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Response to Griffiths

Matthew Leifer

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

"First of all, I would like to thank Prof. Griffith for his comments. The exchange has reminded me of the series of letters that appeared in Physics Today following the publication of an article by Chandralekha Singh, Mario Belloni, and Wolfgang Christian on improving the teaching of undergraduate quantum mechanics (see http://ptonline.aip.org/ journals/doc/PHTOAD-ft/vol_60/iss_3/8_1.shtml). In those responses, both Griffiths and Travis Norsen argued that students’ understanding of quantum mechanics would be vastly improved if they were taught more about the foundations of quantum theory, and I wholeheartedly agree with that sentiment. The thing is, Griffiths argued vociferously that this should be done by teaching students according to his approach, as outlined in his textbook Consistent Quantum Theory, whilst Norsen argued that it should be done by teaching students the de Broglie-Bohm theory, i.e. precisely the sort of theory that Griffiths argues strongly against in his response to my article."

Related papers

Approaches for improving students' understanding of quantum mechanics

Travis Norsen

In their article, Chandralekha Singh, Mario Belloni, and Wolfgang Christian focus exclusively on “functional understanding of quantum mechanics,” which they claim “is quite distinct from the foundational issues alluded to by Feynman.”But are the foundational and the functional really so distinct? The work of other physics education researchers suggests not. For example, in a classic article, Alan Van Heuvelen discusses students’ prevalent and frustrating use of “primitive formula-centered problem-solving strategies” 1 1. A. Van Heuvelen, Am. J. Phys. 59, 891 (1991). https://doi.org/10.1119/1.16667 and suggests that physical, intuitive understanding developed through qualitative diagrams and models “must come before students start using math in problem solving. The equations become crutches that short-circuit attempts at understanding.” Van Heuvelen also urges that “instead of thinking of [problems] as an effort to determine some unknown quantity, [teachers] might … encourage students to think of the problem statement as describing a physical process—a movie of a region of space during a short time interval or of an event at one instant of time.” I suspect Singh, Belloni, and Christian would agree with this advice. They comment that such “qualitative understanding of quantum mechanics is much more challenging than facility with the technical aspects.”But isn't the main barrier to such intuitive, qualitative understanding the nature of quantum mechanics itself—at least, the version of the theory advocated by Niels Bohr, Werner Heisenberg, and virtually every textbook writer since? Why should we expect students to invest the time and energy necessary to, say, visualize the time-dependence of |ψ|2 when we also preach the ambiguous and contradictory Copenhagen dogma that ψ does not represent anything physically real, yet still provides a complete description of physical reality? Why are we surprised that students are confused about, and don't take seriously, something that we assure them is, at best, some kind of algorithmic fantasy? Is there really any difference between “shut up and calculate” and “plug and chug”?Why not teach them Bohmian mechanics—an alternative (deterministic) version of quantum theory in which particles are particles (and really exist, all the time) and the same dynamical laws apply whether anyone is looking or not? 2 2. S. Goldstein, in Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/qm-bohm. About this alternative theory John S. Bell asked, “Why is [it] ignored in text books? Should it not be taught … as an antidote to the prevailing complacency? To show that vagueness, subjectivity, and indeterminism are not forced upon us by experimental facts, but by deliberate theoretical choice?” 3 3. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press, New York (2004), p. 173. https://doi.org/10.1017/CBO9780511815676.021 If we really want to help students understand quantum mechanics, the first step is to reject the confusion-spawning foundational vagueness, ambiguity, and philosophical absurdity of Copenhagen quantum theory, and adopt a clearer, more scientific, less fuzzy version. (See Sheldon Goldstein's two-part article “Quantum Theory Without Observers,” Physics Today, March 1998, page 42, and Physics Today, April 1998, page 38) The first step, in short, is to present them with a theory that can be understood.REFERENCESSection:ChooseTop of pageREFERENCES <<1. A. Van Heuvelen, Am. J. Phys. 59, 891 (1991). https://doi.org/10.1119/1.16667 , Google ScholarCrossref2. S. Goldstein, in Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/qm-bohm. Google Scholar3. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press, New York (2004), p. 173. https://doi.org/10.1017/CBO9780511815676.021 , Google ScholarCrossref© 2007 American Institute of Physics.

Physics Today•Mar 1, 2007•0 citations

Approaches for improving students' understanding of quantum mechanics

Robert B. Griffiths

In the first sentence of their article “Improving Students’ Understanding of Quantum Mechanics” ( Physics Today, August 2006, page 43), Chandralekha Singh, Mario Belloni, and Wolfgang Christian refer to Richard Feynman's well-known assertion that nobody understands quantum mechanics. But thereafter they ignore it, and apparently assume that student misconceptions when learning quantum mechanics are not connected with foundational issues. I argue the contrary, that Feynman's statement should be a central concern in all efforts to improve quantum pedagogy. If we teachers do not understand a topic, we pass our own misconceptions on to our students and make the subject much more difficult for them.Many conceptual difficulties, including those Feynman was referring to, arise from the problem of introducing probabilities into quantum theory in a useful and consistent way. Textbooks avoid the problem by assigning probabilities to macroscopic measurement outcomes rather than to microscopic quantum systems. Although that approach avoids inconsistencies, it gives rise to some serious misconceptions: Measurements are somehow special and unrelated to other quantum phenomena; they require a “classical” apparatus that functions outside the scope of quantum mechanics (where is one to find such a thing nowadays?); they produce physical effects at long distances; one can say nothing sensible about what a quantum system is doing in the absence of measurements; measurements can be used to predict the future of the measured system but tell us nothing about its past; and so forth. These misconceptions are not unrelated to those that Singh and coauthors have reported.Students learning quantum mechanics could benefit greatly if their instructors used advances in our understanding that have occurred during the 40 years since Feynman unashamedly confessed his perplexity. He seems to have reacted favorably to a preliminary version of the new ideas (see the letter from Murray Gell-Mann and James Hartle in Physics Today, February 1999, page 11), so he might have appreciated the more mature form now available. In brief, we now know how to consistently assign probabilities directly to microscopic systems without referring to measurements, and we can show that under appropriate conditions a properly constructed measurement apparatus, described in fully quantum terms, will reveal properties the measured system possessed before the measurement took place. In such circumstances the probabilities of measurement outcomes are the same as those of the measured properties, and measurements are no longer an essential conceptual tool: One can think directly in physical terms about what the quantum system is doing at different times. This gets rid of a major source of student difficulties and misconceptions.Consider the example reported by Singh and coauthors in which students used a calculation employing 〈A〉 = 〈ψ|A|ψ〉 to find the expectation of an observable A, rather than simply using a probability distribution they had worked out previously. (In that article, A was the energy, but the same principle applies to any observable.) This failure is not surprising given that textbooks lack a good discussion of how to assign probability distributions to observables. So the student memorizes an independent formula 〈A〉 = 〈ψ|A|ψ〉, which is a good way of calculating something that comes up in homework and exams, but whose physical significance is not particularly clear (to student or instructor). What the student should be taught is that A is the quantum counterpart of a random variable in ordinary probability theory, and its average can be obtained from its probability distribution in exactly the same way. Defining 〈A〉 in this manner before introducing 〈ψ|A|ψ〉 as a convenient formula for calculating it would make things clearer. But quantum textbooks do not contain the necessary tools, and for good reason. With two noncommuting observables A and B, it is easy to poke either of them into the 〈ψ|A|ψ〉 formula, whereas assigning probabilities leads into a vast swamp, which work on quantum foundations has shown to be filled with nasty paradoxes ready to bite the unwary. Retreating to macroscopic measurements allows textbook writers to avoid the swamp, but with a serious loss in clarity of thought and physical intuition. It is better to drain the swamp of its root cause: a failed attempt to meld classical and quantum modes of reasoning, instead of consistently applying quantum concepts at all levels, microscopic and macroscopic, which is something we now know how to do.Another misconception reported in the Physics Today article, that measurement of a physical observable causes the system to be stuck forever in the measured eigenstate, is hardly surprising when students are taught that measurements and wavefunction collapse are part of the axiomatic, and thus unanalyzable, structure of quantum theory. Instead, they need to think about measurements as quantum physical processes, governed by the same laws as the rest of the quantum world, and learn how to use conditional probabilities to relate measurement outcomes to the past as well as the future behavior of a measured system. Once again, outdated ideas make the subject harder to learn.For 10 years I have been teaching advanced undergraduate and beginning graduate quantum mechanics courses and courses in quantum information, using the new perspective in which quantum mechanics is based on probabilistic laws of universal validity, with measurements being only one application. Reactions have generally been positive, though the students show signs of shock when I tell them that by the end of the course, provided they do their homework, they will understand some aspects of quantum mechanics better than Feynman did. Presenting the new ideas takes somewhat longer than the material they replace, but not enormously so. Some time will be regained in courses that include an introduction to quantum entanglement and Einstein-Podolsky-Rosen, since circuitous arguments invoking Bell's inequality and the like, which can leave students quite confused, are replaced by a short, clear treatment of the essentials.Although I can see the value of computer simulations of Schrödinger's equation, I think it is more effective to first introduce students to basic quantum dynamics, both unitary and stochastic, through the use of “toy models.” I included various examples in Consistent Quantum Theory . 1 1. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002). Some chapters and a few exercises are available at http://quantum.phys.cmu.edu. The properties of such models are easily worked out with a pencil on a small sheet of paper, like the back of an envelope. Working through them helps students master new concepts and get rid of certain misconceptions about quantum measurements. The fact that students in my courses have been able to learn how to apply probabilities consistently to microscopic systems, in a way that disposes of numerous difficulties and conceptual paradoxes, suggests it might be worthwhile for other teachers to invest some time in learning post-Feynman ideas. The main difficulty is the absence of a textbook. I have used reference 1 as a supplement, though it is not ideal. It has no exercises, although a few are available on the corresponding website. I would be happy to hear from anyone skilled in textbook writing who wants to revise an older one or start something new.In conclusion, I strongly favor every effort to improve students’ understanding of quantum mechanics, and I consider the research reported by Singh and coauthors a valuable contribution to that end. However, if we want our students to genuinely understand quantum mechanics and not simply calculate things, I believe a much bigger step forward is possible by combining the efforts reported in the article with advances in quantum foundations.REFERENCESection:ChooseTop of pageREFERENCE <<1. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002). Some chapters and a few exercises are available at http://quantum.phys.cmu.edu. Google Scholar© 2007 American Institute of Physics.

Physics Today•Mar 1, 2007•0 citations

Quantum

Scott Aaronson

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.

Cambridge University Press eBooks•Mar 14, 2013•1 citation

1 Refined Characterization of Student Perspectives on Quantum Physics

Charles Baily, Noah D. Finkelstein

The perspectives of introductory classical physics students can often negatively influence how those students later interpret quantum phenomena when taking an introductory course in modern physics. A detailed exploration of student perspectives on the interpretation of quantum physics is needed, both to characterize student understanding of physics concepts, and to inform how we might teach traditional content. Our previous investigations of student perspectives on quantum physics have indicated they can be highly nuanced, and may vary both within and across contexts. In order to better understand the contextual and often seemingly contradictory stances of students on matters of interpretation, we interviewed 19 students from four introductory modern physics courses taught at the University of Colorado. We find that students have attitudes and opinions that often parallel the stances of expert physicists when arguing for their favored interpretations of quantum mechanics, allowing for more nuanced characterizations of student perspectives in terms of three key interpretive themes. We present a framework for characterizing student perspectives on quantum mechanics, and demonstrate its utility in interpreting the sometimes-contradictory nature of student responses to previous surveys. We further find that students most often vacillate in their responses when what makes intuitive sense to them is not in agreement with what they consider to be a correct response, underscoring the need to distinguish between the personal and the public perspectives of introductory modern physics students.

•Sep 1, 2010•27 citations

Principles of Quantum Mechanics

R. Shankar

Given the number of books that already exist on the subject of quantum mechanics, one would think that the public needs one more as much as it does, say, the latest version of the Table oflntegers. But this does not deter me (as it didn't my predecessors) from trying to circulate my own version of how it ought to be taught. The approach to be presented here (to be described in a moment) was first tried on a group of Harvard undergraduates in the summer of '76, once again in the summer of '77, and more recently at Yale on undergraduates ('77-'78) and graduates ('78- '79) taking a year-long course on the subject.

•Jan 21, 2021•0 citations

Comment on Griffiths about locality, realism and Bell experiments

Emilio Santos

I argue that quantum mechanics is a realistic theory, but it violates either strong locality (no superluminal influences) or strict causality (diiferent effects cannot follow from the same cause).

arXiv:1512.07431•Dec 23, 2015•0 citations
"First of all, I would like to thank Prof. Griffith for his comments. The exchange has reminded me of the series of letters that appeared in Physics Today following the publication of an article by Chandralekha Singh, Mario Belloni, and Wolfgang Christian on improving the teaching of undergraduate quantum mechanics (see http://ptonline.aip.org/ journals/doc/PHTOAD-ft/vol_60/iss_3/8_1.shtml). In those responses, both Griffiths and Travis Norsen argued that students’ understanding of quantum mechanics would be vastly improved if they were taught more about the foundations of quantum theory, and I wholeheartedly agree with that sentiment. The thing is, Griffiths argued vociferously that this should be done by teaching students according to his approach, as outlined in his textbook Consistent Quantum Theory, whilst Norsen argued that it should be done by teaching students the de Broglie-Bohm theory, i.e. precisely the sort of theory that Griffiths argues strongly against in his response to my article."
In their article, Chandralekha Singh, Mario Belloni, and Wolfgang Christian focus exclusively on “functional understanding of quantum mechanics,” which they claim “is quite distinct from the foundational issues alluded to by Feynman.”But are the foundational and the functional really so distinct? The work of other physics education researchers suggests not. For example, in a classic article, Alan Van Heuvelen discusses students’ prevalent and frustrating use of “primitive formula-centered problem-solving strategies” 1 1. A. Van Heuvelen, Am. J. Phys. 59, 891 (1991). https://doi.org/10.1119/1.16667 and suggests that physical, intuitive understanding developed through qualitative diagrams and models “must come before students start using math in problem solving. The equations become crutches that short-circuit attempts at understanding.” Van Heuvelen also urges that “instead of thinking of [problems] as an effort to determine some unknown quantity, [teachers] might … encourage students to think of the problem statement as describing a physical process—a movie of a region of space during a short time interval or of an event at one instant of time.” I suspect Singh, Belloni, and Christian would agree with this advice. They comment that such “qualitative understanding of quantum mechanics is much more challenging than facility with the technical aspects.”But isn't the main barrier to such intuitive, qualitative understanding the nature of quantum mechanics itself—at least, the version of the theory advocated by Niels Bohr, Werner Heisenberg, and virtually every textbook writer since? Why should we expect students to invest the time and energy necessary to, say, visualize the time-dependence of |ψ|2 when we also preach the ambiguous and contradictory Copenhagen dogma that ψ does not represent anything physically real, yet still provides a complete description of physical reality? Why are we surprised that students are confused about, and don't take seriously, something that we assure them is, at best, some kind of algorithmic fantasy? Is there really any difference between “shut up and calculate” and “plug and chug”?Why not teach them Bohmian mechanics—an alternative (deterministic) version of quantum theory in which particles are particles (and really exist, all the time) and the same dynamical laws apply whether anyone is looking or not? 2 2. S. Goldstein, in Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/qm-bohm. About this alternative theory John S. Bell asked, “Why is [it] ignored in text books? Should it not be taught … as an antidote to the prevailing complacency? To show that vagueness, subjectivity, and indeterminism are not forced upon us by experimental facts, but by deliberate theoretical choice?” 3 3. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press, New York (2004), p. 173. https://doi.org/10.1017/CBO9780511815676.021 If we really want to help students understand quantum mechanics, the first step is to reject the confusion-spawning foundational vagueness, ambiguity, and philosophical absurdity of Copenhagen quantum theory, and adopt a clearer, more scientific, less fuzzy version. (See Sheldon Goldstein's two-part article “Quantum Theory Without Observers,” Physics Today, March 1998, page 42, and Physics Today, April 1998, page 38) The first step, in short, is to present them with a theory that can be understood.REFERENCESSection:ChooseTop of pageREFERENCES <<1. A. Van Heuvelen, Am. J. Phys. 59, 891 (1991). https://doi.org/10.1119/1.16667 , Google ScholarCrossref2. S. Goldstein, in Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/qm-bohm. Google Scholar3. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press, New York (2004), p. 173. https://doi.org/10.1017/CBO9780511815676.021 , Google ScholarCrossref© 2007 American Institute of Physics.
In the first sentence of their article “Improving Students’ Understanding of Quantum Mechanics” ( Physics Today, August 2006, page 43), Chandralekha Singh, Mario Belloni, and Wolfgang Christian refer to Richard Feynman's well-known assertion that nobody understands quantum mechanics. But thereafter they ignore it, and apparently assume that student misconceptions when learning quantum mechanics are not connected with foundational issues. I argue the contrary, that Feynman's statement should be a central concern in all efforts to improve quantum pedagogy. If we teachers do not understand a topic, we pass our own misconceptions on to our students and make the subject much more difficult for them.Many conceptual difficulties, including those Feynman was referring to, arise from the problem of introducing probabilities into quantum theory in a useful and consistent way. Textbooks avoid the problem by assigning probabilities to macroscopic measurement outcomes rather than to microscopic quantum systems. Although that approach avoids inconsistencies, it gives rise to some serious misconceptions: Measurements are somehow special and unrelated to other quantum phenomena; they require a “classical” apparatus that functions outside the scope of quantum mechanics (where is one to find such a thing nowadays?); they produce physical effects at long distances; one can say nothing sensible about what a quantum system is doing in the absence of measurements; measurements can be used to predict the future of the measured system but tell us nothing about its past; and so forth. These misconceptions are not unrelated to those that Singh and coauthors have reported.Students learning quantum mechanics could benefit greatly if their instructors used advances in our understanding that have occurred during the 40 years since Feynman unashamedly confessed his perplexity. He seems to have reacted favorably to a preliminary version of the new ideas (see the letter from Murray Gell-Mann and James Hartle in Physics Today, February 1999, page 11), so he might have appreciated the more mature form now available. In brief, we now know how to consistently assign probabilities directly to microscopic systems without referring to measurements, and we can show that under appropriate conditions a properly constructed measurement apparatus, described in fully quantum terms, will reveal properties the measured system possessed before the measurement took place. In such circumstances the probabilities of measurement outcomes are the same as those of the measured properties, and measurements are no longer an essential conceptual tool: One can think directly in physical terms about what the quantum system is doing at different times. This gets rid of a major source of student difficulties and misconceptions.Consider the example reported by Singh and coauthors in which students used a calculation employing 〈A〉 = 〈ψ|A|ψ〉 to find the expectation of an observable A, rather than simply using a probability distribution they had worked out previously. (In that article, A was the energy, but the same principle applies to any observable.) This failure is not surprising given that textbooks lack a good discussion of how to assign probability distributions to observables. So the student memorizes an independent formula 〈A〉 = 〈ψ|A|ψ〉, which is a good way of calculating something that comes up in homework and exams, but whose physical significance is not particularly clear (to student or instructor). What the student should be taught is that A is the quantum counterpart of a random variable in ordinary probability theory, and its average can be obtained from its probability distribution in exactly the same way. Defining 〈A〉 in this manner before introducing 〈ψ|A|ψ〉 as a convenient formula for calculating it would make things clearer. But quantum textbooks do not contain the necessary tools, and for good reason. With two noncommuting observables A and B, it is easy to poke either of them into the 〈ψ|A|ψ〉 formula, whereas assigning probabilities leads into a vast swamp, which work on quantum foundations has shown to be filled with nasty paradoxes ready to bite the unwary. Retreating to macroscopic measurements allows textbook writers to avoid the swamp, but with a serious loss in clarity of thought and physical intuition. It is better to drain the swamp of its root cause: a failed attempt to meld classical and quantum modes of reasoning, instead of consistently applying quantum concepts at all levels, microscopic and macroscopic, which is something we now know how to do.Another misconception reported in the Physics Today article, that measurement of a physical observable causes the system to be stuck forever in the measured eigenstate, is hardly surprising when students are taught that measurements and wavefunction collapse are part of the axiomatic, and thus unanalyzable, structure of quantum theory. Instead, they need to think about measurements as quantum physical processes, governed by the same laws as the rest of the quantum world, and learn how to use conditional probabilities to relate measurement outcomes to the past as well as the future behavior of a measured system. Once again, outdated ideas make the subject harder to learn.For 10 years I have been teaching advanced undergraduate and beginning graduate quantum mechanics courses and courses in quantum information, using the new perspective in which quantum mechanics is based on probabilistic laws of universal validity, with measurements being only one application. Reactions have generally been positive, though the students show signs of shock when I tell them that by the end of the course, provided they do their homework, they will understand some aspects of quantum mechanics better than Feynman did. Presenting the new ideas takes somewhat longer than the material they replace, but not enormously so. Some time will be regained in courses that include an introduction to quantum entanglement and Einstein-Podolsky-Rosen, since circuitous arguments invoking Bell's inequality and the like, which can leave students quite confused, are replaced by a short, clear treatment of the essentials.Although I can see the value of computer simulations of Schrödinger's equation, I think it is more effective to first introduce students to basic quantum dynamics, both unitary and stochastic, through the use of “toy models.” I included various examples in Consistent Quantum Theory . 1 1. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002). Some chapters and a few exercises are available at http://quantum.phys.cmu.edu. The properties of such models are easily worked out with a pencil on a small sheet of paper, like the back of an envelope. Working through them helps students master new concepts and get rid of certain misconceptions about quantum measurements. The fact that students in my courses have been able to learn how to apply probabilities consistently to microscopic systems, in a way that disposes of numerous difficulties and conceptual paradoxes, suggests it might be worthwhile for other teachers to invest some time in learning post-Feynman ideas. The main difficulty is the absence of a textbook. I have used reference 1 as a supplement, though it is not ideal. It has no exercises, although a few are available on the corresponding website. I would be happy to hear from anyone skilled in textbook writing who wants to revise an older one or start something new.In conclusion, I strongly favor every effort to improve students’ understanding of quantum mechanics, and I consider the research reported by Singh and coauthors a valuable contribution to that end. However, if we want our students to genuinely understand quantum mechanics and not simply calculate things, I believe a much bigger step forward is possible by combining the efforts reported in the article with advances in quantum foundations.REFERENCESection:ChooseTop of pageREFERENCE <<1. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002). Some chapters and a few exercises are available at http://quantum.phys.cmu.edu. Google Scholar© 2007 American Institute of Physics.
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.
The perspectives of introductory classical physics students can often negatively influence how those students later interpret quantum phenomena when taking an introductory course in modern physics. A detailed exploration of student perspectives on the interpretation of quantum physics is needed, both to characterize student understanding of physics concepts, and to inform how we might teach traditional content. Our previous investigations of student perspectives on quantum physics have indicated they can be highly nuanced, and may vary both within and across contexts. In order to better understand the contextual and often seemingly contradictory stances of students on matters of interpretation, we interviewed 19 students from four introductory modern physics courses taught at the University of Colorado. We find that students have attitudes and opinions that often parallel the stances of expert physicists when arguing for their favored interpretations of quantum mechanics, allowing for more nuanced characterizations of student perspectives in terms of three key interpretive themes. We present a framework for characterizing student perspectives on quantum mechanics, and demonstrate its utility in interpreting the sometimes-contradictory nature of student responses to previous surveys. We further find that students most often vacillate in their responses when what makes intuitive sense to them is not in agreement with what they consider to be a correct response, underscoring the need to distinguish between the personal and the public perspectives of introductory modern physics students.
Given the number of books that already exist on the subject of quantum mechanics, one would think that the public needs one more as much as it does, say, the latest version of the Table oflntegers. But this does not deter me (as it didn't my predecessors) from trying to circulate my own version of how it ought to be taught. The approach to be presented here (to be described in a moment) was first tried on a group of Harvard undergraduates in the summer of '76, once again in the summer of '77, and more recently at Yale on undergraduates ('77-'78) and graduates ('78- '79) taking a year-long course on the subject.