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Physics Today

More on the quantum measurement problem

Gregory N. Derry

Published Nov 1, 2022• 2 citations
Publisher

Abstract

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.

DOI
10.1063/pt.3.5111

Related papers

Measured responses to quantum Bayesianism

Michael Nauenberg

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

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

More on the quantum measurement problem

Art Hobson

In his June 2022 Quick Study (page 62), David Mermin argues that “the quantum state of a system expresses only the belief of the particular physicist who assigns it to the system.” Applying that to quantum measurements, he finds that “the acquisition of further information by that physicist … can lead to an abrupt change in those probabilities and thus to an updating of the quantum state that the physicist uses to represent them. There is no quantum measurement problem.”But wavefunctions have been collapsing ever since the Big Bang, with no assistance from physicists. An apparatus’s display of a measurement outcome occurs even if the experimenters happen to be out of the room. When a cosmic-ray proton strikes a sand grain on Mars and moves the grain, a quantum measurement occurs and the proton’s wavefunction collapses regardless of the absence of humans.Roger Carpenter and Andrew Anderson of the University of Cambridge performed a “Schrödinger’s cat” experiment that demolishes Mermin’s interpretation. Instead of connecting a Geiger counter to a cat-killing device, they mercifully connected it to a hammer that would fall without harm. Their strategy was to split information about the experimental result between two observers in such a way that neither observer can know the outcome. The observers learn the outcome later by sharing their information. The question is then, Did the hammer fall at the time of the experiment or later, when the observers became conscious of the outcome? The result: The hammer fell when the nucleus decayed, not later when the observers became conscious of the outcome. I think nearly all physicists would have predicted that. My hat is off to Carpenter and Anderson, who reported it with a straight face.11. R. H. S. Carpenter, A. J. Anderson, Ann. Fond. Louis de Broglie 31, 45 (2006).Humans and their consciousness have nothing to do with quantum physics. Photons, electrons, and the like, as well as their states, are real configurations of fields that have existed throughout the universe since the Big Bang.22. A. Hobson, Am. J. Phys. 81, 211 (2013). https://doi.org/10.1119/1.4789885Nevertheless, I agree with Mermin’s title: There is no quantum measurement problem, because quantum physics, with no special interpretation and without a collapse postulate, logically implies that superpositions collapse nonlocally to a single definite outcome.33. A. Hobson, Quantum Eng. 2022, 1 (2022). https://doi.org/10.1155/2022/5889159ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. R. H. S. Carpenter, A. J. Anderson, Ann. Fond. Louis de Broglie 31, 45 (2006). Google Scholar2. A. Hobson, Am. J. Phys. 81, 211 (2013). https://doi.org/10.1119/1.4789885, Google ScholarCrossref, ISI3. A. Hobson, Quantum Eng. 2022, 1 (2022). https://doi.org/10.1155/2022/5889159, Google ScholarCrossref© 2022 American Institute of Physics.

Physics Today•Nov 1, 2022•1 citation

More on the quantum measurement problem

Sean M. Carroll

I appreciate David Mermin’s letter. There is, of course, an ongoing debate in the philosophy of probability about whether probability is best thought of as objective or subjective. Experts continue to disagree, which suggests that we might want to acknowledge a “problem” in that wider-than-quantum context, even if we think we have the right answer.Whatever our stance is toward probability, we can still wonder about reality (ontology). People disagree about that too, and there are respectable but mutually incompatible possibilities—which represents another problem.In particular, one can be a subjectivist about probability (as I am myself!) within different approaches to the quantum measurement problem. Both Everettian and Bohmian quantum theories invoke subjective probabilities, concerning which branch of the wavefunction you are on (Everettian) or the values of the hidden variables (Bohmian), although they treat quantum measurements differently. Taking a subjective stance toward probability does not by itself resolve the measurement problem.Objective-collapse models, by contrast, sit more comfortably in (as the name suggests) an objective picture of probability. To the extent that such models are empirically viable, it seems wrong to deny the existence of the quantum measurement problem, since, again, they address it very differently than other models.I am optimistic that the quantum measurement problem is solvable and will be solved, but I am wary about prematurely declaring victory. Section:ChooseTop of page <<© 2022 American Institute of Physics.

Physics Today•Nov 1, 2022•0 citations

Mermin habitually answers opinions, real and abstract

Rodney Brooks

I am that friend of David Mermin’s “who was enchanted by the revelation that quantum fields were the real stuff that makes up the world.” I plead guilty to reification and offer the following defense.I started out, as I think we all did, with the notion that there is a reality out there and that space and time are part of it—not just “an extremely effective way to represent relations between distinct events.” When I read Arthur Eddington’s The Nature of the Physical World (J. M. Dent & Sons, 1942) in high school, I learned that reality was not what it seemed—that Eddington’s solid writing desk, for example, was mostly empty space. The next step in my understanding of reality came in college when I found that the electromagnetic field offered a more satisfying picture of the world than action at a distance, which even Isaac Newton derided. 1 1. H. Boorse, L. Motz, eds., The World of the Atom, Basic Books, New York (1966), p. 319. When I encountered quantum mechanics, of course, everything became confusion. However, along with David, I was fortunate to attend Julian Schwinger’s courses at Harvard University just after he had perfected his treatment of quantum field theory. 2 2. J. Schwinger, Ann. Phys. 2, 407 (1957). https://doi.org/10.1016/0003-4916(57)90015-5 I sat enthralled throughout the three-year series (1956–59), in which Schwinger developed QFT as a seemingly inevitable consequence of the most basic assumptions.However, I came away with a different understanding of QFT than David’s. I understood that the fields are physical properties of space that are described by field strengths—just as in classical physics, except that in QFT the state of the field at each point is represented by a vector in Hilbert space rather than by a pure number. That use of Hilbert space, which followed naturally from Schwinger’s “measurement algebra,” allows superpositions of values. The operators in Hilbert space, as I understood it, are mathematical tools that describe the evolution of the state vectors, and they are not to be reified.When I saw how QFT resolves the paradoxes of modern physics, it became irresistible. The special relativity paradoxes—for example, Lorentz contraction and time dilation—are a natural result of the way fields behave. 3 3. J. Schwinger wrote a six-part series on the theory of quantized fields: Phys. Rev. 82, 914 (1951); 91, 713 (1953); https://doi.org/10.1103/PhysRev.82.914 91, 728 (1953); 92, 1283 (1953); 93, 615 (1954); 94, 1362 (1954). The spacetime curvature of general relativity, which I could never really visualize, does not exist in QFT; the gravitational field equations are equivalent to spacetime curvature for those who can visualize it, but equivalent is not the same as identical. 4 4. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York (1972), pp. vii–147. Finally, the mysterious wave–particle duality of quantum mechanics vanishes; in QFT, reality consists of fields and only fields.Because QFT is so neglected by the public (and by many physicists), I am writing a book that presents it without equations. A draft copy of the work, The Theory That Escaped Einstein, can be found through an internet search. Feedback is appreciated.For those who can’t kick the reification habit, QFT is the way to go. It is the only theory that offers a consistent and visualizable picture of reality. Reifiers of the world, unite! You have nothing to lose but your abstractions.REFERENCESSection:ChooseTop of pageREFERENCES <<1. H. Boorse, L. Motz, eds., The World of the Atom, Basic Books, New York (1966), p. 319. Google Scholar2. J. Schwinger, Ann. Phys. 2, 407 (1957). https://doi.org/10.1016/0003-4916(57)90015-5 , Google ScholarCrossref, ISI3. J. Schwinger wrote a six-part series on the theory of quantized fields: Phys. Rev. 82, 914 (1951); 91, 713 (1953); https://doi.org/10.1103/PhysRev.82.914 , Google ScholarCrossref, ISI 91, 728 (1953); , Google Scholar 92, 1283 (1953); Google Scholar 93, 615 (1954); Google Scholar 94, 1362 (1954). Google Scholar4. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York (1972), pp. vii–147. Google Scholar© 2009 American Institute of Physics.

Physics Today•Sep 1, 2009•0 citations

Quantum Mechanics

Peter E. Hodgson

The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.

Routledge eBooks•Sep 8, 2017•0 citations
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.
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.
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.
In his June 2022 Quick Study (page 62), David Mermin argues that “the quantum state of a system expresses only the belief of the particular physicist who assigns it to the system.” Applying that to quantum measurements, he finds that “the acquisition of further information by that physicist … can lead to an abrupt change in those probabilities and thus to an updating of the quantum state that the physicist uses to represent them. There is no quantum measurement problem.”But wavefunctions have been collapsing ever since the Big Bang, with no assistance from physicists. An apparatus’s display of a measurement outcome occurs even if the experimenters happen to be out of the room. When a cosmic-ray proton strikes a sand grain on Mars and moves the grain, a quantum measurement occurs and the proton’s wavefunction collapses regardless of the absence of humans.Roger Carpenter and Andrew Anderson of the University of Cambridge performed a “Schrödinger’s cat” experiment that demolishes Mermin’s interpretation. Instead of connecting a Geiger counter to a cat-killing device, they mercifully connected it to a hammer that would fall without harm. Their strategy was to split information about the experimental result between two observers in such a way that neither observer can know the outcome. The observers learn the outcome later by sharing their information. The question is then, Did the hammer fall at the time of the experiment or later, when the observers became conscious of the outcome? The result: The hammer fell when the nucleus decayed, not later when the observers became conscious of the outcome. I think nearly all physicists would have predicted that. My hat is off to Carpenter and Anderson, who reported it with a straight face.11. R. H. S. Carpenter, A. J. Anderson, Ann. Fond. Louis de Broglie 31, 45 (2006).Humans and their consciousness have nothing to do with quantum physics. Photons, electrons, and the like, as well as their states, are real configurations of fields that have existed throughout the universe since the Big Bang.22. A. Hobson, Am. J. Phys. 81, 211 (2013). https://doi.org/10.1119/1.4789885Nevertheless, I agree with Mermin’s title: There is no quantum measurement problem, because quantum physics, with no special interpretation and without a collapse postulate, logically implies that superpositions collapse nonlocally to a single definite outcome.33. A. Hobson, Quantum Eng. 2022, 1 (2022). https://doi.org/10.1155/2022/5889159ReferencesSection:ChooseTop of pageReferences <<CITING ARTICLES1. R. H. S. Carpenter, A. J. Anderson, Ann. Fond. Louis de Broglie 31, 45 (2006). Google Scholar2. A. Hobson, Am. J. Phys. 81, 211 (2013). https://doi.org/10.1119/1.4789885, Google ScholarCrossref, ISI3. A. Hobson, Quantum Eng. 2022, 1 (2022). https://doi.org/10.1155/2022/5889159, Google ScholarCrossref© 2022 American Institute of Physics.
I appreciate David Mermin’s letter. There is, of course, an ongoing debate in the philosophy of probability about whether probability is best thought of as objective or subjective. Experts continue to disagree, which suggests that we might want to acknowledge a “problem” in that wider-than-quantum context, even if we think we have the right answer.Whatever our stance is toward probability, we can still wonder about reality (ontology). People disagree about that too, and there are respectable but mutually incompatible possibilities—which represents another problem.In particular, one can be a subjectivist about probability (as I am myself!) within different approaches to the quantum measurement problem. Both Everettian and Bohmian quantum theories invoke subjective probabilities, concerning which branch of the wavefunction you are on (Everettian) or the values of the hidden variables (Bohmian), although they treat quantum measurements differently. Taking a subjective stance toward probability does not by itself resolve the measurement problem.Objective-collapse models, by contrast, sit more comfortably in (as the name suggests) an objective picture of probability. To the extent that such models are empirically viable, it seems wrong to deny the existence of the quantum measurement problem, since, again, they address it very differently than other models.I am optimistic that the quantum measurement problem is solvable and will be solved, but I am wary about prematurely declaring victory. Section:ChooseTop of page <<© 2022 American Institute of Physics.
I am that friend of David Mermin’s “who was enchanted by the revelation that quantum fields were the real stuff that makes up the world.” I plead guilty to reification and offer the following defense.I started out, as I think we all did, with the notion that there is a reality out there and that space and time are part of it—not just “an extremely effective way to represent relations between distinct events.” When I read Arthur Eddington’s The Nature of the Physical World (J. M. Dent & Sons, 1942) in high school, I learned that reality was not what it seemed—that Eddington’s solid writing desk, for example, was mostly empty space. The next step in my understanding of reality came in college when I found that the electromagnetic field offered a more satisfying picture of the world than action at a distance, which even Isaac Newton derided. 1 1. H. Boorse, L. Motz, eds., The World of the Atom, Basic Books, New York (1966), p. 319. When I encountered quantum mechanics, of course, everything became confusion. However, along with David, I was fortunate to attend Julian Schwinger’s courses at Harvard University just after he had perfected his treatment of quantum field theory. 2 2. J. Schwinger, Ann. Phys. 2, 407 (1957). https://doi.org/10.1016/0003-4916(57)90015-5 I sat enthralled throughout the three-year series (1956–59), in which Schwinger developed QFT as a seemingly inevitable consequence of the most basic assumptions.However, I came away with a different understanding of QFT than David’s. I understood that the fields are physical properties of space that are described by field strengths—just as in classical physics, except that in QFT the state of the field at each point is represented by a vector in Hilbert space rather than by a pure number. That use of Hilbert space, which followed naturally from Schwinger’s “measurement algebra,” allows superpositions of values. The operators in Hilbert space, as I understood it, are mathematical tools that describe the evolution of the state vectors, and they are not to be reified.When I saw how QFT resolves the paradoxes of modern physics, it became irresistible. The special relativity paradoxes—for example, Lorentz contraction and time dilation—are a natural result of the way fields behave. 3 3. J. Schwinger wrote a six-part series on the theory of quantized fields: Phys. Rev. 82, 914 (1951); 91, 713 (1953); https://doi.org/10.1103/PhysRev.82.914 91, 728 (1953); 92, 1283 (1953); 93, 615 (1954); 94, 1362 (1954). The spacetime curvature of general relativity, which I could never really visualize, does not exist in QFT; the gravitational field equations are equivalent to spacetime curvature for those who can visualize it, but equivalent is not the same as identical. 4 4. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York (1972), pp. vii–147. Finally, the mysterious wave–particle duality of quantum mechanics vanishes; in QFT, reality consists of fields and only fields.Because QFT is so neglected by the public (and by many physicists), I am writing a book that presents it without equations. A draft copy of the work, The Theory That Escaped Einstein, can be found through an internet search. Feedback is appreciated.For those who can’t kick the reification habit, QFT is the way to go. It is the only theory that offers a consistent and visualizable picture of reality. Reifiers of the world, unite! You have nothing to lose but your abstractions.REFERENCESSection:ChooseTop of pageREFERENCES <<1. H. Boorse, L. Motz, eds., The World of the Atom, Basic Books, New York (1966), p. 319. Google Scholar2. J. Schwinger, Ann. Phys. 2, 407 (1957). https://doi.org/10.1016/0003-4916(57)90015-5 , Google ScholarCrossref, ISI3. J. Schwinger wrote a six-part series on the theory of quantized fields: Phys. Rev. 82, 914 (1951); 91, 713 (1953); https://doi.org/10.1103/PhysRev.82.914 , Google ScholarCrossref, ISI 91, 728 (1953); , Google Scholar 92, 1283 (1953); Google Scholar 93, 615 (1954); Google Scholar 94, 1362 (1954). Google Scholar4. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York (1972), pp. vii–147. Google Scholar© 2009 American Institute of Physics.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.