Bohm's Theorem

W. Michael Dickson

Mark D. Semon, John R. Taylor

In a recent paper [D. H. Kobe, V. C. Aguilera-Navarro, and R. M. Ricotta, Phys. Rev. A 45, 6192 (1992)], Kobe et al. have calculated the expectation values of position and momentum in the Aharonov-Bohm effect and have found that both are shifted by the Aharonov-Bohm potentials. Although these shifts appear to contradict certain ``no-shift'' theorems proved by various authors, we show that this apparent contradiction is the result of different assumptions. Specifically, one of the assumptions on which the no-shift theorems are based does not hold for the parameters used by Kobe et al.; that is, with their parameters, there is no reason to expect the no-shift theorems to hold. On the other hand, with the parameters of actual two-slit experiments, all of the conditions of the no-shift theorems do hold and the no-shift theorems do apply.

Maria Becker, Giulio Guzzinati, Armand Béché +2 more

Abstract Decades ago, Aharonov and Bohm showed that electrons are affected by electromagnetic potentials in the absence of forces due to fields. Zeilinger’s theorem describes this absence of classical force in quantum terms as the “dispersionless” nature of the Aharonov-Bohm effect. Shelankov predicted the presence of a quantum “force” for the same Aharonov-Bohm physical system as elucidated by Berry. Here, we report an experiment designed to test Shelankov’s prediction and we provide a theoretical analysis that is intended to elucidate the relation between Shelankov’s prediction and Zeilinger’s theorem. The experiment consists of the Aharonov-Bohm physical system; free electrons pass a magnetized nanorod and far-field electron diffraction is observed. The diffraction pattern is asymmetric confirming one of Shelankov’s predictions and giving indirect experimental evidence for the presence of a quantum “force”. Our theoretical analysis shows that Zeilinger’s theorem and Shelankov’s result are both special cases of one theorem.

Mary Beth Ruskai

Maria Becker, Giulio Guzzinati, Armand Béché +2 more

Decades ago, Aharonov and Bohm showed that electrons are affected by electromagnetic potentials in the absence of forces due to fields. Zeilinger's theorem describes this absence of classical force in quantum terms as the "dispersionless" nature of the Aharonov-Bohm effect. Shelankov predicted the presence of a quantum "force" for the same Aharonov-Bohm physical system as elucidated by Berry. Here, we report an experiment designed to test Shelankov's prediction and we provide a theoretical analysis that is intended to elucidate the relation between Shelankov's prediction and Zeilinger's theorem. The experiment consists of the Aharonov-Bohm physical system; free electrons pass a magnetized nanorod and far-field electron diffraction is observed. The diffraction pattern is asymmetric confirming one of Shelankov's predictions and giving indirect experimental evidence for the presence of a quantum "force". Our theoretical analysis shows that Zeilinger's theorem and Shelankov's result are both special cases of one theorem.