The Ehrenberg-Siday-Aharonov-Bohm Effect

Peter Andrew Sturrock, T. R. Groves

Having read “The Aharonov-Bohm Effects: Variations on a Subtle Theme” by Herman Batelaan and Akira Tono-mura (Physics Today, September 2009, page 38), we note with some dismay that the principal effect, that related to magnetic flux, continues to be attributed to its re-discoverers rather than to the original discoverers. Batelaan and Tonomura write, “The AB effect was already implicit in the 1926 Schrödinger equation, but it would be another three decades before theorists Yakir Aharonov and David Bohm pointed it out.” 1 1. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). That is incorrect: It took only two decades before the effect was pointed out, not by Aharonov and Bohm but by Werner Ehrenberg and Raymond “Rory” Siday. 2 2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Aharonov and Bohm cited that prior publication in their second article. 3 3. Y. Aharonov, D. Bohm, Phys. Rev. 123, 1511(1961). According to Bohm’s biographer F. David Peat, “After their first paper had been published, Bohm learned that the effect had already been postulated by a maverick physicist called Rory E. Siday.” 4 4. F. D. Peat, Infinite Potential: The Life and Times of David Bohm, Addison-Wesley, Reading, MA (1997), p. It seems curious that the biographer should use the term “postulated” rather than “proposed” and that he should comment on Siday’s personality but not on Ehrenberg’s. One of us (Sturrock) knew them both: Raymond was very smart but somewhat brash; Werner was erudite and a model of propriety, who would never have subscribed his name to an article unless he was convinced it was correct.It seems that the main scientific, rather than sociological, reason that the AB proposal was taken more seriously than the ES proposal is that the former was presented in the context of quantum mechanics, the latter in the context of electron optics. Aharonov and Bohm made a rapid transition from quantum mechanics to wave theory. Ehrenberg and Siday made a more detailed transition from geometrical optics to wave theory. For the case of magnetic flux, the two articles presented identical theoretical predictions. Our view is that the ES article was tedious but conceptually sound, whereas the AB article was lively but involved a questionable conceptual leap—namely, a relativistic generalization based on a noncovariant analysis. Soon after Sturrock arrived at Stanford University in 1955, and before the Aharonov-Bohm publication, he asked Leonard Schiff, Stanford’s quantum mechanics expert, whether Schiff found the Ehrenberg-Siday proposal convincing. He did.In the interests of accuracy and of giving credit where credit is due, we think it would be appropriate to use “Ehrenberg-Siday effect” for the case of magnetic interference and to reserve “Aharonov-Bohm effect” for electrical interference.We are indebted to Elliott Bloom, Dieter Kern, Walt Harrison, Peter Hawkes, Garret Moddel, Fabian Pease, Jeff Scargle, and Lenny Susskind for helpful discussions on this matter.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). Google ScholarCrossref, ISI2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Google ScholarCrossref3. Y. Aharonov, D. Bohm, Phys. Rev. 123, 1511(1961). Google ScholarCrossref, ISI4. F. D. Peat, Infinite Potential: The Life and Times of David Bohm, Addison-Wesley, Reading, MA (1997), p. Google Scholar© 2010 American Institute of Physics.

David K. Ferry

Michael Berry

Writing about what is usually termed the Aharonov-Bohm (AB) effect, Peter Sturrock and Timothy Groves argue (Physics Today, April 2010, page 8) that the same physics was discovered a decade earlier 1 1. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). and should rightly be called the Ehrenberg-Siday effect. I agree that Werner Ehrenberg and Raymond Siday deserve recognition for their anticipation of AB. Indeed, in recent talks celebrating the 50th anniversary of AB, I began by describing the unfairly neglected paper by Ehrenberg and Siday. Nevertheless, I have come to a different conclusion from Sturrock and Groves: The expression “Aharonov-Bohm effect” is justified, for two reasons.First, although there is no doubt that the work by Ehrenberg and Siday anticipated how inaccessible magnetic flux can influence electron interference, that was as a curiosity, at the end of a paper whose main emphasis was the Hamiltonian analysis of electron optics. By contrast, Yakir Aharonov and David Bohm emphasized from the start, as an essential and general aspect of quantum mechanics, the physical influence of inaccessible fields that act nonlocally through the vector potential.Second, Ehrenberg and Siday’s semi-classical approximation—essentially applying the Dirac magnetic phase factor to electrons traveling on either side of the flux—implies a wavefunction that is multivalued and therefore not the correct solution of Schrödinger’s equation. The lack of a single-valued wavefunction leaves their prediction open to doubt. By contrast, Aharonov and Bohm derived the exact single-valued solution for waves scattered by a flux line. Recently, it was shown that the Ehrenberg-Siday approximation corresponds to the first terms in a “many-whirls” representation that treats the exact AB wavefunction as a topological sum over paths circling the flux. 2 2. M. V. Berry, J. Phys. A (in press). Attribution of credit is a delicate matter. It tends to excite strong feelings, and I write about it reluctantly. But the Ehrenberg-Siday paper does seem to exemplify the unfortunate phenomenon identified by Alfred North White-head in a 1916 address to the British Association for the Advancement of Science: “Everything of importance has been said before, by someone who did not discover it.”In a companion letter in the April 2010 issue, Alexander Ershkovich correctly points out that the AB effect is present in classical Hamiltonian mechanics, even though remote magnetic fields cannot influence Newtonian trajectories. He advocates a “search for experiments that might prove … a classical analogue of the Aharonov-Bohm effect.” Such an experiment exists already. In the classical physics of waves on a moving medium, the flow velocity acts like the vector potential in quantum mechanics, so the flow vorticity acts like the magnetic field; the analogy is precise. Fine details of the AB wavefunction were observed in ripples on the surface of water swirling irrotationally into a bathtub vortex, 3 3. M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, Eur. J. Phys. 1, 154 (1980). whose core is the analogue of inaccessible magnetic flux. REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Google ScholarCrossref2. M. V. Berry, J. Phys. A (in press). Google Scholar3. M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, Eur. J. Phys. 1, 154 (1980). Google ScholarCrossref© 2010 American Institute of Physics.

Ya.A. Smorodinskii

Peter Andrew Sturrock, T. R. Groves

The magnetic version of the effects commonly attributed to Aharonov and Bohm had been published ten years earlier by Ehrenberg and Siday. We compare the two articles, and conclude that their essential contents are identical. We therefore advocate that the magnetic effect be referred to as the Ehrenberg-Siday Effect, and that the term Aharonov-Bohm Effect be reserved for the electrical case.