued that weak values are classical statistic quantities, which gave rise to a number of rebuttals [8][9][10][11][12]. In particular, Pusey [13] showed that anomalous (imaginary, negative, and unbounded) weak values are non-classical and proofs of contextuality.…”

“…Moreover, Ferrie and Combes [6,7] argued that weak values are classical statistic quantities, which gave rise to a number of rebuttals [8][9][10][11][12]. In particular, Pusey [13] showed that anomalous (imaginary, negative, and unbounded) weak values are non-classical and proofs of contextuality.…”