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Physics Today

Could Feynman Have Said This?

N. David Mermin

Published May 1, 2004• 133 citations
Publisher

Abstract

Fifteen years ago, I mused in a Reference Frame column on how different generations of physicists differed in the degree to which they thought that the interpretation of quantum mechanics remains a serious problem (Physics Today, Physics Today 0031-9228 42 4 1989 9 https://doi.org/10.1063/1.2810963. April 1989, page 9 ). I declared myself to be among those who feel uncomfortable when asked to articulate what we really think about the quantum theory, adding that "If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be "Shut up and calculate!"In the intervening years, I've come to hold a milder and more nuanced opinion of the Copenhagen view, but that should be the subject of another column. The subject of this one is the habit of misquotation or misattribution that afflicts our profession, a rather different example of which I pointed out a few months ago (February 2004, page 10).Given my capacity for intellectual development ("inconsistency," in the terminology deployed in the current American political season), it's fortunate that I've now reached an age at which I tend to forget about things I've written more than a few years ago. Indeed, I find it downright irritating when somebody asks me questions about papers I wrote a mere half dozen years ago, naively identifying me with the author of those ancient texts. Until quite recently, I had no memory of ever having written such a childishly brusque dismissal of such an exquisitely subtle point of view, much less of having published it in so widely read a venue.This amnesia, combined with the evolution in my thinking that had distanced me from my long forgotten words, may explain why I was initially somewhat puzzled by the slight sensation of discomfort that passed over me when, browsing the e-print archive earlier this year, I read a characterization of Max Born's probability rule as "the favorite ingredient of what has been nicknamed, after Feynman's famous dictum, the shut up and calculate interpretation of quantum mechanics."I yield to nobody in my admiration for Richard Feynman's aphorisms on the nature of quantum mechanics. Indeed, long ago I published a poem (Physics Today, April 1985, page 47) consisting of nothing more than a resetting as verse of a paragraph Feynman had written about his own attitude toward the quantum theory, in his now (but not then) famous article that launched the whole field of quantum computation. I like to think I have devoured everything Feynman ever wrote on the character of quantum mechanics. But while "shut up and calculate" sounded dimly familiar to me as a characterization of a certain interpretive stance, I couldn't recall where Feynman had written it. Mulling this over, a terrible thought began to dawn on me. Could it be that I myself had once used the phrase? If so, then it would appear that I had picked it up from something by Feynman, forgotten the source, and presented it as my own. Devastating!It was devastating because I have a horror of writing or uttering any witticism that is not original with me, unless I make it absolutely clear where and (if known) from whom I got it. I don't even like to tell jokes unless I've made them up myself. (I digress to offer you my favorite:Question: What is the difference between theoretical physics and mathematical physics? Answer: Theoretical physics is done by physicists who lack the necessary skills to do real experiments; mathematical physics is done by mathematicians who lack the necessary skills to do real mathematics. Mathematical physicists tend not to like this joke, but other physicists seem to. Nonphysicists, of course, are entirely immune to its charms.)So with growing trepidation, I searched through my past writings on quantum mechanics. I was dismayed when I came upon my 1989 column, which confirmed my worst fears. Not only had I appropriated without proper attribution a Feynman quote, but it appeared to be a famous one. How humiliating! I was afflicted with visions of knowledgeable Physics Today readers shaking their heads 15 years ago at what must have struck them as my shameless attempt to ride to literary glory on the unacknowledged shoulders of Feynman.So I went to the Web to find the source, hoping I could then salvage my reputation by persuading Physics Today to print an addendum or erratum. Google gives more than 130 hits containing both "shut up and calculate" and "feynman." Most of these do not directly link the two, but about a dozen do. Here are a few: "Shut up and calculate" was a motto of Richard Feynman.For example, there's Feynman's "shut up and calculate."My personal philosophy is that of the famous physicist Richard Feynman, who said: "Shut up and calculate."When asked which interpretation of QM he favored, Feynman replied "Shut up and calculate."Richard Feynman foreslog ligefrem en "shut up and calculate" fortolkning af kvantemekanikken.Shut up and calculate—Richard Feynman.Just to make sure, I also searched for "shut up and calculate" and "mermin." I found only 10 hits, all of them mentioning me in ways that had nothing to do with their use, elsewhere, of "shut up and calculate." So it would have been clear to the world that I had indeed passed off Feynman's words as my own.Or had I …?I noticed that not a single one of the Web sites attributing the phrase to Feynman cited a source or hinted at the circumstances under which he had said it. A ray of hope flickered on: Could I once again have become a victim of the Matthew effect?The Matthew effect was enunciated by the great sociologist of science, Robert Merton. 1 1. R. K. Merton, Science 159, 56 (1968). https://doi.org/10.1126/science.159.3810.56 Merton worked in those innocent days when sociologists were interested only in the behavior of scientists and not in the content of their science. (To be fair to contemporary sociologists of science, I should modify that last phrase to "and not in the manifestations of that behavior in the content of their science.") I first learned of the Matthew effect more than 20 years ago, on the occasion of my first and, perhaps until now, only, victimization at the hands of the New York Times.I learned the name for what the Times had done to me when I received a very nice note from P. W. Anderson in which he expressed his regret that the newspaper had given him exclusive credit for a nomenclatural advance that was entirely due to me. "A depressingly typical example of the Matthew effect" was how he characterized the misattribution. (I reported the entire history of this contretemps in these pages back in those dark ages [April 1981, page 46] before there were Reference Frame columns.) When I wrote back asking him what the Matthew effect was, he referred me to Merton.It was Merton who identified and named the tendency always to assign exclusive scientific credit to the most eminent among all the plausible candidates. At least I hope it was he, though I'm sure Merton, who invented many wonderful jokes himself, would have been delighted if the credit for it turned out to be misattributed to him. Merton named the effect after the Gospel According to Matthew, because there it is written, For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath.—Matthew 25:29.Could the widespread attribution of my wretched witticism to Feynman be another instance of this same deplorable practice? Had I once again been matthewed?Although I didn't say so in my old Reference-Frame article, what inspired this not so terribly bon mot were vivid memories of the responses my conceptual inquiries elicited from my professors—whom I viewed as agents of Copenhagen—when I was first learning quantum mechanics as a graduate student at Harvard, a mere 30 years after the birth of the subject. "You'll never get a PhD if you allow yourself to be distracted by such frivolities," they kept advising me, "so get back to serious business and produce some results." "Shut up," in other words, "and calculate." And so I did, and probably turned out much the better for it. At Harvard, they knew how to administer tough love in those olden days.This bit of history is relevant to the question of whether Feynman's abundance might have been augmented by a portion of the little that I had. Can you imagine the young Feynman ever having had a similar experience that seared "shut up and calculate" into his tender consciousness? No, of course you can't! Nobody could ever have had the slightest reason to direct the best human calculator that ever was to shut up and calculate.But perhaps Feynman was offering such advice to others who were searching for a better understanding of the quantum mechanical formalism. I can't believe that. He said that he "always had a great deal of difficulty understanding the world view that quantum mechanics represents," and added, "I still get nervous with it." 2 2. R. P. Feynman, Int. J. Theor. Phys. 21, 471 (1982). https://doi.org/10.1007/BF02650179 Nobody who felt that way would ever respond with "shut up and calculate" to conceptual inquiries from the perplexed.Well maybe Feynman, like me, was merely dismissing an interpretive position of others by lampooning it as a "shut up and calculate interpretation." I find this unlikely. For one thing, his strong preference for working things out for himself and, of course, his well-known disdain for philosophy make me doubt that he ever paid much attention to the interpretive positions of others. For another, would one for whom calculation was so effortless and understanding so important be likely to translate anybody's admonition against fruitless speculation into such terms?In short, I suspect that it is only Feynman's habitual irreverence that has linked him in the minds of many to the phrase "shut up and calculate." Who else among the high and mighty—and Merton has taught us that it is only among the high and mighty that people tend to look—could have said it? Albert Einstein? Don't be silly. Erwin Schrödinger? Of course not. Niels Bohr? Don't make me laugh. None of them besides Feynman could have said it. Does that mean that Feynman said it? No!Broaden the search to embrace the low and powerless. Among them am I, who hereby put forth the hypothesis that I was the first to use "shut up and calculate" in the context of quantum foundations. I'm not proud of having said it. It's not a beautiful phrase. It's not very clever. It's snide and mindlessly dismissive. But, damn it, if I'm the one who said it first, then that means I did not, even unconsciously, appropriate the words of Richard Feynman and pass them off as my own. So I have nothing to be ashamed of other than having characterized the Copenhagen interpretation in such foolish terms—a lesser offense than unconscious plagiarism, in my moral bookkeeping.So, dear reader, if you have evidence that Feynman really did say "shut up and calculate," please send it to me. I will not be happy to receive it. I'd rather be a Matthew victim than a plagiarist. But I'd like to know the truth.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. R. K. Merton, Science 159, 56 (1968). https://doi.org/10.1126/science.159.3810.56 , Google ScholarCrossref, ISI2. R. P. Feynman, Int. J. Theor. Phys. 21, 471 (1982). https://doi.org/10.1007/BF02650179 , Google ScholarCrossref, ISI© 2004 American Institute of Physics.

DOI
10.1063/1.1768652

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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

Measured responses to quantum Bayesianism

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Some time ago, John Bell and I wrote a tongue-in-cheek article on the interpretation of quantum mechanics;11. J. S. Bell, M. Nauenberg, in Preludes in Theoretical Physics, A. de Shalit, H. Feshbach, L. van Hove, eds., North Holland, Amsterdam (1966), p. 270;reprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge U. Press, New York (1987), p. 24. in it we remarked that only a minority of physicists had any interest in the topic and that the typical physicist thought he would understand it “if ever he can spare twenty minutes to think about it.” According to David Mermin, however, that situation has changed dramatically, and “new interpretations [of quantum mechanics] appear every year.”Actually, most textbooks on the subject continue to be based on the well-established Born interpretation of quantum mechanics, which postulates that the absolute square of the Schrödinger wavefunction, projected onto a particular quantum state, gives the probability for the occurrence of that state after an appropriate measurement has been made. Mermin indicated that the problem with the Born interpretation involves a confusion, “prevalent among physicists,” regarding the nature of probability. He presented his preference for a “personalist Bayesian view,” which leads separate “agents,” like Eugene Wigner and his friend, to make different probability assignments based on their beliefs. But as Richard Feynman remarked, “Nature does not know what you are looking at, and she behaves the way she is going to behave whether you bother to take down the data or not.”22. R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, vol. 3, Addison-Wesley, Redwood City, CA (1989), p. 3–7.Indeed, as applied to experiments, probability simply corresponds to the relative frequency for the occurrence of a given final state after identical states are prepared initially and measurements are made by appropriate detectors—devices that, through an irreversible macroscopic process, provide a permanent record of the outcome. Hence, the results of an experiment are independent of any observers, whose only role is to set up appropriate measurement devices, calculate the probabilities from quantum theory, and then write papers based on the recorded results.As Max Born also emphasized, in classical mechanics the situation is analogous, when one takes into account that in practice initial conditions in an experiment are known only imprecisely.33. M. Born, Dan. Mat. Fys. Medd. 30 (2), 1 (1955). Hence the observed evolution of the system is also determined by a probability function that satisfies the Liouville equation. But in that case, after a measurement is performed, no one talks about the “collapse” of this classical function, whereas in quantum mechanics it is common to use that controversial expression for the Schrödinger wavefunction.Mermin discussed a “shifty split” between the classical and the quantum domain, a split that supposedly “haunts quantum mechanics.” He claimed that “regardless of what is split from what, all versions of the shifty split are vague and ambiguous.” However, that is not always the case, as a simple example shows. Consider an initial quantum wavepacket for a particle under an attractive central force that varies inversely with the square of the radial distance—the classic problem of planetary motion from the viewpoint of quantum mechanics, for example, or an excited electron in a Rydberg atom. For a finite time, the wavepacket will follow a classical Keplerian elliptic orbit, but like the Liouville distribution for the analogous classical problem, from the outset it will disperse due to the spread in initial position and momentum.For the classical distribution to be in close correspondence with the quantum wavepacket, its initial spread is assumed to satisfy the uncertainty relation. Eventually, however, the head of the wavepacket, like in the classical distribution, will catch up with its tail. Afterwards, further spreading of the wavepacket leads to interference effects between the two components, and the classical–quantum correspondence ceases to be valid. The time when such interference effects first appear is of order nτ/3, where n is the mean principal quantum number of the wavepacket and τ is the Kepler period.44. M. Nauenberg, Phys. Rev. A 40, 1133 (1989). https://doi.org/10.1103/PhysRevA.40.1133 Experimentally, that transition has been observed to agree with theory in Rydberg atoms55. M. Nauenberg, C. Stroud, J. Yeazell, Sci. Am., June 1994, p. 44. https://doi.org/10.1038/scientificamerican0694-44 for n = 100, τ = 152 picoseconds, and nothing shifty about this classical–quantum correspondence is found. For planetary orbits, however, n is of order 1070, and therefore the answer to Albert Einstein’s often repeated remark “Is the moon there when nobody looks?” (see David Mermin, Physics Today, April 1985, page 38) is yes.REFERENCESSection:ChooseTop of pageREFERENCES <<1. J. S. Bell, M. Nauenberg, in Preludes in Theoretical Physics, A. de Shalit, H. Feshbach, L. van Hove, eds., North Holland, Amsterdam (1966), p. 270; Google Scholarreprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge U. Press, New York (1987), p. 24. Google Scholar2. R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, vol. 3, Addison-Wesley, Redwood City, CA (1989), p. 3–7. Google Scholar3. M. Born, Dan. Mat. Fys. Medd. 30 (2), 1 (1955). Google Scholar4. M. Nauenberg, Phys. Rev. A 40, 1133 (1989). https://doi.org/10.1103/PhysRevA.40.1133, Google ScholarCrossref, CAS5. M. Nauenberg, C. Stroud, J. Yeazell, Sci. Am., June 1994, p. 44. https://doi.org/10.1038/scientificamerican0694-44, Google ScholarCrossref© 2012 American Institute of Physics.

Physics Today•Nov 30, 2012•0 citations
Fifteen years ago, I mused in a Reference Frame column on how different generations of physicists differed in the degree to which they thought that the interpretation of quantum mechanics remains a serious problem (Physics Today, Physics Today 0031-9228 42 4 1989 9 https://doi.org/10.1063/1.2810963. April 1989, page 9 ). I declared myself to be among those who feel uncomfortable when asked to articulate what we really think about the quantum theory, adding that "If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be "Shut up and calculate!"In the intervening years, I've come to hold a milder and more nuanced opinion of the Copenhagen view, but that should be the subject of another column. The subject of this one is the habit of misquotation or misattribution that afflicts our profession, a rather different example of which I pointed out a few months ago (February 2004, page 10).Given my capacity for intellectual development ("inconsistency," in the terminology deployed in the current American political season), it's fortunate that I've now reached an age at which I tend to forget about things I've written more than a few years ago. Indeed, I find it downright irritating when somebody asks me questions about papers I wrote a mere half dozen years ago, naively identifying me with the author of those ancient texts. Until quite recently, I had no memory of ever having written such a childishly brusque dismissal of such an exquisitely subtle point of view, much less of having published it in so widely read a venue.This amnesia, combined with the evolution in my thinking that had distanced me from my long forgotten words, may explain why I was initially somewhat puzzled by the slight sensation of discomfort that passed over me when, browsing the e-print archive earlier this year, I read a characterization of Max Born's probability rule as "the favorite ingredient of what has been nicknamed, after Feynman's famous dictum, the shut up and calculate interpretation of quantum mechanics."I yield to nobody in my admiration for Richard Feynman's aphorisms on the nature of quantum mechanics. Indeed, long ago I published a poem (Physics Today, April 1985, page 47) consisting of nothing more than a resetting as verse of a paragraph Feynman had written about his own attitude toward the quantum theory, in his now (but not then) famous article that launched the whole field of quantum computation. I like to think I have devoured everything Feynman ever wrote on the character of quantum mechanics. But while "shut up and calculate" sounded dimly familiar to me as a characterization of a certain interpretive stance, I couldn't recall where Feynman had written it. Mulling this over, a terrible thought began to dawn on me. Could it be that I myself had once used the phrase? If so, then it would appear that I had picked it up from something by Feynman, forgotten the source, and presented it as my own. Devastating!It was devastating because I have a horror of writing or uttering any witticism that is not original with me, unless I make it absolutely clear where and (if known) from whom I got it. I don't even like to tell jokes unless I've made them up myself. (I digress to offer you my favorite:Question: What is the difference between theoretical physics and mathematical physics? Answer: Theoretical physics is done by physicists who lack the necessary skills to do real experiments; mathematical physics is done by mathematicians who lack the necessary skills to do real mathematics. Mathematical physicists tend not to like this joke, but other physicists seem to. Nonphysicists, of course, are entirely immune to its charms.)So with growing trepidation, I searched through my past writings on quantum mechanics. I was dismayed when I came upon my 1989 column, which confirmed my worst fears. Not only had I appropriated without proper attribution a Feynman quote, but it appeared to be a famous one. How humiliating! I was afflicted with visions of knowledgeable Physics Today readers shaking their heads 15 years ago at what must have struck them as my shameless attempt to ride to literary glory on the unacknowledged shoulders of Feynman.So I went to the Web to find the source, hoping I could then salvage my reputation by persuading Physics Today to print an addendum or erratum. Google gives more than 130 hits containing both "shut up and calculate" and "feynman." Most of these do not directly link the two, but about a dozen do. Here are a few: "Shut up and calculate" was a motto of Richard Feynman.For example, there's Feynman's "shut up and calculate."My personal philosophy is that of the famous physicist Richard Feynman, who said: "Shut up and calculate."When asked which interpretation of QM he favored, Feynman replied "Shut up and calculate."Richard Feynman foreslog ligefrem en "shut up and calculate" fortolkning af kvantemekanikken.Shut up and calculate—Richard Feynman.Just to make sure, I also searched for "shut up and calculate" and "mermin." I found only 10 hits, all of them mentioning me in ways that had nothing to do with their use, elsewhere, of "shut up and calculate." So it would have been clear to the world that I had indeed passed off Feynman's words as my own.Or had I …?I noticed that not a single one of the Web sites attributing the phrase to Feynman cited a source or hinted at the circumstances under which he had said it. A ray of hope flickered on: Could I once again have become a victim of the Matthew effect?The Matthew effect was enunciated by the great sociologist of science, Robert Merton. 1 1. R. K. Merton, Science 159, 56 (1968). https://doi.org/10.1126/science.159.3810.56 Merton worked in those innocent days when sociologists were interested only in the behavior of scientists and not in the content of their science. (To be fair to contemporary sociologists of science, I should modify that last phrase to "and not in the manifestations of that behavior in the content of their science.") I first learned of the Matthew effect more than 20 years ago, on the occasion of my first and, perhaps until now, only, victimization at the hands of the New York Times.I learned the name for what the Times had done to me when I received a very nice note from P. W. Anderson in which he expressed his regret that the newspaper had given him exclusive credit for a nomenclatural advance that was entirely due to me. "A depressingly typical example of the Matthew effect" was how he characterized the misattribution. (I reported the entire history of this contretemps in these pages back in those dark ages [April 1981, page 46] before there were Reference Frame columns.) When I wrote back asking him what the Matthew effect was, he referred me to Merton.It was Merton who identified and named the tendency always to assign exclusive scientific credit to the most eminent among all the plausible candidates. At least I hope it was he, though I'm sure Merton, who invented many wonderful jokes himself, would have been delighted if the credit for it turned out to be misattributed to him. Merton named the effect after the Gospel According to Matthew, because there it is written, For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath.—Matthew 25:29.Could the widespread attribution of my wretched witticism to Feynman be another instance of this same deplorable practice? Had I once again been matthewed?Although I didn't say so in my old Reference-Frame article, what inspired this not so terribly bon mot were vivid memories of the responses my conceptual inquiries elicited from my professors—whom I viewed as agents of Copenhagen—when I was first learning quantum mechanics as a graduate student at Harvard, a mere 30 years after the birth of the subject. "You'll never get a PhD if you allow yourself to be distracted by such frivolities," they kept advising me, "so get back to serious business and produce some results." "Shut up," in other words, "and calculate." And so I did, and probably turned out much the better for it. At Harvard, they knew how to administer tough love in those olden days.This bit of history is relevant to the question of whether Feynman's abundance might have been augmented by a portion of the little that I had. Can you imagine the young Feynman ever having had a similar experience that seared "shut up and calculate" into his tender consciousness? No, of course you can't! Nobody could ever have had the slightest reason to direct the best human calculator that ever was to shut up and calculate.But perhaps Feynman was offering such advice to others who were searching for a better understanding of the quantum mechanical formalism. I can't believe that. He said that he "always had a great deal of difficulty understanding the world view that quantum mechanics represents," and added, "I still get nervous with it." 2 2. R. P. Feynman, Int. J. Theor. Phys. 21, 471 (1982). https://doi.org/10.1007/BF02650179 Nobody who felt that way would ever respond with "shut up and calculate" to conceptual inquiries from the perplexed.Well maybe Feynman, like me, was merely dismissing an interpretive position of others by lampooning it as a "shut up and calculate interpretation." I find this unlikely. For one thing, his strong preference for working things out for himself and, of course, his well-known disdain for philosophy make me doubt that he ever paid much attention to the interpretive positions of others. For another, would one for whom calculation was so effortless and understanding so important be likely to translate anybody's admonition against fruitless speculation into such terms?In short, I suspect that it is only Feynman's habitual irreverence that has linked him in the minds of many to the phrase "shut up and calculate." Who else among the high and mighty—and Merton has taught us that it is only among the high and mighty that people tend to look—could have said it? Albert Einstein? Don't be silly. Erwin Schrödinger? Of course not. Niels Bohr? Don't make me laugh. None of them besides Feynman could have said it. Does that mean that Feynman said it? No!Broaden the search to embrace the low and powerless. Among them am I, who hereby put forth the hypothesis that I was the first to use "shut up and calculate" in the context of quantum foundations. I'm not proud of having said it. It's not a beautiful phrase. It's not very clever. It's snide and mindlessly dismissive. But, damn it, if I'm the one who said it first, then that means I did not, even unconsciously, appropriate the words of Richard Feynman and pass them off as my own. So I have nothing to be ashamed of other than having characterized the Copenhagen interpretation in such foolish terms—a lesser offense than unconscious plagiarism, in my moral bookkeeping.So, dear reader, if you have evidence that Feynman really did say "shut up and calculate," please send it to me. I will not be happy to receive it. I'd rather be a Matthew victim than a plagiarist. But I'd like to know the truth.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. R. K. Merton, Science 159, 56 (1968). https://doi.org/10.1126/science.159.3810.56 , Google ScholarCrossref, ISI2. R. P. Feynman, Int. J. Theor. Phys. 21, 471 (1982). https://doi.org/10.1007/BF02650179 , Google ScholarCrossref, ISI© 2004 American Institute of Physics.
Fifteen years ago, I mused in a Reference Frame column on how different generations of physicists differed in the degree to which they thought that the interpretation of quantum mechanics remains a serious problem. I declared myself to be among those who feel uncomfortable when asked to articulate what we really think about the quantum theory, adding that “If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be ‘Shut up and calculate!’” In the intervening years, I've come to hold a milder and more nuanced opinion of the Copenhagen view, but that should be the subject of another column. The subject of this one is the habit of misquotation or misattribution that afflicts our profession, a rather different example of which I pointed out a few months ago. Given my capacity for intellectual development (“inconsistency,” in the terminology deployed in the current American political season), it's fortunate that I've now reached an age at which I tend to forget about things I've written more than a few years ago. Indeed, I find it downright irritating when somebody asks me questions about papers I wrote a mere half dozen years ago, naively identifying me with the author of those ancient texts. Until quite recently, I had no memory of ever having written such a childishly brusque dismissal of such an exquisitely subtle point of view, much less of having published it in so widely read a venue. This amnesia, combined with the evolution in my thinking that had distanced me from my long-forgotten words, may explain why I was initially somewhat puzzled by the slight sensation of discomfort that passed over me when, browsing the e-print archive earlier this year, I read a characterization of Max Born's probability rule as “the favorite ingredient of what has been nicknamed, after Feynman's famous dictum, the shut up and calculate interpretation of quantum mechanics.” I yield to nobody in my admiration for Richard Feynman's aphorisms on the nature of quantum mechanics. Indeed, long ago I published a poem consisting of nothing more than a resetting as verse of a paragraph Feynman had written about his own attitude toward the quantum theory, in his now (but not then) famous article that launched the whole field of quantum computation. I like to think I have devoured everything Feynman ever wrote on the character of quantum mechanics.
If you have a restless intellect, it is very likely that you have played at some point with the idea of investigating the meaning and conceptual foundations of quantum mechanics. It is also probable (albeit not certain) that your intentions have been stopped on their tracks by an encounter with some version of the "Shut up and calculate" command. You may have heard that everything is already understood. That understanding is not your job. Or, if it is, it is either impossible or very difficult. Maybe somebody explained to you that physics is concerned with "hows" and not with "whys"; that whys are the business of "philosophy" ---you know, that dirty word. That what you call "understanding" is just being Newtonian; which of course you cannot ask quantum mechanics to be. Perhaps they also added some norms: The important thing a theory must do is predict; a theory must only talk about measurable quantities. It may also be the case that you almost asked "OK, and why is that?", but you finally bit your tongue. If you persisted in your intentions and the debate got a little heated up, it is even possible that it was suggested that you suffered of some type of moral or epistemic weakness that tend to disappear as you grow up. Maybe you received some job advice such as "Don't work in that if you ever want to own a house". I have certainly met all these objections in my short career, and I think that they are all just wrong. In this somewhat personal document, I try to defend that making sense of quantum mechanics is an exciting, challenging, important and open scientific endeavor. I do this by compulsively quoting Feynman (and others), and I provide some arguments that you might want to use the next time you confront the mentioned "opinions". By analogy with the anti-rationalistic Copenhagen command, all the arguments are subsumed in a standard answer to it: "Shut up and let me think"
Attitudes toward quantum mechanics differ interestingly from one generation of physicists to the next. The first generation are the founding fathers, who struggled through the welter of confusing and self-contradictory constructions to emerge with the modern theory of the atomic world and supply it with the “Copenhagen interpretation.” On the whole they seem to have taken the view that while the theory is extraordinarily strange (Bohr is said to have remarked that if it didn't make you dizzy then you didn't really understand it), the strangeness arises out of some deeply ingrained but invalid modes of thought. Once these are recognized and abandoned the theory makes sense in a perfectly straightforward way. The word “irrational,” which appears frequently in Bohr's early writings about the quantum theory, is almost entirely absent from his later essays. The second generation, those who were students of the founding fathers in the early postrevolutionary period, seem firmly—at times even ferociously—committed to the position that there is really nothing peculiar about the quantum world at all. Far from making bons mots about dizziness, or the opposite of deep truths being deep truths, they appear to go out of their way to make quantum mechanics sound as boringly ordinary as possible. The third generation—mine—were born a decade or so after the revolution and learned about the quantum as kids from popular books like George Gamow's. We seem to be much more relaxed about it than the other two. Few of us brood about what it all means, any more than we worry about how to define mass or time when we use classical mechanics. In contemplative moments some of us think the theory is wonderfully strange and others think it isn't; but we don't hold these views with great passion. Most of us, in fact, feel irritated, bored, or downright uncomfortable when asked to articulate what we really think about quantum mechanics. I'm one of the uncomfortable ones. If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be “Shut up and calculate!” But I won't shut up. I would rather celebrate the strangeness of quantum theory than deny it, because I believe it still has interesting things to teach us about how certain powerful but flawed verbal and mental tools we once took for granted continue to infect our thinking in subtly hidden ways.
The Copenhagen Interpretation of quantum mechanics has become the standard way of explaining the physical philosophical meaning of the mathematics of microscopic behavior. It developed from the thought of people who attended the Institute for Theoretical Physics of the University of Copenhagen during the 40 years that Niels Bohr directed it, from 1920 to 1962. Bohr took a large part in developing the Copenhagen Interpretation, he didn't escape all controversy over it (although the quote above is a bit of an exaggeration). Bohr did die before the experimental theoretical developments that have transposed the debate over the appropriateness adequacy of the Copenhagen Interpretation into a new key, he may well have been lucky to have escaped when he did. There is no authoritative codification of CI [the Copenhagen Interpretation], write T Gornitz C. E von Weizsacker of the Max Planck Institute in Starnberg, West Germany in' their formal presentation to the recent Loyola Conference on Mathematical Interpretational Problems in Relativistic Quantum Theory, and under the conditions of its origin there probably could not be one.... All prominent authors of the time who wrote on these questions, like Bohr, [Werner] Heisenberg, [Wolfgang] Pauli, J[ohn] v[on] Neumann on one side, [Albert] Einstein [Erwin] Schrodinger on the other, fell, so we feel, into some stammering when they tried to express their own positions. Nevertheless there is what might be called a Copenhagen attitude. It concentrates on observable phenomena, makes statistics probability central to its understanding, considers quantum mechanics primarily a theory of knowledge or information becomes a kind of physica negativa (analogous to a theologia negativa) in trying not to say too much about things that can't be seen or felt. For example, it doesn't much care whether the orbits of electrons in atoms are real or not and, in fact, tends to regard them as unreal. It appears in most textbooks as the standard way of looking at things.
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.
Some time ago, John Bell and I wrote a tongue-in-cheek article on the interpretation of quantum mechanics;11. J. S. Bell, M. Nauenberg, in Preludes in Theoretical Physics, A. de Shalit, H. Feshbach, L. van Hove, eds., North Holland, Amsterdam (1966), p. 270;reprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge U. Press, New York (1987), p. 24. in it we remarked that only a minority of physicists had any interest in the topic and that the typical physicist thought he would understand it “if ever he can spare twenty minutes to think about it.” According to David Mermin, however, that situation has changed dramatically, and “new interpretations [of quantum mechanics] appear every year.”Actually, most textbooks on the subject continue to be based on the well-established Born interpretation of quantum mechanics, which postulates that the absolute square of the Schrödinger wavefunction, projected onto a particular quantum state, gives the probability for the occurrence of that state after an appropriate measurement has been made. Mermin indicated that the problem with the Born interpretation involves a confusion, “prevalent among physicists,” regarding the nature of probability. He presented his preference for a “personalist Bayesian view,” which leads separate “agents,” like Eugene Wigner and his friend, to make different probability assignments based on their beliefs. But as Richard Feynman remarked, “Nature does not know what you are looking at, and she behaves the way she is going to behave whether you bother to take down the data or not.”22. R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, vol. 3, Addison-Wesley, Redwood City, CA (1989), p. 3–7.Indeed, as applied to experiments, probability simply corresponds to the relative frequency for the occurrence of a given final state after identical states are prepared initially and measurements are made by appropriate detectors—devices that, through an irreversible macroscopic process, provide a permanent record of the outcome. Hence, the results of an experiment are independent of any observers, whose only role is to set up appropriate measurement devices, calculate the probabilities from quantum theory, and then write papers based on the recorded results.As Max Born also emphasized, in classical mechanics the situation is analogous, when one takes into account that in practice initial conditions in an experiment are known only imprecisely.33. M. Born, Dan. Mat. Fys. Medd. 30 (2), 1 (1955). Hence the observed evolution of the system is also determined by a probability function that satisfies the Liouville equation. But in that case, after a measurement is performed, no one talks about the “collapse” of this classical function, whereas in quantum mechanics it is common to use that controversial expression for the Schrödinger wavefunction.Mermin discussed a “shifty split” between the classical and the quantum domain, a split that supposedly “haunts quantum mechanics.” He claimed that “regardless of what is split from what, all versions of the shifty split are vague and ambiguous.” However, that is not always the case, as a simple example shows. Consider an initial quantum wavepacket for a particle under an attractive central force that varies inversely with the square of the radial distance—the classic problem of planetary motion from the viewpoint of quantum mechanics, for example, or an excited electron in a Rydberg atom. For a finite time, the wavepacket will follow a classical Keplerian elliptic orbit, but like the Liouville distribution for the analogous classical problem, from the outset it will disperse due to the spread in initial position and momentum.For the classical distribution to be in close correspondence with the quantum wavepacket, its initial spread is assumed to satisfy the uncertainty relation. Eventually, however, the head of the wavepacket, like in the classical distribution, will catch up with its tail. Afterwards, further spreading of the wavepacket leads to interference effects between the two components, and the classical–quantum correspondence ceases to be valid. The time when such interference effects first appear is of order nτ/3, where n is the mean principal quantum number of the wavepacket and τ is the Kepler period.44. M. Nauenberg, Phys. Rev. A 40, 1133 (1989). https://doi.org/10.1103/PhysRevA.40.1133 Experimentally, that transition has been observed to agree with theory in Rydberg atoms55. M. Nauenberg, C. Stroud, J. Yeazell, Sci. Am., June 1994, p. 44. https://doi.org/10.1038/scientificamerican0694-44 for n = 100, τ = 152 picoseconds, and nothing shifty about this classical–quantum correspondence is found. For planetary orbits, however, n is of order 1070, and therefore the answer to Albert Einstein’s often repeated remark “Is the moon there when nobody looks?” (see David Mermin, Physics Today, April 1985, page 38) is yes.REFERENCESSection:ChooseTop of pageREFERENCES <<1. J. S. Bell, M. Nauenberg, in Preludes in Theoretical Physics, A. de Shalit, H. Feshbach, L. van Hove, eds., North Holland, Amsterdam (1966), p. 270; Google Scholarreprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge U. Press, New York (1987), p. 24. Google Scholar2. R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, vol. 3, Addison-Wesley, Redwood City, CA (1989), p. 3–7. Google Scholar3. M. Born, Dan. Mat. Fys. Medd. 30 (2), 1 (1955). Google Scholar4. M. Nauenberg, Phys. Rev. A 40, 1133 (1989). https://doi.org/10.1103/PhysRevA.40.1133, Google ScholarCrossref, CAS5. M. Nauenberg, C. Stroud, J. Yeazell, Sci. Am., June 1994, p. 44. https://doi.org/10.1038/scientificamerican0694-44, Google ScholarCrossref© 2012 American Institute of Physics.