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Physics Today

Measured responses to quantum Bayesianism

Michael Nauenberg

Published Nov 30, 2012• 0 citations
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Abstract

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.

DOI
10.1063/pt.3.1800

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Measured responses to quantum Bayesianism

Art Hobson

Because it’s important that physicists discuss the problems of quantum foundations, I was delighted to see David Mermin’s commentary on “fixing the shifty split.” But I must disagree with my friend’s view.There are multiple ways of interpreting probabilities.11. A. Hobson, Concepts in Statistical Mechanics, Gordon and Breach, New York (1971), p. 27. In quantum physics, the Bayesian “degree of belief” interpretation can be appropriate for mixed states, but only the frequentist or “ensemble” interpretation applies to the pure states that Mermin discusses.A recent paper by Matthew Pusey and coauthors22. M. F. Pusey, J. Barrett, T. Rudolph, http://arxiv.org/abs/1111.3328v1. concludes that if two different pure quantum states are assigned to a single physical situation, one of the states is objectively wrong. The proof’s main assumption is that any quantum system has some set of real physical properties, labeled λ. Pusey and coauthors show that two different pure states cannot represent the same λ. So, although their paper implies but does not assume that quantum states are physically real, it does assume that each specific physical situation has behind it some kind of physical reality. Chris Fuchs, quoted favorably by Mermin, might dispute the notion that some kind of physical reality actually exists, but most physicists are probably sufficiently realist to grant that notion. Without such a notion, science lies somewhere between solipsism and superstition.Whenever I hear subjective interpretations of quantum physics, I wonder about such questions as the one Mermin quotes from Albert Einstein: Can a mouse collapse a wavefunction? Mermin’s Bayesian response, that a mouse cannot but a physics student can, doesn’t reassure me. Were wavefunctions not collapsing before there were physicists?The “Wigner’s friend” paradox, as described in Mermin’s commentary, doesn’t need a subjective interpretation to find a solution. In fact, Eugene Wigner abandoned his interpretation around 1970 once he became aware of the ideas underlying quantum decoherence.33. M. Schlosshauer, Decoherence and the Quantum-to-Classical Transition, Springer, Berlin (2007), p. 364. Suppose Wigner’s friend makes a measurement, the outcome of which is known to the friend but not to Wigner. Regardless of whether the outcome is known, and in fact regardless of the presence of the friend, the measurement device must decohere the quantum system that’s being measured, putting the system into a mixed state of the either/or form, with no interferences, just like a coin that’s been flipped. A definite outcome has thus occurred, and Wigner and his friend will both agree on this. Neither the friend nor Wigner affects the outcome. She has simply “looked” and now knows the outcome, while Wigner doesn’t know. That is not paradoxical and does not require a revision of our understanding of pure quantum states.There’s no reason to give up on a realist interpretation of quantum physics, much less a realist interpretation of nature itself.REFERENCESSection:ChooseTop of pageREFERENCES <<1. A. Hobson, Concepts in Statistical Mechanics, Gordon and Breach, New York (1971), p. 27. Google Scholar2. M. F. Pusey, J. Barrett, T. Rudolph, http://arxiv.org/abs/1111.3328v1. Google Scholar3. M. Schlosshauer, Decoherence and the Quantum-to-Classical Transition, Springer, Berlin (2007), p. 364. Google Scholar© 2012 American Institute of Physics.

Physics Today•Nov 30, 2012•1 citation

Measured responses to quantum Bayesianism

N. David Mermin

Mermin replies: Robert Griffiths takes my joke about an undergraduate collapsing a wavepacket to be an attempt to solve the measurement problem. The actual QBist solution—versions of which predate QBism (see, for example, reference 11. J. B. Hartle, Am. J. Phys. 36, 704 (1968). https://doi.org/10.1119/1.1975096)—is that a quantum state is not an objective property of the world but a compendium of probabilities constructed by an agent. When an agent updates her state assignment, nothing changes in her external world. The only change is in the agent’s expectations for her subsequent experience of that world, and therefore there is no measurement problem. Consistent historians agree that collapse is not a physical process, but for entirely different reasons.QBism takes the “mysterious whatever-it-is” that Griffiths criticizes in quantum orthodoxy to be the experience induced in an agent by the world. That, and the fact that different agents may have different experiences, drains the swamp, slays the dragon, and quiets the maddening paradoxes.QBists hold that any agent can indeed apply quantum mechanics to her own external world, from quarks to quasars. Only an agent’s personal, directly perceived experience is boxed off from the domain of applicability. That exclusion disagrees with most versions of the many-worlds interpretation, but it does not limit the scope of science: Alice can apply quantum mechanics to the experience of another agent, Bob, as represented through his words, writings, or drawings, all of which do belong to her external world.The way in which Bob’s experience impinges on Alice resonates with Niels Bohr’s emphasis on the need to state results of experiments in ordinary language. It also addresses Ching Hung Woo’s question of how different agents can come to agreement on their state assignments.Griffiths correctly notes that QBism violates the first desideratum he quotes from my 15-year-old “Ithaca interpretation.” Like Barack Obama’s view of marriage, my thinking about quantum foundations has evolved. But Griffiths wrongly claims that QBism rejects the other desideratum he quotes: locality. Actually, QBism insists on it. The absurdity of quantum nonlocality provides an independent argument that quantum states cannot be objective internal properties of the systems they describe, whether or not one regards probabilities as subjective. Griffiths is probably right, however, that John Bell would not have been pleased with how QBists fix his shifty split.I would not call QBism an “antiquated approach.” It is younger than Griffiths’ consistent histories and, as I have remarked upon elsewhere,22. M. Schlosshauer, ed., Elegance and Enigma: The Quantum Interviews, Springer, Berlin (2011), pp. 177, 280. taking reality itself to be relative to what he calls a framework, is vastly more radical than taking quantum state assignments to be relative to an agent.But foreshadowings of QBism can indeed be found in antiquity. Since writing my commentary, I came across another striking anticipation in a 1931 letter from Erwin Schrödinger to Arnold Sommerfeld:33. K. von Meyenn, ed., Eine Entdeckung von ganz außerordentlicher Tragweite: Schrödingers Briefwechsel zur Wellenmechanik und zum Katzenparadoxon, Springer, Berlin (2011), p. 490. “Quantum mechanics forbids statements about what really exists—statements about the object. It deals only with the object–subject relation. Although this holds, after all, for any description of nature, it appears to hold in a much more radical and far-reaching sense in quantum mechanics” (translated by N. D. Mermin and Ruediger Schack).When Bell and Michael Nauenberg wrote their delightful article in 1966, there was indeed much less interest in quantum foundations than there is today. Most textbooks have wisely steered clear of the many contemporary interpretive positions, since none of them are held by more than a fraction of those physicists with an interest in such issues.QBists do not reject the Born rule for calculating probabilities, but they do reject the objective frequentist interpretation of those probabilities presented by Nauenberg and held by most physicists. The frequentist view is notoriously circular. It defines probability using such notions as “equally probable,” “unlikely,” or (with Nauenberg) “identically prepared,” none of which make sense without a prior definition of probability. “Identically prepared” might seem safe from circularity, but two different preparations cannot be strictly identical. It would be more accurate to say they must differ in unimportant ways. Unimportant for what? For the probabilities of the outcomes.When I started to learn about subjective probability, I was surprised to discover that most of the books were not in Cornell University’s physics or mathematics libraries but in the business school library. In our recent election, Americans have been told that business experience is necessary for being president; I would suggest that it may be even more helpful for understanding quantum mechanics.I cannot tell from Nauenberg’s remarks about the Liouville equation whether he agrees with the view of QBists (and many others) that the collapse of the wavefunction is no more than the updating of a collection of probability distributions.Nauenberg’s example of the Rydberg atom does not contradict the QBist resolution of Bell’s shifty split. The Rydberg atom is part of the world external to the agent, and therefore on the quantum side of her split. There are indeed circumstances under which fully quantum mechanical behavior can look very classical.Art Hobson repeats the common view that only mixed states can be associated with subjective probabilities. QBism takes that to be the very mistake that got us lost for so long in the quantum swamp. Hobson also believes that wavefunctions were collapsing before there were physicists. Does he believe that probabilities were updating before there were statisticians?Hobson wrongly claims that Chris Fuchs “might dispute the notion that some kind of physical reality actually exists.” What he and other QBists do deny is that there are properties of the external world—“elements of reality”—that underlie quantum state assignments. (The argument of Matthew Pusey and coauthors that Hobson cites, implying that quantum states are physically real, relies on such hidden variables.) An agent’s state assignment rests entirely on her experience of the external world. It is neither solipsistic nor superstitious to maintain that any agent’s experience comes fully into being only at the moment it is experienced.Hobson’s treatment of Eugene Wigner and his friend relies on decoherence producing an objective mixed state, which both of them must agree on. But since quantum mechanics holds all the way out to infinity (as Griffiths puts it), even from an objective view of quantum states, that switch from superposition to either/or is at best a FAPP solution, to use Bell’s wonderfully sardonic abbreviation of “for all practical purposes.”QBism does not, as Hobson concludes, give up on a realist interpretation of nature. But it does warn us not to confuse nature with the abstractions we have ingeniously constructed to help any agent deal with the very real impact of nature on his or her own internal experience (see my Reference Frame, Physics Today, May 2009, page 8).I’m glad that Blake Stacey has called attention to some of the more applied spinoffs of QBism. I’m also pleased that he mentions Bruno de Finetti, one of the great 20th-century pioneers of subjective probability. Indeed, since there are objective as well as subjective Bayesians, if I had my way, the B in QBism would stand not for Thomas Bayes, but for Bruno de Finetti, who put the crucial point like this: “The abandonment of superstitious beliefs about the existence of Phlogiston, the Cosmic Ether, Absolute Space and Time … , or Fairies and Witches, was an essential step along the road to scientific thinking. Probability, too, if regarded as something endowed with some kind of objective existence, is no less a misleading misconception, an illusory attempt to exteriorize or materialize our [actual (vero)] probabilistic beliefs.”44. B. de Finetti, Theory of Probability, Interscience, New York (1990), preface.REFERENCESSection:ChooseTop of pageREFERENCES <<1. J. B. Hartle, Am. J. Phys. 36, 704 (1968). https://doi.org/10.1119/1.1975096, Google ScholarCrossref2. M. Schlosshauer, ed., Elegance and Enigma: The Quantum Interviews, Springer, Berlin (2011), pp. 177, 280. Google ScholarCrossref3. K. von Meyenn, ed., Eine Entdeckung von ganz außerordentlicher Tragweite: Schrödingers Briefwechsel zur Wellenmechanik und zum Katzenparadoxon, Springer, Berlin (2011), p. 490. Google ScholarCrossref4. B. de Finetti, Theory of Probability, Interscience, New York (1990), preface. Google Scholar© 2012 American Institute of Physics.

Physics Today•Nov 30, 2012•6 citations

More on the quantum measurement problem

Gregory N. Derry

Although I have neither an objection to nor an endorsement of David Mermin’s major premise in his Quick Study, “There is no quantum measurement problem” (Physics Today, June 2022, page 62), I would like to make several contextual points.Mermin’s argument has an extensive history, along with a comparable history of rebuttal. Five decades ago Max Jammer wrote that “measurements in quantum mechanics are no more or less problematic than in classical physics, for the Hilbert space vector is only a purely formal device for relating the statistics associated with these arrangements to the physics of observations in classical physics.” That seems like a condensed version of the argument Mermin presents. On the following page, however, Jammer notes that a “problematic aspect whose serious implications were only gradually understood was the fact that as long as a quantum mechanical one-body or many-body system does not interact with macroscopic objects, as long as its motion is described by the deterministic Schrödinger time-dependent equation, no events could be considered to take place in the system.”11. M. Jammer, The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective, Wiley (1974), pp. 473, 474.Niels Bohr giving a lecture in Copenhagen in April 1929. (Photograph by Samuel Goudsmit, courtesy of the AIP Emilio Segrè Visual Archives, Goudsmit Collection.)PPT|High resolutionRegarding the quotations from Niels Bohr, Mermin’s point is entirely valid and represents Bohr’s position accurately, but Bohr’s thought is always subtle and difficult to capture completely. Another quotation from Bohr, which is consistent with everything else he wrote, is, “The decisive point is that in neither case does the appropriate widening of our conceptual framework imply any appeal to the observing subject, which would hinder unambiguous communication of experience.”22. N. Bohr, Essays 1958–1962 on Atomic Physics and Human Knowledge, Ox Bow Press (1987), p. 7. That quotation seems inconsistent with Mermin’s paragraph that includes the passage “Why should I insist that my interpretation of science, which I use to make sense of the world that I experience, should never make any mention of me?” Bohr always insisted that his framework was a rational “generalization” of classical objectivity.The last and most conceptually important point concerns the ontological status of probability. I don’t necessarily disagree with Mermin and Bruno de Finetti, but it is by no means obvious that they are correct either. David Hawkins, for example, begins 50 pages of rigorous analysis with a brief statement of a major premise.The obvious and natural interpretation of probability in this context is that it introduces, not something that has to do with the nature of the physical system, but something that has to do with the incompleteness of our knowledge….But this opinion turns out to be false. Ignorance of dynamical regularity may be a motive for resorting to probabilities, but it does not explain the probabilities to which we resort.33. D. Hawkins, The Language of Nature: An Essay in the Philosophy of Science, W. H. Freeman (1964), p. 135.Another example can be found in Jammer’s well-known historical account of quantum theory: “For Einstein the notion of probability … was the traditional conception of classical physics, a mathematical objectivization of the human deficiency of complete or exact knowledge but ultimately a creation of the human mind…. For Born probability, as far as it was related to the wave function, was not merely a mathematical fiction but something endowed with physical reality.”44. M. Jammer, The Conceptual Development of Quantum Mechanics, McGraw-Hill (1966), p. 286.Of course, such examples don’t mean that Mermin’s position is incorrect, but I do think that they demand a better argument than a comparison to “Fairies and Witches.” I am confident that Mermin has such an argument, and I look forward to reading it as I continue working toward a coherent position on the unresolved interpretational issues of quantum theory.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. M. Jammer, The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective, Wiley (1974), pp. 473, 474. Google Scholar2. N. Bohr, Essays 1958–1962 on Atomic Physics and Human Knowledge, Ox Bow Press (1987), p. 7. Google Scholar3. D. Hawkins, The Language of Nature: An Essay in the Philosophy of Science, W. H. Freeman (1964), p. 135. Google Scholar4. M. Jammer, The Conceptual Development of Quantum Mechanics, McGraw-Hill (1966), p. 286. Google Scholar© 2022 American Institute of Physics.

Physics Today•Nov 1, 2022•2 citations

Measured responses to quantum Bayesianism

Robert B. Griffiths

David Mermin, in his commentary in the July 2012 issue of Physics Today (page 8), put forth what he calls the QBist (quantum Bayesian) approach to quantum foundations. He claims that replacing a frequentist approach to quantum probabilities with a Bayesian approach solves the quantum measurement problem and fixes the “shifty split” between classical and quantum that John Bell complained about.11. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd ed., Cambridge U. Press, New York (2004), chap. 23. I disagree. Mermin has not addressed the real issue that besets quantum probabilities, he has not solved the measurement problem, and he has put the shifty split in the wrong place.The quantum measurement problem, understanding an actual physical measurement in fully quantum terms, has two parts. First, unitary time development (Schrödinger’s equation) often results in a quantum superposition of different outcomes—different positions of the apparatus pointer, in the quaint language of quantum foundations. Various equivocations proposed to get rid of that Schrödinger’s cat were among the main targets of Bell’s critique. When this first part is solved the second task is to link the pointer position to the microscopic property the apparatus was designed to measure, at a time before the measurement took place. Experimental physicists talk about detecting a gamma ray emitted by a nucleus, or a neutrino emitted in a supernova explosion, using apparatus that either destroys or violently alters the object under study. They are not fools, though one might think so from reading textbook discussions of measurement that only consider properties of a microscopic system at a time after interacting with the apparatus—best referred to as a preparation, not a measurement.Mermin seems to think that the measurement problem—presumably the first problem—is solved by using the quantum wavefunction to calculate a probability, in a manner easily taught to undergraduates. However, the main conceptual difficulty with quantum probabilities is not in calculating them but in identifying their referents, what it is they are about. When the weatherman assigns a high probability to a severe thunderstorm on Thursday afternoon, both frequentists and Bayesians will want to seek shelter. They will agree that the probability refers to thunderstorms rather than stock-market prices. The first task in constructing a probabilistic model, for the weather or games of chance or radioactive decay, is to identify a sample space of mutually exclusive possibilities, one and only one of which can be correct or occur in a particular experiment or on a particular occasion. Only when a sample space has been defined is it possible to assign probabilities to suitable subsets, averages to random variables, and so forth.A classical phase space is easily turned into a probabilistic sample space: The different points represent distinct physical states of affairs. But a quantum Hilbert space is very different if, following John von Neumann’s thinking, one associates physical properties with (closed) subspaces and associates their negations with orthogonal complements of the subspaces. That classical–quantum difference was the origin of quantum logic,22. G. Birkhoff, J. von Neumann, Ann. Math. 37, 823 (1936). https://doi.org/10.2307/1968621 which, despite early hopes and much hard work, has not resolved the conceptual difficulties of quantum mechanics.33. G. Bacciagaluppi, in Handbook of Quantum Logic and Quantum Structures: Quantum Logic, K. Engesser, D. M. Gabbay, D. Lehmann, eds., North-Holland, Amsterdam (2009), p. 49. But it does point to important issues that need to be considered when discussing quantum probabilities. Mermin and his fellow QBists should pay attention.Quantum orthodoxy has no solution for the fundamental problem of defining a quantum sample space. Instead, it covers with a black box the mysterious whatever-it-is that the quantum wavefunction might have something to do with. Talking about what is under the box is more or less strictly forbidden, for it is well known that physicists who attempt to do so will fall into the quantum swamp, to be eaten by the Great Smoky Dragon or driven insane by the Paradoxes. The black box is my term for Bell’s split between the macroscopic and microscopic, a split forever shifting as experimentalists manage to entangle larger and larger quantum systems. According to Mermin, the QBists place the split “between the world in which an agent lives and her experience of that world.” That is no improvement: The box would then cover the physicist rather than the quantum mystery. Bell would not have been pleased.Bell was unaware of the consistent or decoherent histories approach to quantum mechanics,44. P. C. Hohenberg, Rev. Mod. Phys. 82, 2835 (2010); https://doi.org/10.1103/RevModPhys.82.2835 R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); R. B. Griffiths, Found. Phys. 41, 705 (2011). https://doi.org/10.1007/s10701-010-9512-5 which, unlike QBism, solves both measurement problems in a way fully consistent with the Hilbert space structure of quantum mechanics and consistent with special relativity. It drives the shifty split off to infinity where it belongs: Quantum physics applies at all scales, from the quarks to the quasars. And it gets rid of the spooky nonlocal influences that Einstein found so distasteful. It seems odd that Mermin has thrown his lot in with the QBists rather than paying serious attention to the histories approach which, unlike QBism, clearly satisfies two desiderata for a good quantum interpretation that he himself put forward 15 years ago:55. N. D. Mermin, Pramana 51, 549 (1998). https://doi.org/10.1007/BF02827447 “The theory should describe an objective reality independent of observers and their knowledge” and “objectively real internal properties of an isolated individual system should not change when something is done to another non-interacting system.”Mermin says even undergraduates can be taught enough quantum mechanics to update a quantum state assignment. I remember when my undergraduate quantum mechanics teacher, Robert Dicke of cosmic-background fame, was visibly uncomfortable as he introduced us to wavefunction collapse. For those who share this discomfort, I recommend that rather than telling students to “shut up and calculate,” we‣ Introduce them to the rudiments of probability theory, including the conditional probabilities used by both frequentists and Bayesians; one need not take sides.‣ Explain how to construct quantum sample spaces and assign probabilities in a way that does not generate paradoxes.‣ Explain wavefunction collapse as a tool for calculating certain conditional probabilities that can also be obtained using other methods; it is not a physical process.Readers who want more details can contact me or consult the works cited in reference 44. P. C. Hohenberg, Rev. Mod. Phys. 82, 2835 (2010); https://doi.org/10.1103/RevModPhys.82.2835 R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); R. B. Griffiths, Found. Phys. 41, 705 (2011). https://doi.org/10.1007/s10701-010-9512-5 . I think it is high time we abolished antiquated approaches to teaching quantum theory along with the shifty split that confuses both students and their instructors.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd ed., Cambridge U. Press, New York (2004), chap. 23. Google ScholarCrossref2. G. Birkhoff, J. von Neumann, Ann. Math. 37, 823 (1936). https://doi.org/10.2307/1968621, Google ScholarCrossref3. G. Bacciagaluppi, in Handbook of Quantum Logic and Quantum Structures: Quantum Logic, K. Engesser, D. M. Gabbay, D. Lehmann, eds., North-Holland, Amsterdam (2009), p. 49. Google ScholarCrossref4. P. C. Hohenberg, Rev. Mod. Phys. 82, 2835 (2010); https://doi.org/10.1103/RevModPhys.82.2835 , Google ScholarCrossrefR. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); , Google ScholarR. B. Griffiths, Found. Phys. 41, 705 (2011). https://doi.org/10.1007/s10701-010-9512-5 , Google ScholarCrossref5. N. D. Mermin, Pramana 51, 549 (1998). https://doi.org/10.1007/BF02827447 , Google ScholarCrossref, CAS© 2012 American Institute of Physics.

Physics Today•Nov 30, 2012•1 citation

More on the quantum measurement problem

N. David Mermin

Among Art Hobson’s and Gregory Derry’s letters and Sean Carroll’s July Quick Study (page 62), only Derry’s letter addresses the point I was trying to make in my June Quick Study (page 62): Viewing probabilities as personal judgments eliminates the quantum measurement problem and enables one to make better sense of quantum mechanics.Hobson’s letter expounds his own realistic view of quantum states and their collapse. It belongs with the three examples I mention that eliminate the physicist from the story.Carroll takes what I write about the consequences of a personalist interpretation of probability to be an example of an epistemic interpretation of quantum mechanics. That misses my point.In 1926 Max Born noted that the content of quantum states was the probabilities that they enabled one to calculate. It is strange that after thus elevating probability to a new and foundational role, no physicists then or for the next three-quarters of a century thought it important to reexamine the meaning of probability. For most physicists, probabilities are user-independent frequencies, but for most statisticians, they are guides to action by the person who made the probability assignment. If physicists in 1926 had held a personalist view of probability, it would have required them from the very beginning to hold a personalist (“epistemic”) view of quantum states. There would have been no need for an “interpretation.”I have comments on several issues raised by Derry. Max Jammer and many others have indeed written for over half a century that quantum states are nothing more than formal devices for encapsulating probabilities of observation. But nobody before Carlton Caves, Christopher Fuchs, and Rüdiger Schack ever added that if probabilities are viewed as personal judgments of the person who assigns them, then that same view must be taken of quantum states.Derry quotes Niels Bohr’s statement that he does not “appeal to the observing subject.” Later in that paragraph, Bohr adds that “all subjectivity is avoided by proper attention to the circumstances required for the well-defined use of elementary physical concepts.”11. N. Bohr, Essays 1958–1962 on Atomic Physics and Human Knowledge, Ox Bow Press (1987), p. 7. That does contradict my reading of the two Bohr quotations that appear in my Quick Study. By “experience,” Bohr must have meant collective rather than individual experience. I doubt that Bohr took a personalist view of probability. That Bohr, however, was a personalist is argued interestingly by Ulrich Mohrhoff.22. U. Mohrhoff, https://arxiv.org/abs/1905.07118.I quote Bruno de Finetti on “Fairies and Witches” only to give a poetic statement of the unfamiliar view of probability that I am inviting physicists to examine. My point is that if de Finetti is correct, then it would profoundly affect our understanding of quantum mechanics. For me, the illumination it sheds on the interpretation of quantum mechanics is all by itself a compelling reason for adopting a personalist view of probability.The expansion of my argument that Derry looks forward to reading can be found in the article of mine33. N. D. Mermin, Rep. Prog. Phys. 82, 012002 (2019). https://doi.org/10.1088/1361-6633/aae2c6 cited in my Quick Study along with the rather more technical article44. C. A. Fuchs, R. Schack, Rev. Mod. Phys. 85, 1693 (2013). https://doi.org/10.1103/RevModPhys.85.1693 by Fuchs and Schack that inspired mine.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. N. Bohr, Essays 1958–1962 on Atomic Physics and Human Knowledge, Ox Bow Press (1987), p. 7. Google Scholar2. U. Mohrhoff, https://arxiv.org/abs/1905.07118. Google Scholar3. N. D. Mermin, Rep. Prog. Phys. 82, 012002 (2019). https://doi.org/10.1088/1361-6633/aae2c6, Google ScholarCrossref4. C. A. Fuchs, R. Schack, Rev. Mod. Phys. 85, 1693 (2013). https://doi.org/10.1103/RevModPhys.85.1693, Google ScholarCrossref, ISI© 2022 American Institute of Physics.

Physics Today•Nov 1, 2022•1 citation

THE ROAD NOT TAKEN: A Different Kind of Physics

Rowan Brad Quni-Gudzinas

Quantum mechanics is our most successful physical theory. It predicts the behavior of atoms, molecules, and light to ten decimal places. No experiment has ever contradicted it. It also contains a crack at its foundation. The theory’s central equation—the Schrodinger equation—describes a smooth, continuous, perfectly predictable evolution of the quantum state. But whenever anyone performs a measurement, they get a single, definite result. Which result they get appears to be random. The transition from smooth evolution to random outcome is called the “collapse of the wavefunction,” and after nearly a century of analysis, there is no agreed-upon explanation for what causes it, when it occurs, or whether it occurs at all. This is the measurement problem. The measurement problem is not a minor puzzle at the margins of the theory. It is a failure to explain the most basic operation in science: looking at the result of an experiment. Around it cluster other puzzles. Light behaves like a wave in some experiments and like a particle in others—two contradictory descriptions. Two particles that have interacted remain correlated across arbitrary distances, as though communicating faster than light. The probabilities that govern measurement outcomes appear as a postulate—the Born rule—inserted by hand with no deeper justification. And the theory offers no unified picture of reality: quantum mechanics, general relativity, and the standard model of particle physics speak incompatible mathematical languages. A century of effort has produced many interpretations of quantum mechanics. Copenhagen. Many-worlds. De Broglie-Bohm. Objective collapse. Quantum Bayesianism. None has achieved consensus. The measurement problem remains. This document proposes that the source of these puzzles is not quantum mechanics itself. It is a single, invisible assumption made at the very beginning of the theory in 1900—an assumption so deeply embedded that nobody noticed they were making it. Change that assumption, and the puzzles do not get solved. They dissolve. They stop being puzzles. They become predictable consequences of geometry.

•May 3, 2026•0 citations
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.
Because it’s important that physicists discuss the problems of quantum foundations, I was delighted to see David Mermin’s commentary on “fixing the shifty split.” But I must disagree with my friend’s view.There are multiple ways of interpreting probabilities.11. A. Hobson, Concepts in Statistical Mechanics, Gordon and Breach, New York (1971), p. 27. In quantum physics, the Bayesian “degree of belief” interpretation can be appropriate for mixed states, but only the frequentist or “ensemble” interpretation applies to the pure states that Mermin discusses.A recent paper by Matthew Pusey and coauthors22. M. F. Pusey, J. Barrett, T. Rudolph, http://arxiv.org/abs/1111.3328v1. concludes that if two different pure quantum states are assigned to a single physical situation, one of the states is objectively wrong. The proof’s main assumption is that any quantum system has some set of real physical properties, labeled λ. Pusey and coauthors show that two different pure states cannot represent the same λ. So, although their paper implies but does not assume that quantum states are physically real, it does assume that each specific physical situation has behind it some kind of physical reality. Chris Fuchs, quoted favorably by Mermin, might dispute the notion that some kind of physical reality actually exists, but most physicists are probably sufficiently realist to grant that notion. Without such a notion, science lies somewhere between solipsism and superstition.Whenever I hear subjective interpretations of quantum physics, I wonder about such questions as the one Mermin quotes from Albert Einstein: Can a mouse collapse a wavefunction? Mermin’s Bayesian response, that a mouse cannot but a physics student can, doesn’t reassure me. Were wavefunctions not collapsing before there were physicists?The “Wigner’s friend” paradox, as described in Mermin’s commentary, doesn’t need a subjective interpretation to find a solution. In fact, Eugene Wigner abandoned his interpretation around 1970 once he became aware of the ideas underlying quantum decoherence.33. M. Schlosshauer, Decoherence and the Quantum-to-Classical Transition, Springer, Berlin (2007), p. 364. Suppose Wigner’s friend makes a measurement, the outcome of which is known to the friend but not to Wigner. Regardless of whether the outcome is known, and in fact regardless of the presence of the friend, the measurement device must decohere the quantum system that’s being measured, putting the system into a mixed state of the either/or form, with no interferences, just like a coin that’s been flipped. A definite outcome has thus occurred, and Wigner and his friend will both agree on this. Neither the friend nor Wigner affects the outcome. She has simply “looked” and now knows the outcome, while Wigner doesn’t know. That is not paradoxical and does not require a revision of our understanding of pure quantum states.There’s no reason to give up on a realist interpretation of quantum physics, much less a realist interpretation of nature itself.REFERENCESSection:ChooseTop of pageREFERENCES <<1. A. Hobson, Concepts in Statistical Mechanics, Gordon and Breach, New York (1971), p. 27. Google Scholar2. M. F. Pusey, J. Barrett, T. Rudolph, http://arxiv.org/abs/1111.3328v1. Google Scholar3. M. Schlosshauer, Decoherence and the Quantum-to-Classical Transition, Springer, Berlin (2007), p. 364. Google Scholar© 2012 American Institute of Physics.
Mermin replies: Robert Griffiths takes my joke about an undergraduate collapsing a wavepacket to be an attempt to solve the measurement problem. The actual QBist solution—versions of which predate QBism (see, for example, reference 11. J. B. Hartle, Am. J. Phys. 36, 704 (1968). https://doi.org/10.1119/1.1975096)—is that a quantum state is not an objective property of the world but a compendium of probabilities constructed by an agent. When an agent updates her state assignment, nothing changes in her external world. The only change is in the agent’s expectations for her subsequent experience of that world, and therefore there is no measurement problem. Consistent historians agree that collapse is not a physical process, but for entirely different reasons.QBism takes the “mysterious whatever-it-is” that Griffiths criticizes in quantum orthodoxy to be the experience induced in an agent by the world. That, and the fact that different agents may have different experiences, drains the swamp, slays the dragon, and quiets the maddening paradoxes.QBists hold that any agent can indeed apply quantum mechanics to her own external world, from quarks to quasars. Only an agent’s personal, directly perceived experience is boxed off from the domain of applicability. That exclusion disagrees with most versions of the many-worlds interpretation, but it does not limit the scope of science: Alice can apply quantum mechanics to the experience of another agent, Bob, as represented through his words, writings, or drawings, all of which do belong to her external world.The way in which Bob’s experience impinges on Alice resonates with Niels Bohr’s emphasis on the need to state results of experiments in ordinary language. It also addresses Ching Hung Woo’s question of how different agents can come to agreement on their state assignments.Griffiths correctly notes that QBism violates the first desideratum he quotes from my 15-year-old “Ithaca interpretation.” Like Barack Obama’s view of marriage, my thinking about quantum foundations has evolved. But Griffiths wrongly claims that QBism rejects the other desideratum he quotes: locality. Actually, QBism insists on it. The absurdity of quantum nonlocality provides an independent argument that quantum states cannot be objective internal properties of the systems they describe, whether or not one regards probabilities as subjective. Griffiths is probably right, however, that John Bell would not have been pleased with how QBists fix his shifty split.I would not call QBism an “antiquated approach.” It is younger than Griffiths’ consistent histories and, as I have remarked upon elsewhere,22. M. Schlosshauer, ed., Elegance and Enigma: The Quantum Interviews, Springer, Berlin (2011), pp. 177, 280. taking reality itself to be relative to what he calls a framework, is vastly more radical than taking quantum state assignments to be relative to an agent.But foreshadowings of QBism can indeed be found in antiquity. Since writing my commentary, I came across another striking anticipation in a 1931 letter from Erwin Schrödinger to Arnold Sommerfeld:33. K. von Meyenn, ed., Eine Entdeckung von ganz außerordentlicher Tragweite: Schrödingers Briefwechsel zur Wellenmechanik und zum Katzenparadoxon, Springer, Berlin (2011), p. 490. “Quantum mechanics forbids statements about what really exists—statements about the object. It deals only with the object–subject relation. Although this holds, after all, for any description of nature, it appears to hold in a much more radical and far-reaching sense in quantum mechanics” (translated by N. D. Mermin and Ruediger Schack).When Bell and Michael Nauenberg wrote their delightful article in 1966, there was indeed much less interest in quantum foundations than there is today. Most textbooks have wisely steered clear of the many contemporary interpretive positions, since none of them are held by more than a fraction of those physicists with an interest in such issues.QBists do not reject the Born rule for calculating probabilities, but they do reject the objective frequentist interpretation of those probabilities presented by Nauenberg and held by most physicists. The frequentist view is notoriously circular. It defines probability using such notions as “equally probable,” “unlikely,” or (with Nauenberg) “identically prepared,” none of which make sense without a prior definition of probability. “Identically prepared” might seem safe from circularity, but two different preparations cannot be strictly identical. It would be more accurate to say they must differ in unimportant ways. Unimportant for what? For the probabilities of the outcomes.When I started to learn about subjective probability, I was surprised to discover that most of the books were not in Cornell University’s physics or mathematics libraries but in the business school library. In our recent election, Americans have been told that business experience is necessary for being president; I would suggest that it may be even more helpful for understanding quantum mechanics.I cannot tell from Nauenberg’s remarks about the Liouville equation whether he agrees with the view of QBists (and many others) that the collapse of the wavefunction is no more than the updating of a collection of probability distributions.Nauenberg’s example of the Rydberg atom does not contradict the QBist resolution of Bell’s shifty split. The Rydberg atom is part of the world external to the agent, and therefore on the quantum side of her split. There are indeed circumstances under which fully quantum mechanical behavior can look very classical.Art Hobson repeats the common view that only mixed states can be associated with subjective probabilities. QBism takes that to be the very mistake that got us lost for so long in the quantum swamp. Hobson also believes that wavefunctions were collapsing before there were physicists. Does he believe that probabilities were updating before there were statisticians?Hobson wrongly claims that Chris Fuchs “might dispute the notion that some kind of physical reality actually exists.” What he and other QBists do deny is that there are properties of the external world—“elements of reality”—that underlie quantum state assignments. (The argument of Matthew Pusey and coauthors that Hobson cites, implying that quantum states are physically real, relies on such hidden variables.) An agent’s state assignment rests entirely on her experience of the external world. It is neither solipsistic nor superstitious to maintain that any agent’s experience comes fully into being only at the moment it is experienced.Hobson’s treatment of Eugene Wigner and his friend relies on decoherence producing an objective mixed state, which both of them must agree on. But since quantum mechanics holds all the way out to infinity (as Griffiths puts it), even from an objective view of quantum states, that switch from superposition to either/or is at best a FAPP solution, to use Bell’s wonderfully sardonic abbreviation of “for all practical purposes.”QBism does not, as Hobson concludes, give up on a realist interpretation of nature. But it does warn us not to confuse nature with the abstractions we have ingeniously constructed to help any agent deal with the very real impact of nature on his or her own internal experience (see my Reference Frame, Physics Today, May 2009, page 8).I’m glad that Blake Stacey has called attention to some of the more applied spinoffs of QBism. I’m also pleased that he mentions Bruno de Finetti, one of the great 20th-century pioneers of subjective probability. Indeed, since there are objective as well as subjective Bayesians, if I had my way, the B in QBism would stand not for Thomas Bayes, but for Bruno de Finetti, who put the crucial point like this: “The abandonment of superstitious beliefs about the existence of Phlogiston, the Cosmic Ether, Absolute Space and Time … , or Fairies and Witches, was an essential step along the road to scientific thinking. Probability, too, if regarded as something endowed with some kind of objective existence, is no less a misleading misconception, an illusory attempt to exteriorize or materialize our [actual (vero)] probabilistic beliefs.”44. B. de Finetti, Theory of Probability, Interscience, New York (1990), preface.REFERENCESSection:ChooseTop of pageREFERENCES <<1. J. B. Hartle, Am. J. Phys. 36, 704 (1968). https://doi.org/10.1119/1.1975096, Google ScholarCrossref2. M. Schlosshauer, ed., Elegance and Enigma: The Quantum Interviews, Springer, Berlin (2011), pp. 177, 280. Google ScholarCrossref3. K. von Meyenn, ed., Eine Entdeckung von ganz außerordentlicher Tragweite: Schrödingers Briefwechsel zur Wellenmechanik und zum Katzenparadoxon, Springer, Berlin (2011), p. 490. Google ScholarCrossref4. B. de Finetti, Theory of Probability, Interscience, New York (1990), preface. Google Scholar© 2012 American Institute of Physics.
Although I have neither an objection to nor an endorsement of David Mermin’s major premise in his Quick Study, “There is no quantum measurement problem” (Physics Today, June 2022, page 62), I would like to make several contextual points.Mermin’s argument has an extensive history, along with a comparable history of rebuttal. Five decades ago Max Jammer wrote that “measurements in quantum mechanics are no more or less problematic than in classical physics, for the Hilbert space vector is only a purely formal device for relating the statistics associated with these arrangements to the physics of observations in classical physics.” That seems like a condensed version of the argument Mermin presents. On the following page, however, Jammer notes that a “problematic aspect whose serious implications were only gradually understood was the fact that as long as a quantum mechanical one-body or many-body system does not interact with macroscopic objects, as long as its motion is described by the deterministic Schrödinger time-dependent equation, no events could be considered to take place in the system.”11. M. Jammer, The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective, Wiley (1974), pp. 473, 474.Niels Bohr giving a lecture in Copenhagen in April 1929. (Photograph by Samuel Goudsmit, courtesy of the AIP Emilio Segrè Visual Archives, Goudsmit Collection.)PPT|High resolutionRegarding the quotations from Niels Bohr, Mermin’s point is entirely valid and represents Bohr’s position accurately, but Bohr’s thought is always subtle and difficult to capture completely. Another quotation from Bohr, which is consistent with everything else he wrote, is, “The decisive point is that in neither case does the appropriate widening of our conceptual framework imply any appeal to the observing subject, which would hinder unambiguous communication of experience.”22. N. Bohr, Essays 1958–1962 on Atomic Physics and Human Knowledge, Ox Bow Press (1987), p. 7. That quotation seems inconsistent with Mermin’s paragraph that includes the passage “Why should I insist that my interpretation of science, which I use to make sense of the world that I experience, should never make any mention of me?” Bohr always insisted that his framework was a rational “generalization” of classical objectivity.The last and most conceptually important point concerns the ontological status of probability. I don’t necessarily disagree with Mermin and Bruno de Finetti, but it is by no means obvious that they are correct either. David Hawkins, for example, begins 50 pages of rigorous analysis with a brief statement of a major premise.The obvious and natural interpretation of probability in this context is that it introduces, not something that has to do with the nature of the physical system, but something that has to do with the incompleteness of our knowledge….But this opinion turns out to be false. Ignorance of dynamical regularity may be a motive for resorting to probabilities, but it does not explain the probabilities to which we resort.33. D. Hawkins, The Language of Nature: An Essay in the Philosophy of Science, W. H. Freeman (1964), p. 135.Another example can be found in Jammer’s well-known historical account of quantum theory: “For Einstein the notion of probability … was the traditional conception of classical physics, a mathematical objectivization of the human deficiency of complete or exact knowledge but ultimately a creation of the human mind…. For Born probability, as far as it was related to the wave function, was not merely a mathematical fiction but something endowed with physical reality.”44. M. Jammer, The Conceptual Development of Quantum Mechanics, McGraw-Hill (1966), p. 286.Of course, such examples don’t mean that Mermin’s position is incorrect, but I do think that they demand a better argument than a comparison to “Fairies and Witches.” I am confident that Mermin has such an argument, and I look forward to reading it as I continue working toward a coherent position on the unresolved interpretational issues of quantum theory.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. M. Jammer, The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective, Wiley (1974), pp. 473, 474. Google Scholar2. N. Bohr, Essays 1958–1962 on Atomic Physics and Human Knowledge, Ox Bow Press (1987), p. 7. Google Scholar3. D. Hawkins, The Language of Nature: An Essay in the Philosophy of Science, W. H. Freeman (1964), p. 135. Google Scholar4. M. Jammer, The Conceptual Development of Quantum Mechanics, McGraw-Hill (1966), p. 286. Google Scholar© 2022 American Institute of Physics.
David Mermin, in his commentary in the July 2012 issue of Physics Today (page 8), put forth what he calls the QBist (quantum Bayesian) approach to quantum foundations. He claims that replacing a frequentist approach to quantum probabilities with a Bayesian approach solves the quantum measurement problem and fixes the “shifty split” between classical and quantum that John Bell complained about.11. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd ed., Cambridge U. Press, New York (2004), chap. 23. I disagree. Mermin has not addressed the real issue that besets quantum probabilities, he has not solved the measurement problem, and he has put the shifty split in the wrong place.The quantum measurement problem, understanding an actual physical measurement in fully quantum terms, has two parts. First, unitary time development (Schrödinger’s equation) often results in a quantum superposition of different outcomes—different positions of the apparatus pointer, in the quaint language of quantum foundations. Various equivocations proposed to get rid of that Schrödinger’s cat were among the main targets of Bell’s critique. When this first part is solved the second task is to link the pointer position to the microscopic property the apparatus was designed to measure, at a time before the measurement took place. Experimental physicists talk about detecting a gamma ray emitted by a nucleus, or a neutrino emitted in a supernova explosion, using apparatus that either destroys or violently alters the object under study. They are not fools, though one might think so from reading textbook discussions of measurement that only consider properties of a microscopic system at a time after interacting with the apparatus—best referred to as a preparation, not a measurement.Mermin seems to think that the measurement problem—presumably the first problem—is solved by using the quantum wavefunction to calculate a probability, in a manner easily taught to undergraduates. However, the main conceptual difficulty with quantum probabilities is not in calculating them but in identifying their referents, what it is they are about. When the weatherman assigns a high probability to a severe thunderstorm on Thursday afternoon, both frequentists and Bayesians will want to seek shelter. They will agree that the probability refers to thunderstorms rather than stock-market prices. The first task in constructing a probabilistic model, for the weather or games of chance or radioactive decay, is to identify a sample space of mutually exclusive possibilities, one and only one of which can be correct or occur in a particular experiment or on a particular occasion. Only when a sample space has been defined is it possible to assign probabilities to suitable subsets, averages to random variables, and so forth.A classical phase space is easily turned into a probabilistic sample space: The different points represent distinct physical states of affairs. But a quantum Hilbert space is very different if, following John von Neumann’s thinking, one associates physical properties with (closed) subspaces and associates their negations with orthogonal complements of the subspaces. That classical–quantum difference was the origin of quantum logic,22. G. Birkhoff, J. von Neumann, Ann. Math. 37, 823 (1936). https://doi.org/10.2307/1968621 which, despite early hopes and much hard work, has not resolved the conceptual difficulties of quantum mechanics.33. G. Bacciagaluppi, in Handbook of Quantum Logic and Quantum Structures: Quantum Logic, K. Engesser, D. M. Gabbay, D. Lehmann, eds., North-Holland, Amsterdam (2009), p. 49. But it does point to important issues that need to be considered when discussing quantum probabilities. Mermin and his fellow QBists should pay attention.Quantum orthodoxy has no solution for the fundamental problem of defining a quantum sample space. Instead, it covers with a black box the mysterious whatever-it-is that the quantum wavefunction might have something to do with. Talking about what is under the box is more or less strictly forbidden, for it is well known that physicists who attempt to do so will fall into the quantum swamp, to be eaten by the Great Smoky Dragon or driven insane by the Paradoxes. The black box is my term for Bell’s split between the macroscopic and microscopic, a split forever shifting as experimentalists manage to entangle larger and larger quantum systems. According to Mermin, the QBists place the split “between the world in which an agent lives and her experience of that world.” That is no improvement: The box would then cover the physicist rather than the quantum mystery. Bell would not have been pleased.Bell was unaware of the consistent or decoherent histories approach to quantum mechanics,44. P. C. Hohenberg, Rev. Mod. Phys. 82, 2835 (2010); https://doi.org/10.1103/RevModPhys.82.2835 R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); R. B. Griffiths, Found. Phys. 41, 705 (2011). https://doi.org/10.1007/s10701-010-9512-5 which, unlike QBism, solves both measurement problems in a way fully consistent with the Hilbert space structure of quantum mechanics and consistent with special relativity. It drives the shifty split off to infinity where it belongs: Quantum physics applies at all scales, from the quarks to the quasars. And it gets rid of the spooky nonlocal influences that Einstein found so distasteful. It seems odd that Mermin has thrown his lot in with the QBists rather than paying serious attention to the histories approach which, unlike QBism, clearly satisfies two desiderata for a good quantum interpretation that he himself put forward 15 years ago:55. N. D. Mermin, Pramana 51, 549 (1998). https://doi.org/10.1007/BF02827447 “The theory should describe an objective reality independent of observers and their knowledge” and “objectively real internal properties of an isolated individual system should not change when something is done to another non-interacting system.”Mermin says even undergraduates can be taught enough quantum mechanics to update a quantum state assignment. I remember when my undergraduate quantum mechanics teacher, Robert Dicke of cosmic-background fame, was visibly uncomfortable as he introduced us to wavefunction collapse. For those who share this discomfort, I recommend that rather than telling students to “shut up and calculate,” we‣ Introduce them to the rudiments of probability theory, including the conditional probabilities used by both frequentists and Bayesians; one need not take sides.‣ Explain how to construct quantum sample spaces and assign probabilities in a way that does not generate paradoxes.‣ Explain wavefunction collapse as a tool for calculating certain conditional probabilities that can also be obtained using other methods; it is not a physical process.Readers who want more details can contact me or consult the works cited in reference 44. P. C. Hohenberg, Rev. Mod. Phys. 82, 2835 (2010); https://doi.org/10.1103/RevModPhys.82.2835 R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); R. B. Griffiths, Found. Phys. 41, 705 (2011). https://doi.org/10.1007/s10701-010-9512-5 . I think it is high time we abolished antiquated approaches to teaching quantum theory along with the shifty split that confuses both students and their instructors.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd ed., Cambridge U. Press, New York (2004), chap. 23. Google ScholarCrossref2. G. Birkhoff, J. von Neumann, Ann. Math. 37, 823 (1936). https://doi.org/10.2307/1968621, Google ScholarCrossref3. G. Bacciagaluppi, in Handbook of Quantum Logic and Quantum Structures: Quantum Logic, K. Engesser, D. M. Gabbay, D. Lehmann, eds., North-Holland, Amsterdam (2009), p. 49. Google ScholarCrossref4. P. C. Hohenberg, Rev. Mod. Phys. 82, 2835 (2010); https://doi.org/10.1103/RevModPhys.82.2835 , Google ScholarCrossrefR. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); , Google ScholarR. B. Griffiths, Found. Phys. 41, 705 (2011). https://doi.org/10.1007/s10701-010-9512-5 , Google ScholarCrossref5. N. D. Mermin, Pramana 51, 549 (1998). https://doi.org/10.1007/BF02827447 , Google ScholarCrossref, CAS© 2012 American Institute of Physics.
Among Art Hobson’s and Gregory Derry’s letters and Sean Carroll’s July Quick Study (page 62), only Derry’s letter addresses the point I was trying to make in my June Quick Study (page 62): Viewing probabilities as personal judgments eliminates the quantum measurement problem and enables one to make better sense of quantum mechanics.Hobson’s letter expounds his own realistic view of quantum states and their collapse. It belongs with the three examples I mention that eliminate the physicist from the story.Carroll takes what I write about the consequences of a personalist interpretation of probability to be an example of an epistemic interpretation of quantum mechanics. That misses my point.In 1926 Max Born noted that the content of quantum states was the probabilities that they enabled one to calculate. It is strange that after thus elevating probability to a new and foundational role, no physicists then or for the next three-quarters of a century thought it important to reexamine the meaning of probability. For most physicists, probabilities are user-independent frequencies, but for most statisticians, they are guides to action by the person who made the probability assignment. If physicists in 1926 had held a personalist view of probability, it would have required them from the very beginning to hold a personalist (“epistemic”) view of quantum states. There would have been no need for an “interpretation.”I have comments on several issues raised by Derry. Max Jammer and many others have indeed written for over half a century that quantum states are nothing more than formal devices for encapsulating probabilities of observation. But nobody before Carlton Caves, Christopher Fuchs, and Rüdiger Schack ever added that if probabilities are viewed as personal judgments of the person who assigns them, then that same view must be taken of quantum states.Derry quotes Niels Bohr’s statement that he does not “appeal to the observing subject.” Later in that paragraph, Bohr adds that “all subjectivity is avoided by proper attention to the circumstances required for the well-defined use of elementary physical concepts.”11. N. Bohr, Essays 1958–1962 on Atomic Physics and Human Knowledge, Ox Bow Press (1987), p. 7. That does contradict my reading of the two Bohr quotations that appear in my Quick Study. By “experience,” Bohr must have meant collective rather than individual experience. I doubt that Bohr took a personalist view of probability. That Bohr, however, was a personalist is argued interestingly by Ulrich Mohrhoff.22. U. Mohrhoff, https://arxiv.org/abs/1905.07118.I quote Bruno de Finetti on “Fairies and Witches” only to give a poetic statement of the unfamiliar view of probability that I am inviting physicists to examine. My point is that if de Finetti is correct, then it would profoundly affect our understanding of quantum mechanics. For me, the illumination it sheds on the interpretation of quantum mechanics is all by itself a compelling reason for adopting a personalist view of probability.The expansion of my argument that Derry looks forward to reading can be found in the article of mine33. N. D. Mermin, Rep. Prog. Phys. 82, 012002 (2019). https://doi.org/10.1088/1361-6633/aae2c6 cited in my Quick Study along with the rather more technical article44. C. A. Fuchs, R. Schack, Rev. Mod. Phys. 85, 1693 (2013). https://doi.org/10.1103/RevModPhys.85.1693 by Fuchs and Schack that inspired mine.ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. N. Bohr, Essays 1958–1962 on Atomic Physics and Human Knowledge, Ox Bow Press (1987), p. 7. Google Scholar2. U. Mohrhoff, https://arxiv.org/abs/1905.07118. Google Scholar3. N. D. Mermin, Rep. Prog. Phys. 82, 012002 (2019). https://doi.org/10.1088/1361-6633/aae2c6, Google ScholarCrossref4. C. A. Fuchs, R. Schack, Rev. Mod. Phys. 85, 1693 (2013). https://doi.org/10.1103/RevModPhys.85.1693, Google ScholarCrossref, ISI© 2022 American Institute of Physics.
Quantum mechanics is our most successful physical theory. It predicts the behavior of atoms, molecules, and light to ten decimal places. No experiment has ever contradicted it. It also contains a crack at its foundation. The theory’s central equation—the Schrodinger equation—describes a smooth, continuous, perfectly predictable evolution of the quantum state. But whenever anyone performs a measurement, they get a single, definite result. Which result they get appears to be random. The transition from smooth evolution to random outcome is called the “collapse of the wavefunction,” and after nearly a century of analysis, there is no agreed-upon explanation for what causes it, when it occurs, or whether it occurs at all. This is the measurement problem. The measurement problem is not a minor puzzle at the margins of the theory. It is a failure to explain the most basic operation in science: looking at the result of an experiment. Around it cluster other puzzles. Light behaves like a wave in some experiments and like a particle in others—two contradictory descriptions. Two particles that have interacted remain correlated across arbitrary distances, as though communicating faster than light. The probabilities that govern measurement outcomes appear as a postulate—the Born rule—inserted by hand with no deeper justification. And the theory offers no unified picture of reality: quantum mechanics, general relativity, and the standard model of particle physics speak incompatible mathematical languages. A century of effort has produced many interpretations of quantum mechanics. Copenhagen. Many-worlds. De Broglie-Bohm. Objective collapse. Quantum Bayesianism. None has achieved consensus. The measurement problem remains. This document proposes that the source of these puzzles is not quantum mechanics itself. It is a single, invisible assumption made at the very beginning of the theory in 1900—an assumption so deeply embedded that nobody noticed they were making it. Change that assumption, and the puzzles do not get solved. They dissolve. They stop being puzzles. They become predictable consequences of geometry.