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arXiv:1304.4736

The Early History of the Aharonov-Bohm Effect

Basil J. Hiley

Published Apr 17, 2013• 13 citations
arXivHTMLPDF

Abstract

This paper traces the early history of the Aharonov-Bohm effect. It appears to have been `discovered' at least three times to my knowledge before the defining paper of Aharonov and Bohm appeared in 1959. The first hint of the effect appears in Germany in 1939, immediately disappearing from sight in those troubled times. It reappeared in a paper in 1949, ten years before the defining paper appeared. Here I report the background to the early evolution of this effect, presenting first hand unpublished accounts reported to me by colleagues at Birkbeck College in the University of London.

DOI
10.48550/arxiv.1304.4736

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

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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.

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This paper traces the early history of the Aharonov-Bohm effect. It appears to have been `discovered' at least three times to my knowledge before the defining paper of Aharonov and Bohm appeared in 1959. The first hint of the effect appears in Germany in 1939, immediately disappearing from sight in those troubled times. It reappeared in a paper in 1949, ten years before the defining paper appeared. Here I report the background to the early evolution of this effect, presenting first hand unpublished accounts reported to me by colleagues at Birkbeck College in the University of London.
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.
On Tuesday 27 October 1992 David Bohm died of a heart attack while returning home from College, where we had been discussing the final details of our book The Undivided Universe (90).* We had been colleagues since joining Birkbeck College over 30 years ago and we spent many hours discussing a wide range of topics and writing many papers together. I will never forget those exciting and stimulating meetings. He would never spend any time on ordinary conversation, but he would immediately pick up on what we had been discussing the previous day and there would be no let–up in the discussion that followed until it was time to lecture or to go home. It was exhausting but it was exhilarating. What follows is an account of a radical independent thinker who made important contributions to physics yet had the courage to challenge the orthodoxy long before people realized there was a real problem. I hope that my personal involvment in his later work does not cloud the objectivity of this Memoir too much.
In the year 2007, a slightly nerdy girl fell in love with all things math. Even though she only was exposed to a small part of the immense field of mathematics, she knew that math would always have a place in her heart. Ten years later, that passion for math is still burning inside. She never thought she would be interested in anything other than strictly mathematics. However, she discovered a love for computer science her sophomore year of college. Now, she is graduating college with a double major in both mathematics and computer science.\nThis nerdy girl is me. It was my first semester, freshman year at Ouachita Baptist University when I discovered an interest in cryptography. Discrete Mathematics had a small portion of the class that discussed various types of cryptosystems. These were the simplified versions that were easier to comprehend so that we could truly grasp the underlying concepts of cryptography. However, I craved more. I wanted to delve further into the advanced world of cryptography. It was not until my Honors Directed Study that I was able to do so.\nDuring my directed study, I was able to research the history of cryptography and what it has transformed into today. While it was fascinating to look at all the various cryptosystems that have been created throughout time, one cryptosystem caught my eye in particular—Elliptic Curve Cryptography, commonly referred to as ECC. I had heard of a few cryptosystems but never the ECC. As such, my interest was piqued. Having the opportunity to research Elliptic Curve Cryptography, I was ready to try and understand a new mathematical concept. I was ready to further expand my love and passion for mathematics, and I was not disappointed. Learning even the basics of elliptical curves proved challenging. The math behind ECC is immense and quite frankly, intimidating. Nevertheless, I do not back down from a challenge…at least not a mathematical one.\nMy research of elliptic curves, the basis of Elliptic Curve Cryptography, opened up my eyes to an entirely new field of mathematics. The challenges that arose during my studies, while frustrating at times, are well worth the wealth of knowledge I was able to acquire. The research in my study of elliptical curve cryptography only increased the ten-year passion for mathematics that is still inside the slightly nerdy girl.\nThis paper is the culmination of all my research over elliptic curves. It reflects the knowledge that I was able to acquire while studying elliptic curve cryptography and quantum computers.
Glasses were raised at a conference at the University of South Carolina in December to toast the 30-year-old prediction that gave reality to the magnetic vector potential. According to that prediction, made by Yakir Aharonov (University of South Carolina and the University of Tel Aviv) and David Bohm (Birkbeck College of London University), an electron will experience a phase shift as it encircles an infinitely long solenoid, even though there is no magnetic field—only a vector potential—in the region where it travels. Almost all those who originally doubted this conclusion have long since been persuaded by several elegant experimental confirmations.