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Physics Today

More variations on Aharonov-Bohm

C. Alden Mead

Published Apr 1, 2010• 0 citations
Publisher

Abstract

The article by Herman Batelaan and Akira Tonomura on the Aharonov-Bohm effect brought back memories of a conference I attended at the University of South Carolina in 1989 commemorating both the 30th anniversary of the Aharonov-Bohm paper and the 5th anniversary of the 1984 paper by Michael Berry that introduced the geometric, now known as the Berry phase. David Bohm, Yakir Aharonov, and Berry were all present. I particularly recall a plenary talk given by Bohm. In it, he expressed astonishment that certain physicists refused to accept the AB effect and even went to great lengths to try to disprove it. As he said, “It would be much more revolutionary for this effect to be wrong than for it to be right,” since it was a clear consequence of fundamental quantum mechanics. I considered his remark very Bohmian, in that (a) no one else would have said it that way, and (b) once uttered, it was obviously true. Bohm’s habit, in his soft-spoken way, of making such blindingly original statements is one of the things I most remember about this unorthodox and profound thinker.© 2010 American Institute of Physics.

DOI
10.1063/1.4797320

Related papers

More variations on Aharonov-Bohm

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.

Physics Today•Apr 1, 2010•6 citations

Quantum Phases: 50 years of the Aharonov--Bohm effect and 25 years of the Berry phase

Mark R. Dennis, Sandu Popescu, Lev Vaidman A

This special issue celebrates the discovery of two of the most important aspects of quantum mechanics: the Aharonov–Bohm effect and the Berry phase. The issue includes work presented at two conferences, 50 Years of the Aharonov–Bohm Effect, 11–14 October 2009, Tel Aviv University, Israel, and the Aharonov–Bohm Effect and Berry Phase 50/25 Anniversary, 14–15 December 2009, Bristol University, UK. The Aharonov–Bohm (AB) effect and the Berry phase have many things in common, apart from the happy coincidence that they were discovered 25 years apart, making possible such a joint anniversary. First, they were both discovered in the same place, the H H Wills Physics Laboratory, University of Bristol, UK. Second, they both were there for everybody to see from day one, from the very beginning of quantum mechanics. They were, so to say, right on the surface; there was no need for sophisticated mathematics or involved constructions. Yet it took so long for somebody to see them. The explanation, we dare to speculate, is that they are so unusual, they challenge so much our everyday experience and ingrained intuitions about physics that it was difficult to recognise them. Third, both the AB effect and the Berry phase are quintessentially quantum; they both manifest themselves as topological/geometric quantum phases. The AB effect revolutionized our understanding of the role of potentials in physics. For the first time, it was shown that a particle moving in a field-free region could be affected by a field in a disjoint region. In doing so, it shattered one of the strongest held principles of physics. In the case of the Berry phase, the importance lies in its absolute generality—the topological/geometric phase named after Berry is acquired by all physical systems when the external parameters they depend upon undergo an adiabatic cyclic change. Remarkably this phase depends only on the geometry of the cyclic path in the abstract parameter space, a fact which deepens our appreciation of the underlying geometry of quantum mechanics. The AB effect and the Berry phase are ubiquitous in modern physics and have implications ranging from the most fundamental to the very applied. First and foremost, they give a deeper understanding of the nature of quantum mechanics itself. Furthermore, we find them in fields as varied as cosmology, particle physics, non-abelian gauge theories, condensed matter, chemical and molecular physics, and laser dynamics. Generalizations of the AB effect to non-abelian gauge theories, such as the Wilson and `t Hooft loops, are important tools for studying confinement and spontaneous symmetry breaking. They explain charge quantization, the quantum Hall effect and the Josephson junction and also play a crucial role in electron microscope holography. Without them an understanding of many effects in the new field of mesoscopic physics, where tiny electronic circuits exhibit quantum behaviour, would be impossible. Like good wine, the AB effect and the Berry phase become finer and more appreciated with time. Even though they appear in textbooks and encyclopaedias, the number of researchers thinking and publishing papers on these two effects is increasing annually. The AB effect and the Berry phase keep being observed in new systems and with every day that passes novel applications are routinely found. This special issue is just a small snapshot of the state of the art 50 and 25 years, respectively, from their discoveries.

Journal of Physics A Mathematical and Theoretical•Aug 12, 2010•4 citations

Aptly named Aharonov-Bohm effect has classical analogue, long history

Murray Peshkin

I am an author of the 1961 paper that first called the Aharonov-Bohm effect by that name. 1 1. M. Peshkin, I. Talmi, L. J. Tassie, Ann. Phys. 12, 426 (1961). The term has since appeared in more than 1000 published papers. However, it has been suggested a few times, most recently by Peter Sturrock and Timothy Groves, that the name does not do justice to Werner Ehrenberg and Raymond Siday, who found in 1949 that the motion of electrons can be influenced by magnetic fields confined to regions that the electrons do not enter. 2 2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). I argue that the name Aharonov-Bohm effect is appropriate, although for a reason that I did not fully appreciate in 1961.The 1959 Aharonov-Bohm paper profoundly changed the way we think about electromagnetic fields in quantum mechanics. 3 3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). The gauge-invariant part of the vector potential was promoted to a real physical field, not just a convenient device for summarizing certain information about the electric and magnetic fields. In the words of C. N. Yang, “The electromagnetic field strength fµv in quantum mechanics underdescribes electromagnetism, as the Bohm-Aharonov effect demonstrates … information about the phase factor exp[ie∮(A⋅dx)/ℏc] for all closed loops correctly describes electromagnetism.” 4 4. C. N. Yang, in Proceedings of the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, S. Kamefuchi et al. , eds., Physical Society of Japan, Tokyo (1984), p. 5.See also T. T. Wu, C. N. Yang, Phys. Rev. D 12, 3845 (1975). A century earlier, James Clerk Maxwell changed the way we think about action at a distance by identifying what we now call the Maxwell fields as real physical things that contain energy and momentum and that enable microscopic conservation laws; they are not just mathematical functions that summarize the necessary information about the past motions of charges. Later those physical fields had to be quantized. Yakir Aharonov and David Bohm found that in quantum mechanics the Maxwell fields in a multiply connected region do not contain all the physics; the vector potential must also be endowed with reality to make sense of the subtler interactions in quantum mechanics. Neither Aharonov and Bohm nor Ehrenberg and Siday were the first to observe that magnetic fields in places where a charged particle’s wave function vanishes may influence the motion of that particle. 5 5. P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) F. London, Nature 140, 793 (1937). Paul Dirac, in his 1931 paper on magnetic monopoles, noted that the electron’s wavefunction must vanish on singular flux lines but said nothing about that raising any question of nonlocality. Fritz London pointed out in the 1930s that the motion of electrons in a superconducting ring depends on an external magnetic flux through the hole in the ring, where the electrons cannot go. He wrote in his 1937 paper, “The most stable state of a ring has no current, unless an external magnetic field is applied.” Like Dirac, he said nothing about a nonlocal action of the magnetic field being surprising or unusual. Of course, London, like Dirac, was focusing on something else.Ehrenberg and Siday were also focusing on something else—electron optics—when they found in 1949 that the motion of an electron can depend on the magnetic field in a region from which the electron is excluded. They chose not to mention that curious phenomenon in the abstract of their paper, although they did explicitly say elsewhere that it was “curious.”None of those earlier authors went on to conclude that such a phenomenon implies that the vector potential has to be seen as a real physical field in quantum mechanics. Only Aharonov and Bohm did that.REFERENCESSection:ChooseTop of pageREFERENCES <<1. M. Peshkin, I. Talmi, L. J. Tassie, Ann. Phys. 12, 426 (1961). Google ScholarCrossref, ISI2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Google ScholarCrossref3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). Google ScholarCrossref, ISI4. C. N. Yang, in Proceedings of the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, S. Kamefuchi et al. , eds., Physical Society of Japan, Tokyo (1984), p. 5. Google ScholarSee also T. T. Wu, C. N. Yang, Phys. Rev. D 12, 3845 (1975). Google ScholarCrossref, ISI5. P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) Google ScholarCrossref F. London, Nature 140, 793 (1937). , Google ScholarCrossref© 2010 American Institute of Physics.

Physics Today•Aug 1, 2010•1 citation

Aptly named Aharonov-Bohm effect has classical analogue, long history

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.

Physics Today•Jul 30, 2010•12 citations

Theoretical discovery, experiment, and controversy in the Aharonov-Bohm effect: an oral history interview

Yakir Aharonov, Guy Hetzroni

Abstract This oral history interview provides Yakir Aharonov’s perspective on the theoretical discovery of the Aharonov-Bohm effect in 1959, during his PhD studies in Bristol with David Bohm, the reception of the effect, the efforts to test it empirically (up to Tonomura’s experiment), and some of the debates regarding the existence of the effect and its interpretation. The interview also discusses related later developments until the 1980s, including modular momentum and Berry’s phase. It includes recollections from meetings with Werner Heisenberg, Richard Feynman, and Chen-Ning Yang, also mentioning John Bell, Robert Chambers, Werner Ehrenberg, Sir Charles Frank, Wendell Furry, Gunnar Källén, Maurice Pryce, Nathan Rosen, John Wheeler, and Eugene Wigner.

arXiv:2508.08105•The European Physical Journal H•Sep 1, 2025•2 citations

More Variations on Aharonov-Bohm, Peter A. Sturock, Timothy R. Groves, Alexander Ershkovich, C. Alden Mead, Herman Batelaan and Akira Tonomura: Batelaan and Tonomura Reply

Herman Batelaan, Akira Tonomura

First paragraph: Werner Ehrenberg and Raymond Siday did propose the magnetic version of what is now called the Aharonov-Bohm (AB) effect, as Peter Sturrock and Timothy Groves point out. We had included this reference in the early versions of our manuscript. However, limited space directed the focus of the paper to the "effect without a force" discussion, rather than a historic perspective.

•Jan 1, 2010•0 citations
The article by Herman Batelaan and Akira Tonomura on the Aharonov-Bohm effect brought back memories of a conference I attended at the University of South Carolina in 1989 commemorating both the 30th anniversary of the Aharonov-Bohm paper and the 5th anniversary of the 1984 paper by Michael Berry that introduced the geometric, now known as the Berry phase. David Bohm, Yakir Aharonov, and Berry were all present. I particularly recall a plenary talk given by Bohm. In it, he expressed astonishment that certain physicists refused to accept the AB effect and even went to great lengths to try to disprove it. As he said, “It would be much more revolutionary for this effect to be wrong than for it to be right,” since it was a clear consequence of fundamental quantum mechanics. I considered his remark very Bohmian, in that (a) no one else would have said it that way, and (b) once uttered, it was obviously true. Bohm’s habit, in his soft-spoken way, of making such blindingly original statements is one of the things I most remember about this unorthodox and profound thinker.© 2010 American Institute of Physics.
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.
This special issue celebrates the discovery of two of the most important aspects of quantum mechanics: the Aharonov–Bohm effect and the Berry phase. The issue includes work presented at two conferences, 50 Years of the Aharonov–Bohm Effect, 11–14 October 2009, Tel Aviv University, Israel, and the Aharonov–Bohm Effect and Berry Phase 50/25 Anniversary, 14–15 December 2009, Bristol University, UK. The Aharonov–Bohm (AB) effect and the Berry phase have many things in common, apart from the happy coincidence that they were discovered 25 years apart, making possible such a joint anniversary. First, they were both discovered in the same place, the H H Wills Physics Laboratory, University of Bristol, UK. Second, they both were there for everybody to see from day one, from the very beginning of quantum mechanics. They were, so to say, right on the surface; there was no need for sophisticated mathematics or involved constructions. Yet it took so long for somebody to see them. The explanation, we dare to speculate, is that they are so unusual, they challenge so much our everyday experience and ingrained intuitions about physics that it was difficult to recognise them. Third, both the AB effect and the Berry phase are quintessentially quantum; they both manifest themselves as topological/geometric quantum phases. The AB effect revolutionized our understanding of the role of potentials in physics. For the first time, it was shown that a particle moving in a field-free region could be affected by a field in a disjoint region. In doing so, it shattered one of the strongest held principles of physics. In the case of the Berry phase, the importance lies in its absolute generality—the topological/geometric phase named after Berry is acquired by all physical systems when the external parameters they depend upon undergo an adiabatic cyclic change. Remarkably this phase depends only on the geometry of the cyclic path in the abstract parameter space, a fact which deepens our appreciation of the underlying geometry of quantum mechanics. The AB effect and the Berry phase are ubiquitous in modern physics and have implications ranging from the most fundamental to the very applied. First and foremost, they give a deeper understanding of the nature of quantum mechanics itself. Furthermore, we find them in fields as varied as cosmology, particle physics, non-abelian gauge theories, condensed matter, chemical and molecular physics, and laser dynamics. Generalizations of the AB effect to non-abelian gauge theories, such as the Wilson and `t Hooft loops, are important tools for studying confinement and spontaneous symmetry breaking. They explain charge quantization, the quantum Hall effect and the Josephson junction and also play a crucial role in electron microscope holography. Without them an understanding of many effects in the new field of mesoscopic physics, where tiny electronic circuits exhibit quantum behaviour, would be impossible. Like good wine, the AB effect and the Berry phase become finer and more appreciated with time. Even though they appear in textbooks and encyclopaedias, the number of researchers thinking and publishing papers on these two effects is increasing annually. The AB effect and the Berry phase keep being observed in new systems and with every day that passes novel applications are routinely found. This special issue is just a small snapshot of the state of the art 50 and 25 years, respectively, from their discoveries.
I am an author of the 1961 paper that first called the Aharonov-Bohm effect by that name. 1 1. M. Peshkin, I. Talmi, L. J. Tassie, Ann. Phys. 12, 426 (1961). The term has since appeared in more than 1000 published papers. However, it has been suggested a few times, most recently by Peter Sturrock and Timothy Groves, that the name does not do justice to Werner Ehrenberg and Raymond Siday, who found in 1949 that the motion of electrons can be influenced by magnetic fields confined to regions that the electrons do not enter. 2 2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). I argue that the name Aharonov-Bohm effect is appropriate, although for a reason that I did not fully appreciate in 1961.The 1959 Aharonov-Bohm paper profoundly changed the way we think about electromagnetic fields in quantum mechanics. 3 3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). The gauge-invariant part of the vector potential was promoted to a real physical field, not just a convenient device for summarizing certain information about the electric and magnetic fields. In the words of C. N. Yang, “The electromagnetic field strength fµv in quantum mechanics underdescribes electromagnetism, as the Bohm-Aharonov effect demonstrates … information about the phase factor exp[ie∮(A⋅dx)/ℏc] for all closed loops correctly describes electromagnetism.” 4 4. C. N. Yang, in Proceedings of the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, S. Kamefuchi et al. , eds., Physical Society of Japan, Tokyo (1984), p. 5.See also T. T. Wu, C. N. Yang, Phys. Rev. D 12, 3845 (1975). A century earlier, James Clerk Maxwell changed the way we think about action at a distance by identifying what we now call the Maxwell fields as real physical things that contain energy and momentum and that enable microscopic conservation laws; they are not just mathematical functions that summarize the necessary information about the past motions of charges. Later those physical fields had to be quantized. Yakir Aharonov and David Bohm found that in quantum mechanics the Maxwell fields in a multiply connected region do not contain all the physics; the vector potential must also be endowed with reality to make sense of the subtler interactions in quantum mechanics. Neither Aharonov and Bohm nor Ehrenberg and Siday were the first to observe that magnetic fields in places where a charged particle’s wave function vanishes may influence the motion of that particle. 5 5. P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) F. London, Nature 140, 793 (1937). Paul Dirac, in his 1931 paper on magnetic monopoles, noted that the electron’s wavefunction must vanish on singular flux lines but said nothing about that raising any question of nonlocality. Fritz London pointed out in the 1930s that the motion of electrons in a superconducting ring depends on an external magnetic flux through the hole in the ring, where the electrons cannot go. He wrote in his 1937 paper, “The most stable state of a ring has no current, unless an external magnetic field is applied.” Like Dirac, he said nothing about a nonlocal action of the magnetic field being surprising or unusual. Of course, London, like Dirac, was focusing on something else.Ehrenberg and Siday were also focusing on something else—electron optics—when they found in 1949 that the motion of an electron can depend on the magnetic field in a region from which the electron is excluded. They chose not to mention that curious phenomenon in the abstract of their paper, although they did explicitly say elsewhere that it was “curious.”None of those earlier authors went on to conclude that such a phenomenon implies that the vector potential has to be seen as a real physical field in quantum mechanics. Only Aharonov and Bohm did that.REFERENCESSection:ChooseTop of pageREFERENCES <<1. M. Peshkin, I. Talmi, L. J. Tassie, Ann. Phys. 12, 426 (1961). Google ScholarCrossref, ISI2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Google ScholarCrossref3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). Google ScholarCrossref, ISI4. C. N. Yang, in Proceedings of the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, S. Kamefuchi et al. , eds., Physical Society of Japan, Tokyo (1984), p. 5. Google ScholarSee also T. T. Wu, C. N. Yang, Phys. Rev. D 12, 3845 (1975). Google ScholarCrossref, ISI5. P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) Google ScholarCrossref F. London, Nature 140, 793 (1937). , Google ScholarCrossref© 2010 American Institute of Physics.
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.
Abstract This oral history interview provides Yakir Aharonov’s perspective on the theoretical discovery of the Aharonov-Bohm effect in 1959, during his PhD studies in Bristol with David Bohm, the reception of the effect, the efforts to test it empirically (up to Tonomura’s experiment), and some of the debates regarding the existence of the effect and its interpretation. The interview also discusses related later developments until the 1980s, including modular momentum and Berry’s phase. It includes recollections from meetings with Werner Heisenberg, Richard Feynman, and Chen-Ning Yang, also mentioning John Bell, Robert Chambers, Werner Ehrenberg, Sir Charles Frank, Wendell Furry, Gunnar Källén, Maurice Pryce, Nathan Rosen, John Wheeler, and Eugene Wigner.