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arXiv:2610.30998
A Personal History in Quantum Foundations: an Oral History Interview Yakir Aharonov, Guy Hetzroni
physics.hist-ph quant-ph Submitted Oct 22, 2026 • Announced Oct 23, 2026 • 0 citations • Revised Oct 26, 2026 (v2)
v1 · Oct 22, 2026 v2 · Oct 26, 2026 Abstract This oral history interview provides Yakir Aharonov's personal and conceptual recollections from the 1950s to the 2000s, focusing on his academic trajectory, some of his major contributions to quantum foundations, and his perspective on the development of the field. The interview traces Aharonov's academic career through the Technion, University of Bristol, Brandeis University, Yeshiva University, University of South Carolina, Tel Aviv University, George Mason University, and Chapman University. The interview also traces the development of Aharonov's work and collaborations on the EPR paradox, time-energy uncertainty relations, quantum measurement theory, quantum frames of reference, the two-state vector formalism, weak values, protective measurements, and several other contributions. It includes recollections of meetings and discussions with David Bohm, Niels Bohr, John Clauser, Paul Dirac, Rudolf Peierls, Aage Petersen, and Abner Shimony. Also mentioned: David Albert, Jeeva Anandan, Peter Bergmann, Gideon Carmi, Avshalom Elitzur, Dave Finkelstein, Vladimir Fock, Itzhak Kalugai, Ed Lerner, Joel Lebowitz, Stanley Mandelstam, Yuval Ne'eman, Sandu Popescu, Maurice Pryce, Daniel Rohrlich, Nathan Rosen, Joseph Safko, Paul Singer, Daniele Struppa, Leonard Susskind, Lev Vaidman, Chien-Shiung Wu.
Comments 29 pages, 2 figures. Oral history interview; accepted for publication in EPJ H Related papers 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
Consistent treatments of quantum mechanics
Robert B. Griffiths
The Letters reply by Yakir Aharonov, Sandu Popescu, and Jeff Tollaksen gives a misleading impression of the consistent histories interpretation of quantum mechanics. As I pointed out in the same issue, consistent histories is an alternative to their time-symmetric formulation. It resolves the “collapse problem” of quantum foundations, which Aharonov and coauthors admit they have failed to do. However, that is not its only or even its principal virtue. It also solves what I call the second quantum measurement problem: how to infer from the measurement outcome the state of the measured system at an earlier time before the measurement took place. Thus the consistent histories approach, without any fuzzy references to “ensembles,” provides a proper probabilistic framework for inferring that Sx for a spin-1⁄2 particle actually was −1⁄2 before the measurement took place. This approach evades the criticisms expressed by Michael Nauenberg and Art Hobson in their letters in the same issue.Furthermore, consistent histories, unlike certain aspects of the approach of Aharonov and coauthors, is fully consistent with the Hilbert-space structure of quantum mechanics introduced by John von Neumann and now taught to all students of the subject. Indeed, with a consistent histories analysis one can locate fairly precisely11. R. E. Kastner, Stud. Hist. Phil. Mod. Phys. 35, 57 (2004), http://arxiv.org/abs/quant-ph/0207182. https://doi.org/10.1016/j.shpsb.2003.02.001 the error in reasoning that leads to claims such as that the measured spin of a spin-1⁄2 particle can equal 100.22. Y. Aharonov, D. Z. Albert, L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988). https://doi.org/10.1103/PhysRevLett.60.1351 Claims about what weak measurements actually measure, when made by those who have not yet solved either the collapse problem or the second measurement problem, should be treated with great caution.The claim that the consistent histories approach is controversial was true back in the 1990s, and the controversy led to a clearer formulation of the interpretation. However, no significant problems have come to light in the decade since the publication of my book.33. R. B. Griffiths, Consistent Quantum Theory Cambridge U. Press, New York (2002), http://quantum.phys.cmu.edu/CQT/. The fact that something has been ignored does not imply it is controversial. Admirers of Richard Feynman, some of whose writings were cited by Aharonov and coauthors in their reply, may be interested to know that shortly before his death he was quite sympathetic to an early form of the consistent histories or decoherent histories approach to understanding quantum mechanics (see PHYSICS TODAY, February 1999, page 11)—an open-mindedness worth imitating.REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. E. Kastner, Stud. Hist. Phil. Mod. Phys. 35, 57 (2004), http://arxiv.org/abs/quant-ph/0207182. https://doi.org/10.1016/j.shpsb.2003.02.001 , Google ScholarCrossref, ISI2. Y. Aharonov, D. Z. Albert, L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988). https://doi.org/10.1103/PhysRevLett.60.1351 , Google ScholarCrossref, ISI3. R. B. Griffiths, Consistent Quantum Theory Cambridge U. Press, New York (2002), http://quantum.phys.cmu.edu/CQT/. Google Scholar© 2011 American Institute of Physics.
Physics Today • Oct 1, 2011• 1 citation
Quantum coherence and reality : in celebration of the 60th birthday of Yakir Aharonov : International Conference on Fundamental Aspects of Quantum Theory, University of South Carolina, Columbia, USA, 10-12 December 1992
Jeeva S. Anandan, John L. Safko
Dynamic observation of flux lines based on the AB effect principle, A. Tonomura Aharonov effects for two slits and separated oscillatory fields interferences, N. Ramsey faster than Fourier, M. Berry quantum phase in action, A. Zee liberating exotic slaves, F. Wilczek evidence for a massive black hole in the center of our galaxy, C. Townes black holes, wormholes and the disappearance of global charge, S. Coleman unitarity of the black hole scattering matrix, G. t'Hooft topological phases and duality in electromagnetic and gravitational fields, J. Anandan non locality and objectivity in quantum state reduction, R. Penrose a non-polarization EPR experiment - observation of high-visibility Franson interference fringes, R.Y. Chiao et al toward It from Bit, J.A. Wheeler (para)bosons, (para)fermions, quons and other beasts in the menagerie of particle statistics, O.W. Greenberg et al a new formulation of quantum mechanics, Y. Aharonov. (Part contents).
WORLD SCIENTIFIC eBooks • Jan 1, 1994• 8 citations
Time-symmetric quantum mechanics questioned and defended
Robert B. Griffiths
Readers of the article by Yakir Aharonov, Sandu Popescu, and Jeff Tollaksen might be interested in an alternative time-symmetric formulation of quantum mechanics, known as “consistent histories,” that was developed over roughly the same time period as Aharonov’s work (see the article by Robert Griffiths and Roland Omnès, PHYSICS TODAY, August 1999, page 26). Closely related is the “decoherent histories” approach of Murray Gell-Mann and James Hartle,11. M. Gell-Mann, J. B. Hartle, in Complexity, Entropy and the Physics of InformationW. H. Zurek,ed.,Addison-Wesley, Redwood City, CA (1990), p. 425. but as that is not usually formulated in a way that is transparently time-symmetric, the following remarks refer to the consistent histories approach; see reference 22. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); available online at http://quantum.phys.cmu.edu/CQT. for an up-to-date formulation.Both the consistent histories approach and that of Aharonov and coworkers pay attention to events at several different times, are formulated in a way that is time-symmetrical, and address a number of quantum paradoxes. Both are consistent with the calculational procedures taught to students in a typical quantum mechanics course, so they are “standard quantum mechanics,” without the additional variables of de Broglie–Bohm or the additional collapses of Ghirardi-Rimini-Weber. And both approaches do not accept the “shut up and calculate” mentality that alas continues to dominate much classroom instruction. So far as I can tell, all the results mentioned by Aharonov and coauthors and in the earlier work they cite are fairly readily translated into the language of consistent histories, though the reverse is not true (see below); therefore, the consistent histories view is more general.In the treatment by Aharonov and coauthors, measurement, as in textbook quantum theory, remains a black box: It collapses the wavefunction, but nothing more can be said. And for good reason: The textbook approach of introducing probabilities by reference to measurement yields what appear to be insoluble difficulties if one attempts to apply quantum theory to the measurement process itself—that is, to actual apparatus constructed out of entities that are quantum mechanical. In the consistent histories approach, that difficulty does not arise, because it treats quantum dynamics as fundamentally probabilistic, not deterministic, and the same rules apply to measurements as to all other physical processes. Speaking metaphorically, the probabilistic approach used in consistent histories allows one to open the black measurement box and watch the quantum gears turn.The other major difference between the two approaches is their treatment of quantum paradoxes. We owe many of the most striking and delightful paradoxes of quantum theory to Aharonov and his coworkers, and he and Daniel Rohrlich have written a book on the topic.33. Y. Aharonov, D. Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed, Wiley, Weinheim, Germany (2005) . But he leaves the paradoxes largely unresolved; the reader is encouraged to study but not unravel them. The consistent histories approach is exactly opposite: Paradoxes should be—and a large number of them have been—resolved by the correct application of well-formulated and fully consistent quantum principles (see reference 22. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); available online at http://quantum.phys.cmu.edu/CQT. , chapters 19–25).Students new to quantum theory are often confused and deserve reasoned responses to their queries. Although paradoxes are valuable illustrations of how the quantum world differs from our everyday experience, I prefer to provide students with the conceptual tools needed to resolve and make sense of them. In particular, students benefit from learning a fully consistent approach to probabilities in the quantum domain, one not based on measurements but on general quantum principles. A colleague and I have just finished using that approach in teaching the first term of our introductory graduate quantum mechanics course. Although it requires extra time and effort to learn how to think about quantum processes rather than just do calculations, the reward comes in a deeper understanding of how the real (quantum) world works.REFERENCESSection:ChooseTop of pageREFERENCES <<1. M. Gell-Mann, J. B. Hartle, in Complexity, Entropy and the Physics of InformationW. H. Zurek,ed.,Addison-Wesley, Redwood City, CA (1990), p. 425. Google Scholar2. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); available online at http://quantum.phys.cmu.edu/CQT. Google Scholar3. Y. Aharonov, D. Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed, Wiley, Weinheim, Germany (2005) . Google ScholarCrossref© 2011 American Institute of Physics.
Physics Today • May 1, 2011• 1 citation
Arthur I. Miller
Meanwhile, on 18 September 1931, Heisenberg wrote to Bohr that ‘my work seems to be somewhat gray on gray’ (Pauli, 1985). By 1931 the bright future for quantum physics that seemed just over the horizon in the fall of 1927 paled with the formulation of relativistic quantum mechanics. Besides the as yet uninterpreted negative energy states, there was the electron's divergent self-energy and the continuous energy spectrum of β-particles in the supposedly two-body final state of nuclear β-decay, which implied that energy was not conserved in nuclear reactions (Bohr, 1932) and that perhaps quantum mechanics was not valid within the nucleus (to be discussed in Chapter 5). Measurement problems in a quantum theory of the electromagnetic field At the 20–25 October 1930 Solvay Conference, Bohr, Dirac, Heisenberg and Pauli concurred that fundamental difficulties in quantum electrodynamics might be clarified by investigating measurability of electromagnetic field quantities. Upon his return to Copenhagen from Brussels, Bohr continued discussing field measurements with Lev Landau, who happened to be visiting at Bohr's institute. In December 1930 Landau went on to Zürich, where he interested Pauli's assistant Rudolf Peierls in field measurements. Their deliberations led to a joint 1931 publication entitled ‘Extension of the uncertainty principle to relativistic quantum theory’ (Landau and Peierls, 1931). Measurement of an electric field can be accomplished through measuring the change in momentum of a charged test body placed in the field.
Cambridge University Press eBooks • Jan 6, 1994• 10 citations
This oral history interview provides Yakir Aharonov's personal and conceptual recollections from the 1950s to the 2000s, focusing on his academic trajectory, some of his major contributions to quantum foundations, and his perspective on the development of the field. The interview traces Aharonov's academic career through the Technion, University of Bristol, Brandeis University, Yeshiva University, University of South Carolina, Tel Aviv University, George Mason University, and Chapman University. The interview also traces the development of Aharonov's work and collaborations on the EPR paradox, time-energy uncertainty relations, quantum measurement theory, quantum frames of reference, the two-state vector formalism, weak values, protective measurements, and several other contributions. It includes recollections of meetings and discussions with David Bohm, Niels Bohr, John Clauser, Paul Dirac, Rudolf Peierls, Aage Petersen, and Abner Shimony. Also mentioned: David Albert, Jeeva Anandan, Peter Bergmann, Gideon Carmi, Avshalom Elitzur, Dave Finkelstein, Vladimir Fock, Itzhak Kalugai, Ed Lerner, Joel Lebowitz, Stanley Mandelstam, Yuval Ne'eman, Sandu Popescu, Maurice Pryce, Daniel Rohrlich, Nathan Rosen, Joseph Safko, Paul Singer, Daniele Struppa, Leonard Susskind, Lev Vaidman, Chien-Shiung Wu.
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.
A Guide through the Mysteries of Quantum Physics!Yakir Aharonov is one of the pioneers in measuring theory, the nature of quantum correlations, superselection rules, and geometric phases and has been awarded numerous scientific honors. The author has contributed monumental concepts to theoretical physics, especially the Aharonov-Bohm effect and the Aharonov-Casher effect. Together with Daniel Rohrlich of the Weizmann Institute, Israel, he has written a pioneering work on the remaining mysteries of quantum mechanics. From the perspective of a preeminent researcher in the fundamental aspects of quantum mechanics, the text combines mathematical rigor with penetrating and concise language
The Letters reply by Yakir Aharonov, Sandu Popescu, and Jeff Tollaksen gives a misleading impression of the consistent histories interpretation of quantum mechanics. As I pointed out in the same issue, consistent histories is an alternative to their time-symmetric formulation. It resolves the “collapse problem” of quantum foundations, which Aharonov and coauthors admit they have failed to do. However, that is not its only or even its principal virtue. It also solves what I call the second quantum measurement problem: how to infer from the measurement outcome the state of the measured system at an earlier time before the measurement took place. Thus the consistent histories approach, without any fuzzy references to “ensembles,” provides a proper probabilistic framework for inferring that Sx for a spin-1⁄2 particle actually was −1⁄2 before the measurement took place. This approach evades the criticisms expressed by Michael Nauenberg and Art Hobson in their letters in the same issue.Furthermore, consistent histories, unlike certain aspects of the approach of Aharonov and coauthors, is fully consistent with the Hilbert-space structure of quantum mechanics introduced by John von Neumann and now taught to all students of the subject. Indeed, with a consistent histories analysis one can locate fairly precisely11. R. E. Kastner, Stud. Hist. Phil. Mod. Phys. 35, 57 (2004), http://arxiv.org/abs/quant-ph/0207182. https://doi.org/10.1016/j.shpsb.2003.02.001 the error in reasoning that leads to claims such as that the measured spin of a spin-1⁄2 particle can equal 100.22. Y. Aharonov, D. Z. Albert, L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988). https://doi.org/10.1103/PhysRevLett.60.1351 Claims about what weak measurements actually measure, when made by those who have not yet solved either the collapse problem or the second measurement problem, should be treated with great caution.The claim that the consistent histories approach is controversial was true back in the 1990s, and the controversy led to a clearer formulation of the interpretation. However, no significant problems have come to light in the decade since the publication of my book.33. R. B. Griffiths, Consistent Quantum Theory Cambridge U. Press, New York (2002), http://quantum.phys.cmu.edu/CQT/. The fact that something has been ignored does not imply it is controversial. Admirers of Richard Feynman, some of whose writings were cited by Aharonov and coauthors in their reply, may be interested to know that shortly before his death he was quite sympathetic to an early form of the consistent histories or decoherent histories approach to understanding quantum mechanics (see PHYSICS TODAY, February 1999, page 11)—an open-mindedness worth imitating.REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. E. Kastner, Stud. Hist. Phil. Mod. Phys. 35, 57 (2004), http://arxiv.org/abs/quant-ph/0207182. https://doi.org/10.1016/j.shpsb.2003.02.001 , Google ScholarCrossref, ISI2. Y. Aharonov, D. Z. Albert, L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988). https://doi.org/10.1103/PhysRevLett.60.1351 , Google ScholarCrossref, ISI3. R. B. Griffiths, Consistent Quantum Theory Cambridge U. Press, New York (2002), http://quantum.phys.cmu.edu/CQT/. Google Scholar© 2011 American Institute of Physics.
Dynamic observation of flux lines based on the AB effect principle, A. Tonomura Aharonov effects for two slits and separated oscillatory fields interferences, N. Ramsey faster than Fourier, M. Berry quantum phase in action, A. Zee liberating exotic slaves, F. Wilczek evidence for a massive black hole in the center of our galaxy, C. Townes black holes, wormholes and the disappearance of global charge, S. Coleman unitarity of the black hole scattering matrix, G. t'Hooft topological phases and duality in electromagnetic and gravitational fields, J. Anandan non locality and objectivity in quantum state reduction, R. Penrose a non-polarization EPR experiment - observation of high-visibility Franson interference fringes, R.Y. Chiao et al toward It from Bit, J.A. Wheeler (para)bosons, (para)fermions, quons and other beasts in the menagerie of particle statistics, O.W. Greenberg et al a new formulation of quantum mechanics, Y. Aharonov. (Part contents).
Readers of the article by Yakir Aharonov, Sandu Popescu, and Jeff Tollaksen might be interested in an alternative time-symmetric formulation of quantum mechanics, known as “consistent histories,” that was developed over roughly the same time period as Aharonov’s work (see the article by Robert Griffiths and Roland Omnès, PHYSICS TODAY, August 1999, page 26). Closely related is the “decoherent histories” approach of Murray Gell-Mann and James Hartle,11. M. Gell-Mann, J. B. Hartle, in Complexity, Entropy and the Physics of InformationW. H. Zurek,ed.,Addison-Wesley, Redwood City, CA (1990), p. 425. but as that is not usually formulated in a way that is transparently time-symmetric, the following remarks refer to the consistent histories approach; see reference 22. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); available online at http://quantum.phys.cmu.edu/CQT. for an up-to-date formulation.Both the consistent histories approach and that of Aharonov and coworkers pay attention to events at several different times, are formulated in a way that is time-symmetrical, and address a number of quantum paradoxes. Both are consistent with the calculational procedures taught to students in a typical quantum mechanics course, so they are “standard quantum mechanics,” without the additional variables of de Broglie–Bohm or the additional collapses of Ghirardi-Rimini-Weber. And both approaches do not accept the “shut up and calculate” mentality that alas continues to dominate much classroom instruction. So far as I can tell, all the results mentioned by Aharonov and coauthors and in the earlier work they cite are fairly readily translated into the language of consistent histories, though the reverse is not true (see below); therefore, the consistent histories view is more general.In the treatment by Aharonov and coauthors, measurement, as in textbook quantum theory, remains a black box: It collapses the wavefunction, but nothing more can be said. And for good reason: The textbook approach of introducing probabilities by reference to measurement yields what appear to be insoluble difficulties if one attempts to apply quantum theory to the measurement process itself—that is, to actual apparatus constructed out of entities that are quantum mechanical. In the consistent histories approach, that difficulty does not arise, because it treats quantum dynamics as fundamentally probabilistic, not deterministic, and the same rules apply to measurements as to all other physical processes. Speaking metaphorically, the probabilistic approach used in consistent histories allows one to open the black measurement box and watch the quantum gears turn.The other major difference between the two approaches is their treatment of quantum paradoxes. We owe many of the most striking and delightful paradoxes of quantum theory to Aharonov and his coworkers, and he and Daniel Rohrlich have written a book on the topic.33. Y. Aharonov, D. Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed, Wiley, Weinheim, Germany (2005) . But he leaves the paradoxes largely unresolved; the reader is encouraged to study but not unravel them. The consistent histories approach is exactly opposite: Paradoxes should be—and a large number of them have been—resolved by the correct application of well-formulated and fully consistent quantum principles (see reference 22. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); available online at http://quantum.phys.cmu.edu/CQT. , chapters 19–25).Students new to quantum theory are often confused and deserve reasoned responses to their queries. Although paradoxes are valuable illustrations of how the quantum world differs from our everyday experience, I prefer to provide students with the conceptual tools needed to resolve and make sense of them. In particular, students benefit from learning a fully consistent approach to probabilities in the quantum domain, one not based on measurements but on general quantum principles. A colleague and I have just finished using that approach in teaching the first term of our introductory graduate quantum mechanics course. Although it requires extra time and effort to learn how to think about quantum processes rather than just do calculations, the reward comes in a deeper understanding of how the real (quantum) world works.REFERENCESSection:ChooseTop of pageREFERENCES <<1. M. Gell-Mann, J. B. Hartle, in Complexity, Entropy and the Physics of InformationW. H. Zurek,ed.,Addison-Wesley, Redwood City, CA (1990), p. 425. Google Scholar2. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); available online at http://quantum.phys.cmu.edu/CQT. Google Scholar3. Y. Aharonov, D. Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed, Wiley, Weinheim, Germany (2005) . Google ScholarCrossref© 2011 American Institute of Physics.
Meanwhile, on 18 September 1931, Heisenberg wrote to Bohr that ‘my work seems to be somewhat gray on gray’ (Pauli, 1985). By 1931 the bright future for quantum physics that seemed just over the horizon in the fall of 1927 paled with the formulation of relativistic quantum mechanics. Besides the as yet uninterpreted negative energy states, there was the electron's divergent self-energy and the continuous energy spectrum of β-particles in the supposedly two-body final state of nuclear β-decay, which implied that energy was not conserved in nuclear reactions (Bohr, 1932) and that perhaps quantum mechanics was not valid within the nucleus (to be discussed in Chapter 5). Measurement problems in a quantum theory of the electromagnetic field At the 20–25 October 1930 Solvay Conference, Bohr, Dirac, Heisenberg and Pauli concurred that fundamental difficulties in quantum electrodynamics might be clarified by investigating measurability of electromagnetic field quantities. Upon his return to Copenhagen from Brussels, Bohr continued discussing field measurements with Lev Landau, who happened to be visiting at Bohr's institute. In December 1930 Landau went on to Zürich, where he interested Pauli's assistant Rudolf Peierls in field measurements. Their deliberations led to a joint 1931 publication entitled ‘Extension of the uncertainty principle to relativistic quantum theory’ (Landau and Peierls, 1931). Measurement of an electric field can be accomplished through measuring the change in momentum of a charged test body placed in the field.