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New Journal of Physics

Comment on Reply to Comment on ‘Electromagnetic lensing using the Aharonov–Bohm effect’

Markus Lentzen

Published May 1, 2025• 0 citations
Publisher

Abstract

Abstract Recently, Schreiber and Wolf (2024 New J. Phys. 26 118002) have questioned the validity of Stokes’ theorem, one of the most important tools in the theory of electromagnetism, by stating a counterexample. In this comment it is shown that the counterexample is invalid.
DOI
10.1088/1367-2630/add67f

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Abstract Recently, Schreiber et al (2024 New J. Phys. 26 043012) have presented the theory of an electron lens acting through the Aharonov–Bohm effect in the field-free opening of a static toroidal magnetic field. In this Comment, three key results of this theory are shown to be incorrect due to six basic calculation errors. The errors are corrected, and three correspondingly modified key results are derived. These results are discussed with respect to the hypothetical lens effect and the underlying Aharonov–Bohm effect.
The preceding Comment challenged my claim that potentials might be just auxiliary mathematical tools and that they are not necessary for explaining physical phenomena. The Comment did not confront my explanation without the potentials of the Aharonov-Bohm effects that appeared in the original article, but stated that I cannot apply this explanation for seven other examples. In my reply, using my method, I provide explanations of one of the examples, show that two other examples are not relevant, and agree that the remaining examples require further analysis. However, I argue that none of the examples provides robust counterexamples to my claim, similar to the original Aharonov-Bohm setups which were explained in my article, so the Comment does not refute my claim.
It is argued that the proofs [W. D. Sharp and N. Shanks, Philos. Sci. 60, 488 (1993); O. Cohen, Phys. Rev. A 51, 4373 (1995); D. J. Miller, Phys. Lett. A 222, 31 (1996)] of the general nonvalidity of the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz rule [Y. Aharonov, P. G. Bergmann, and J. L. Lebowitz, Phys. Rev. 134, B1410 (1964)] are perfectly valid, and that Vaidman's rejection of these proofs [L. Vaidman, Phys. Rev. A (Comment for which this paper is the Reply)] is unsustainable. It is demonstrated that Vaidman's proposed formulation of ``counterfactual probability,'' on which his rejection of these proofs depends, is problematic and inconsistent in several respects.