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arXiv:quant-ph/0404128 · European Journal of Physics

How to teach quantum mechanics

O. Passon

Published Sep 1, 2004• 8 citations
arXivHTMLPDF

Abstract

In the spirit and style of John S. Bell's well known paper on How to Teach Special Relativity it is argued, that a ``Bohmian pedagogy''provides a very useful tool to illustrate the relation between classical and quantum physics and illuminates the peculiar features of the latter.
DOI
10.1088/0143-0807/25/6/008

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How to teach Quantum Mechanics

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In the spirit and style of John S. Bell’s well known paper on How to Teach Special Relativity [1] it is argued, that a “Bohmian pedagogy”provides a very useful tool to illustrate the relation between classical and quantum physics and illuminates the peculiar features of the latter. The paper by Bell on How to Teach Special Relativity introduces the subject with the following remark: I have for long thought that if I had the opportunity to teach this subject, I would emphasize the continuity with earlier ideas. Usually it is the discontinuity which is stressed, the radical break with more primitive notions of space and time. Often the result is to destroy completely the confidence of the student in perfectly sound and useful concepts already acquired. 1 In the following Bell gives an account of the Lorentzian interpretation of relativistic effects, in which the Lorentz transformations are explained by a dynamical

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Jean Bricmont’s review of Travis Norsen’s Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory (Physics Today, April 2018, page 58) stresses the virtues of Louis de Broglie and David Bohm’s pilot-wave interpretation of quantum mechanics, also referred to as Bohmian mechanics (BM), but the review omits mention of some of that interpretation’s rather serious defects. As Bricmont notes, in BM the standard Schrödinger wavefunction ψ(r, t) for a particle is augmented with a classical trajectory r(t) that is interpreted as the actual precise physical position of the particle as a function of time. 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He notes that a Bohmian particle cannot cross the symmetry plane separating the upper slit and detector from their lower counterparts, and thus a particle arriving at the upper detector actually came from the upper slit: first it moved downward, but when it arrived in the region where the beams cross, it “bounced” back upward toward the upper detector.Years ago I published an analysis that contradicted Bell and showed that the answer he regarded as naive—the particle passes through the crossing region without bouncing—was perfectly good quantum mechanics.22. R. B. Griffiths, Phys. Lett. A 261, 227 (1999). https://doi.org/10.1016/S0375-9601(99)00542-3 I am still waiting for someone in the Bohmian community to publish a reply.Norsen is troubled because the nonlocal, often superluminal influences needed to make sense of BM are hard to reconcile with special relativity. 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Phys. 41, 705 (2011), and references therein. https://doi.org/10.1007/s10701-010-9512-5 Thus a consistent Hilbert-space formulation of quantum theory without hidden variables removes any worry about a conflict with special relativity.Although Bohmian mechanics was worthy of consideration and has been useful in the development of quantum foundations, ignoring more recent developments is not the way to honor the memory of one of the great physicists of the last century. I hope that a second edition of Norsen’s well-written book will take account of more recent work.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press (1987). Google Scholar2. R. B. Griffiths, Phys. Lett. A 261, 227 (1999). https://doi.org/10.1016/S0375-9601(99)00542-3, Google ScholarCrossref3. See R. B. Griffiths, Found. Phys. 41, 705 (2011), and references therein. https://doi.org/10.1007/s10701-010-9512-5, Google ScholarCrossref4. J. von Neumann, Mathematical Foundations of Quantum Mechanics, R. T. Beyer, trans., Princeton U. Press (1955), chap. 3.5. Google Scholar© 2019 American Institute of Physics.

Physics Today•Oct 1, 2019•5 citations

Why Bohmian Mechanics? One- and Two-Time Position Measurements, Bell Inequalities, Philosophy, and Physics

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In Bohmian mechanics, particles follow continuous trajectories, so two-time position correlations have been well defined. However, Bohmian mechanics predicts the violation of Bell inequalities. Motivated by this fact, we investigate position measurements in Bohmian mechanics by coupling the particles to macroscopic pointers. This explains the violation of Bell inequalities despite two-time position correlations. We relate this fact to so-called surrealistic trajectories that, in our model, correspond to slowly moving pointers. Next, we emphasize that Bohmian mechanics, which does not distinguish between microscopic and macroscopic systems, implies that the quantum weirdness of quantum physics also shows up at the macro-scale. Finally, we discuss the fact that Bohmian mechanics is attractive to philosophers but not so much to physicists and argue that the Bohmian community is responsible for the latter.

arXiv:1509.00767•Entropy•Feb 2, 2018•24 citations
In the spirit and style of John S. Bell’s well known paper on How to Teach Special Relativity [1] it is argued, that a “Bohmian pedagogy”provides a very useful tool to illustrate the relation between classical and quantum physics and illuminates the peculiar features of the latter. The paper by Bell on How to Teach Special Relativity introduces the subject with the following remark: I have for long thought that if I had the opportunity to teach this subject, I would emphasize the continuity with earlier ideas. Usually it is the discontinuity which is stressed, the radical break with more primitive notions of space and time. Often the result is to destroy completely the confidence of the student in perfectly sound and useful concepts already acquired. 1 In the following Bell gives an account of the Lorentzian interpretation of relativistic effects, in which the Lorentz transformations are explained by a dynamical
John S Bell 1987 Cambridge: Cambridge University Press vii + 212 pp price £25 ISBN 0 521 33495 0 This book is a collection of John Bell's papers dealing explicitly with the foundations of quantum mechanics (or, as he puts it, ' quantum philosophy '), plus one paper on the pedagogy of special relativity. The first two are the classic papers of 1 966 and 1 964, which respectively demolished the 'impossibility proofs' concerning hidden variables and proved the famous theorem on the incompatibility of the predictions of local hidden-variable theories with those of quantum mechanics.
There are two ways to teach quantum mechanics. The first way – which for most physicists today is still the only way – follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then, you learn about the “blackbody paradox” and various strange experimental results, and the great crisis these things posed for physics. Next, you learn a complicated patchwork of ideas that physicists invented between 1900 and 1926 to try to make the crisis go away. Then, if you're lucky, after years of study, you finally get around to the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes that can be positive, negative, or even complex. Look, obviously the physicists had their reasons for teaching quantum mechanics that way, and it works great for a certain kind of student. But the “historical” approach also has disadvantages, which in the quantum information age are becoming increasingly apparent. For example, I’ve had experts in quantum field theory – people who've spent years calculating path integrals of mind-boggling complexity – ask me to explain the Bell inequality to them , or other simple conceptual things like Grover's algorithm. I felt as if Andrew Wiles had asked me to explain the Pythagorean Theorem.
Jean Bricmont’s review of Travis Norsen’s Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory (Physics Today, April 2018, page 58) stresses the virtues of Louis de Broglie and David Bohm’s pilot-wave interpretation of quantum mechanics, also referred to as Bohmian mechanics (BM), but the review omits mention of some of that interpretation’s rather serious defects. As Bricmont notes, in BM the standard Schrödinger wavefunction ψ(r, t) for a particle is augmented with a classical trajectory r(t) that is interpreted as the actual precise physical position of the particle as a function of time. Sometimes that Bohmian trajectory can provide a helpful intuitive picture, but in other cases it is quite misleading.John Bell presented an example of how Bohmian trajectories can mislead: a modified double-slit experiment with a lens placed right after each slit so that the emerging beams cross on their way to two distant detectors located beyond the crossing point.11. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press (1987). The beam from the lower slit arrives at the upper detector, and that from the upper slit at the lower detector. If a particle arrives at the upper detector, which slit did it pass through?Bell claims that the naive answer—that the particle came from the lower slit, based on the intuition that particles move in straight lines in a vacuum—is wrong. He notes that a Bohmian particle cannot cross the symmetry plane separating the upper slit and detector from their lower counterparts, and thus a particle arriving at the upper detector actually came from the upper slit: first it moved downward, but when it arrived in the region where the beams cross, it “bounced” back upward toward the upper detector.Years ago I published an analysis that contradicted Bell and showed that the answer he regarded as naive—the particle passes through the crossing region without bouncing—was perfectly good quantum mechanics.22. R. B. Griffiths, Phys. Lett. A 261, 227 (1999). https://doi.org/10.1016/S0375-9601(99)00542-3 I am still waiting for someone in the Bohmian community to publish a reply.Norsen is troubled because the nonlocal, often superluminal influences needed to make sense of BM are hard to reconcile with special relativity. Indeed, the widely accepted no-signaling principle of quantum mechanics asserts that those influences cannot transmit information, so a direct experimental detection of them is out of reach. Defenders of BM say they know that nonlocal influences exist because quantum mechanics violates Bell’s inequalities. But as I and others have pointed out, the hidden variables used in derivations of Bell inequalities are fundamentally classical,33. See R. B. Griffiths, Found. Phys. 41, 705 (2011), and references therein. https://doi.org/10.1007/s10701-010-9512-5 in contrast to the representation of quantum properties by Hilbert subspaces, as introduced by John von Neumann.44. J. von Neumann, Mathematical Foundations of Quantum Mechanics, R. T. Beyer, trans., Princeton U. Press (1955), chap. 3.5. Projectors on those subspaces do not generally commute, which clearly distinguishes quantum physics from classical. Thus that feature, rather than a failure of locality, is why Bell’s inequalities do not agree with quantum theory and experiment.The BM particle trajectories are instances of classical hidden variables, so the nonlocality of the pilot-wave interpretation of quantum mechanics is not surprising. Indeed, when proper account is taken of noncommutativity, one can show that quantum theory satisfies a principle of locality that Albert Einstein might well have agreed with: Objective properties of an isolated individual system do not change when something is done to another, noninteracting system.33. See R. B. Griffiths, Found. Phys. 41, 705 (2011), and references therein. https://doi.org/10.1007/s10701-010-9512-5 Thus a consistent Hilbert-space formulation of quantum theory without hidden variables removes any worry about a conflict with special relativity.Although Bohmian mechanics was worthy of consideration and has been useful in the development of quantum foundations, ignoring more recent developments is not the way to honor the memory of one of the great physicists of the last century. I hope that a second edition of Norsen’s well-written book will take account of more recent work.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press (1987). Google Scholar2. R. B. Griffiths, Phys. Lett. A 261, 227 (1999). https://doi.org/10.1016/S0375-9601(99)00542-3, Google ScholarCrossref3. See R. B. Griffiths, Found. Phys. 41, 705 (2011), and references therein. https://doi.org/10.1007/s10701-010-9512-5, Google ScholarCrossref4. J. von Neumann, Mathematical Foundations of Quantum Mechanics, R. T. Beyer, trans., Princeton U. Press (1955), chap. 3.5. Google Scholar© 2019 American Institute of Physics.
In Bohmian mechanics, particles follow continuous trajectories, so two-time position correlations have been well defined. However, Bohmian mechanics predicts the violation of Bell inequalities. Motivated by this fact, we investigate position measurements in Bohmian mechanics by coupling the particles to macroscopic pointers. This explains the violation of Bell inequalities despite two-time position correlations. We relate this fact to so-called surrealistic trajectories that, in our model, correspond to slowly moving pointers. Next, we emphasize that Bohmian mechanics, which does not distinguish between microscopic and macroscopic systems, implies that the quantum weirdness of quantum physics also shows up at the macro-scale. Finally, we discuss the fact that Bohmian mechanics is attractive to philosophers but not so much to physicists and argue that the Bohmian community is responsible for the latter.