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Physics Today

More on the quantum measurement problem

Donald G. Truhlar

Published Nov 1, 2022• 0 citations
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Abstract

Sean Carroll’s July Quick Study, “Addressing the quantum measurement problem” (page 62), brings up the following question: Does the wavefunction still obey the Schrödinger equation when a measurement is made? A system being measured (or interacting with its environment in any other way) is actually a subsystem, and a subsystem is properly described by a reduced density matrix. The density matrix for an entire system corresponds to a wavefunction—that is, to a pure state—but the density matrix for a subsystem does not necessarily correspond to a wavefunction. The reduced density matrix of a subsystem may correspond to an impure state, also called a mixture or an incoherent combination,11. A. Bohm, Quantum Mechanics: Foundations and Applications, 3rd ed., Springer (1993), p. 72. which does not have well-defined pure-state content.22. See, for example, L. E. Ballentine, Quantum Mechanics: A Modern Development, 2nd ed., World Scientific (2015), chap. 2. In the words of Kurt Gottfried and Tung-Mow Yan, “systems in the real world are rarely in pure states.”33. K. Gottfried, T.-M. Yan, Quantum Mechanics: Fundamentals, 2nd ed., Springer (2003), p. 46.The proper way to discuss a measurement is not using a wavefunction but rather a reduced density matrix. The density matrix of a pure state evolves according to the Liouville–von Neumann equation, which is equivalent to the unitary evolution of the wavefunction by the time-dependent Schrödinger equation. For a subsystem (that is, for any system except the entire universe), the reduced density matrix evolves according to the nonunitary Liouville–von Neumann equation, which has an additional contribution causing decoherence and dissipation.44. See, for example, D. A. Micha, Int. J. Quantum Chem. 80, 394 (2000). https://doi.org/10.1002/1097-461X(2000)80:3<394::AID-QUA9>3.0.CO;2-U The nature of the measurement—or, more generally, the nature of the subsystem–environment interaction—selects a preferred basis, called the pointer basis, and the subsystem decoheres into an effectively classical mixture in the pointer basis. (See the article by Wojciech Zurek, Physics Today, October 1991, page 36.)ReferencesSection:ChooseTop of pageReferences <<1. A. Bohm, Quantum Mechanics: Foundations and Applications, 3rd ed., Springer (1993), p. 72. Google Scholar2. See, for example, L. E. Ballentine, Quantum Mechanics: A Modern Development, 2nd ed., World Scientific (2015), chap. 2. Google Scholar3. K. Gottfried, T.-M. Yan, Quantum Mechanics: Fundamentals, 2nd ed., Springer (2003), p. 46. Google ScholarCrossref4. See, for example, D. A. Micha, Int. J. Quantum Chem. 80, 394 (2000). https://doi.org/10.1002/1097-461X(2000)80:3<394::AID-QUA9>3.0.CO;2-U, Google ScholarCrossref© 2022 American Institute of Physics.

DOI
10.1063/pt.3.5113

Related papers

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

On measurement and quantum nondemolition

H. D. Zeh

In his letter, Christopher Monroe recommends that the term “quantum nondemolition” be abandoned (PHYSICS TODAY, January 2011, page 8). I agree, but for somewhat different reasons. Quantum measurement theory has always used the concept of ideal measurements, or “measurements of the first kind,” in which the state of the measured system does not change—that is, it is not “demolished”—if it is already in an eigenstate of the observable. Although an ideal measurement is often a good approximation when dealing with conserved particles, its realization requires special effort in the case of photons, which are usually absorbed while being measured. The concept of ideal measurements is certainly meaningful, but I do not agree with the suggestion that the repeated preparation of the same photon state should be regarded as being equivalent to its nondemolition during a measurement. The term nondemolition may be quite useful in photon experiments or in the construction of gravitational-wave antennae, where it was first used, as far as I know. But in a general context, the traditional terminology would be more to the point, since nonabsorption of the measured photon does not necessarily define an ideal measurement.Much of the confusion originates in the abridged description of a measurement as a stochastic jump from a superposition a∣0〉 + b∣1〉 of a microscopic system into ∣0〉 or ∣1〉 with probabilities ∣a∣2 or ∣b∣2, respectively. That description is a relic from the times when quantum theory was expected to apply only to isolated atoms, electrons, and so forth. (It does not seem to be a genuine part of the Copenhagen interpretation, which describes measurement outcomes in classical terms and often assumes that the wavefunction loses its meaning thereafter.) In most situations, though, one has to include other interacting systems in the unitary description. In fact, all of the much-discussed weirdness of quantum theory has been derived by using entangled quantum states for all involved systems. Therefore, most of the inflationary confusing vocabulary of quantum weirdness—including spooky action, quantum teleportation, quantum eraser, quantum Darwinism, sudden death, quantum information, and even quantum jumps—could be abandoned if one used instead a consistent description in terms of entangled wavefunctions, at least as far as this entanglement remains relevant.11. See, for example, H. D. Zeh, Foundations of Physics 40 9-10 1476 (2010). https://doi.org/10.1007/s10701-009-9383-9 Usually this is so until irreversible decoherence, which was itself derived from unitary interaction with the environment, has occurred in the chain of interactions leading to observation. However, I think it is definitely wrong to say that decoherence theory allows us to “think of any measurement as a [quantum nondemolition] measurement plus a possible interaction with a reservoir.” Although I personally prefer the assumption that unitary dynamics is universal, I agree that some stochastic dynamics has to be used somewhere along the chain of interactions that ends at the observer. It does not matter whether you describe this observed indeterminism in terms of a collapse or a branching of a universal wavefunction into dynamically autonomous components (unlike the collapse, the branching does not require any new dynamical postulate; it is a consequence of the Schrödinger equation with local interactions). Such a real or apparent collapse is an important part of the effective dynamics of “our quantum world”—our “branch,” if you like—that should be carefully analyzed rather than being used ad hoc in a pragmatic and confusing manner. In neither case would it describe a mere increase of information about an initially incompletely known quantum state of the involved systems; the indeterminism is described by a change of a state, which is known to be different from an ensemble of potential states.REFERENCESSection:ChooseTop of pageREFERENCES <<1. See, for example, H. D. Zeh, Foundations of Physics 40 9-10 1476 (2010). https://doi.org/10.1007/s10701-009-9383-9 , Google ScholarCrossref, ISI© 2011 American Institute of Physics.

Physics Today•Jul 1, 2011•2 citations

Quantum mechanics does not suffer from the measurement problem

William Heartspring

We demonstrate that the measurement problem is resolved by providing the right mechanism of how a measurement basis is selected. The measurement basis of a subsystem is what diagonalizes subsystem's reduced density matrix. As expected empirically, the measurement problem ceases to be relevant for actual measurements, due to semi-classical nature of measurement apparatuses. The collapse interpretation is consistent with continuous evolution of the pure state vector of the universe. Quantum mechanics thus is safe, both in practice and in theory.

•Oct 2, 2019•0 citations

Quantum measurements: cats, clouds and everything else

Lawrence S. Schulman

Quantum measurement theory addresses several problems. All of them arise from applying a microscopically valid theory to the macroscopic domain. The most famous is the Schrödinger cat example in which the ordinary use of quantum rules suggests a superposition of macroscopically different states, something we do not seem to experience. Another problem is the Einstein-Podolsky-Rosen (EPR) paradox in which a fundamental quantum concept, entanglement, creates subtle and non-classical correlations among remote sets of measurements. Although it seems mere word play to observe that such an apparent micro-macro conflict ought to be viewed as a problem in statistical mechanics—by virtue of the way that discipline is defined—until recently the importance of this observation was seldom recognized. The founders, Bohr, Schrödinger, Heisenberg, Einstein did not emphasize this direction, but over the years the realization that measurement necessarily involves macroscopic objects—objects with potentially mischievous degrees of freedom of their own—began to be felt. For me this was brought home by the now classic fourth chapter of Gottfried's text on quantum mechanics. He takes up the following problem. The density matrix ρ 0 for a normalized pure state is ρ 0 = |ψ〉 〈ψ|. It follows that Tr ρ 0 = Tr ρ 0 2 = 1. After a non-trivial measurement, the density matrix ρ is supposed to be diagonal in the basis denned by the measured observable, with Tr ρ = 1 but Tr ρ 2 < 1.

Cambridge University Press eBooks•Jul 31, 1997•0 citations

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

Another Visit with Wolfgang Pauli

Karl von Meÿenn, E. L. Schücking

SCHUCKING AND VON MEYENN REPLY: Yes, indeed, it was at the Solvay Conference in 1930 that Bohr reminded Einstein of his elevator. How the wrong date crept into our manuscript baffles us still.Kurt Gottfried is surprised that Pauli thought of Dirac as a formalist. Dirac was a formalist. He wrote in 1931: “The most powerful method of advance that can be suggested at present is to employ all the resources of pure mathematics in attempts to perfect and generalize the mathematical formalism that forms the existing basis of theoretical physics, and after each success in this direction, to try to interpret the new mathematical features in terms of physical entities.” 1 1. P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931) https://doi.org/10.1098/rspa.1931.0130. We disagree with Gottfried’s characterization of the Pauli equation for the electron as merely an elegant restatement of a Heisenberg–Jordan paper. Paul Ehrenfest wrote on 25 March 1931 about the Pauli equation: “This work has become very important. It has opened the way to Dirac’s ingenious work on the spin-electrons and probably also to Heisenberg’s famous work about the helium spectrum.” 2 2. W. Pauli, Scientific Correspondence, Vol. 2, K. von Meyenn, ed., Springer-Verlag, New York (1985) p. 71. Pauli introduced spinors into quantum mechanics and thus—in hindsight—made the step from two to four components not such a giant leap.We agree with Gottfried that the golden rule 3 3. K. Gottfried, Quantum Mechanics, Addison-Wesley, Redwood City, Calif. (1989), eq. 35, p. 444. is due to Dirac. When Pauli derived this equation using Dirac’s time-dependent perturbation theory, he analyzed its domain of validity using the uncertainty relation for time and energy that he had first pointed out in a letter to Heisenberg. Apparently, Pauli and Heisenberg 4 4. W. Pauli, Scientific Correspondence, Vol. 1, A. Hermann, ed., Springer-Verlag, New York (1979), p. 460. had first thought that Dirac had “gemogelt” (cheated) in its derivation.We both cherish Dirac’s beautiful physics, but his approach to theory was different from Pauli’s or Heisenberg’s. By praising Galileo, one does not demean Kepler.On Dirac’s comment about Schrödinger, we stand corrected. Luis Boya also may have a point on vacuum degeneracy. But Pauli’s crucial role in the Heisenberg theory still needs clarification. There are 144 letters from the correspondence between Pauli and Heisenberg in 1957 and 1958, up to 30 pages in length, which still await analysis.With regard to the early history of quantum field theory, we agree that much more could be said about it, and we refer Boya to Tian Yu Cao. 5 5. T. Y. Cao, Conceptual Developments of 20th Century Field Theories, Cambridge U. Press, New York (1997) https://doi.org/10.1017/CBO9780511563997. For the history of nuclear magnetism, we suggest that Boya might consult Hendrik Casimir. 6 6. H. Casimir, Haphazard Reality, Harper & Row, New York (1983); appendix B, p. 322. Boya remarks that Heisenberg “never tried using his newborn matrix mechanics to solve for the hydrogen spectrum.” On 3 November 1925 Heisenberg wrote to Pauli: “After your first letter, I had also tried at once the calculation in three dimensions and was busy just this afternoon with the evaluation of the last equations and the elimination of the many possible mistakes in calculation when the postman entered and made my work superfluous.” 7 7. See ref. 4, p. 252. The postman had brought Pauli’s three-dimensional calculation for the H-atom. We believe that Boya underrates the role Pauli played in the dialogue with Heisenberg and that a careful reading of their correspondence supports our view. Freeman Dyson, with his unique insight into physics and the ways of physicists seems to agree with our assessment.Finally, we thank Gottfried, Boya, and Dyson for their comments.REFERENCESSection:ChooseTop of pageREFERENCES <<1. P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931) https://doi.org/10.1098/rspa.1931.0130. Google ScholarCrossref, CAS2. W. Pauli, Scientific Correspondence, Vol. 2, K. von Meyenn, ed., Springer-Verlag, New York (1985) p. 71. Google Scholar3. K. Gottfried, Quantum Mechanics, Addison-Wesley, Redwood City, Calif. (1989), eq. 35, p. 444. Google Scholar4. W. Pauli, Scientific Correspondence, Vol. 1, A. Hermann, ed., Springer-Verlag, New York (1979), p. 460. Google Scholar5. T. Y. Cao, Conceptual Developments of 20th Century Field Theories, Cambridge U. Press, New York (1997) https://doi.org/10.1017/CBO9780511563997. Google ScholarCrossref6. H. Casimir, Haphazard Reality, Harper & Row, New York (1983); appendix B, p. 322. Google Scholar7. See ref. 4, p. 252. Google Scholar© 2001 American Institute of Physics.

Physics Today•Aug 1, 2001•0 citations
Sean Carroll’s July Quick Study, “Addressing the quantum measurement problem” (page 62), brings up the following question: Does the wavefunction still obey the Schrödinger equation when a measurement is made? A system being measured (or interacting with its environment in any other way) is actually a subsystem, and a subsystem is properly described by a reduced density matrix. The density matrix for an entire system corresponds to a wavefunction—that is, to a pure state—but the density matrix for a subsystem does not necessarily correspond to a wavefunction. The reduced density matrix of a subsystem may correspond to an impure state, also called a mixture or an incoherent combination,11. A. Bohm, Quantum Mechanics: Foundations and Applications, 3rd ed., Springer (1993), p. 72. which does not have well-defined pure-state content.22. See, for example, L. E. Ballentine, Quantum Mechanics: A Modern Development, 2nd ed., World Scientific (2015), chap. 2. In the words of Kurt Gottfried and Tung-Mow Yan, “systems in the real world are rarely in pure states.”33. K. Gottfried, T.-M. Yan, Quantum Mechanics: Fundamentals, 2nd ed., Springer (2003), p. 46.The proper way to discuss a measurement is not using a wavefunction but rather a reduced density matrix. The density matrix of a pure state evolves according to the Liouville–von Neumann equation, which is equivalent to the unitary evolution of the wavefunction by the time-dependent Schrödinger equation. For a subsystem (that is, for any system except the entire universe), the reduced density matrix evolves according to the nonunitary Liouville–von Neumann equation, which has an additional contribution causing decoherence and dissipation.44. See, for example, D. A. Micha, Int. J. Quantum Chem. 80, 394 (2000). https://doi.org/10.1002/1097-461X(2000)80:3<394::AID-QUA9>3.0.CO;2-U The nature of the measurement—or, more generally, the nature of the subsystem–environment interaction—selects a preferred basis, called the pointer basis, and the subsystem decoheres into an effectively classical mixture in the pointer basis. (See the article by Wojciech Zurek, Physics Today, October 1991, page 36.)ReferencesSection:ChooseTop of pageReferences <<1. A. Bohm, Quantum Mechanics: Foundations and Applications, 3rd ed., Springer (1993), p. 72. Google Scholar2. See, for example, L. E. Ballentine, Quantum Mechanics: A Modern Development, 2nd ed., World Scientific (2015), chap. 2. Google Scholar3. K. Gottfried, T.-M. Yan, Quantum Mechanics: Fundamentals, 2nd ed., Springer (2003), p. 46. Google ScholarCrossref4. See, for example, D. A. Micha, Int. J. Quantum Chem. 80, 394 (2000). https://doi.org/10.1002/1097-461X(2000)80:3<394::AID-QUA9>3.0.CO;2-U, Google ScholarCrossref© 2022 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.
In his letter, Christopher Monroe recommends that the term “quantum nondemolition” be abandoned (PHYSICS TODAY, January 2011, page 8). I agree, but for somewhat different reasons. Quantum measurement theory has always used the concept of ideal measurements, or “measurements of the first kind,” in which the state of the measured system does not change—that is, it is not “demolished”—if it is already in an eigenstate of the observable. Although an ideal measurement is often a good approximation when dealing with conserved particles, its realization requires special effort in the case of photons, which are usually absorbed while being measured. The concept of ideal measurements is certainly meaningful, but I do not agree with the suggestion that the repeated preparation of the same photon state should be regarded as being equivalent to its nondemolition during a measurement. The term nondemolition may be quite useful in photon experiments or in the construction of gravitational-wave antennae, where it was first used, as far as I know. But in a general context, the traditional terminology would be more to the point, since nonabsorption of the measured photon does not necessarily define an ideal measurement.Much of the confusion originates in the abridged description of a measurement as a stochastic jump from a superposition a∣0〉 + b∣1〉 of a microscopic system into ∣0〉 or ∣1〉 with probabilities ∣a∣2 or ∣b∣2, respectively. That description is a relic from the times when quantum theory was expected to apply only to isolated atoms, electrons, and so forth. (It does not seem to be a genuine part of the Copenhagen interpretation, which describes measurement outcomes in classical terms and often assumes that the wavefunction loses its meaning thereafter.) In most situations, though, one has to include other interacting systems in the unitary description. In fact, all of the much-discussed weirdness of quantum theory has been derived by using entangled quantum states for all involved systems. Therefore, most of the inflationary confusing vocabulary of quantum weirdness—including spooky action, quantum teleportation, quantum eraser, quantum Darwinism, sudden death, quantum information, and even quantum jumps—could be abandoned if one used instead a consistent description in terms of entangled wavefunctions, at least as far as this entanglement remains relevant.11. See, for example, H. D. Zeh, Foundations of Physics 40 9-10 1476 (2010). https://doi.org/10.1007/s10701-009-9383-9 Usually this is so until irreversible decoherence, which was itself derived from unitary interaction with the environment, has occurred in the chain of interactions leading to observation. However, I think it is definitely wrong to say that decoherence theory allows us to “think of any measurement as a [quantum nondemolition] measurement plus a possible interaction with a reservoir.” Although I personally prefer the assumption that unitary dynamics is universal, I agree that some stochastic dynamics has to be used somewhere along the chain of interactions that ends at the observer. It does not matter whether you describe this observed indeterminism in terms of a collapse or a branching of a universal wavefunction into dynamically autonomous components (unlike the collapse, the branching does not require any new dynamical postulate; it is a consequence of the Schrödinger equation with local interactions). Such a real or apparent collapse is an important part of the effective dynamics of “our quantum world”—our “branch,” if you like—that should be carefully analyzed rather than being used ad hoc in a pragmatic and confusing manner. In neither case would it describe a mere increase of information about an initially incompletely known quantum state of the involved systems; the indeterminism is described by a change of a state, which is known to be different from an ensemble of potential states.REFERENCESSection:ChooseTop of pageREFERENCES <<1. See, for example, H. D. Zeh, Foundations of Physics 40 9-10 1476 (2010). https://doi.org/10.1007/s10701-009-9383-9 , Google ScholarCrossref, ISI© 2011 American Institute of Physics.
We demonstrate that the measurement problem is resolved by providing the right mechanism of how a measurement basis is selected. The measurement basis of a subsystem is what diagonalizes subsystem's reduced density matrix. As expected empirically, the measurement problem ceases to be relevant for actual measurements, due to semi-classical nature of measurement apparatuses. The collapse interpretation is consistent with continuous evolution of the pure state vector of the universe. Quantum mechanics thus is safe, both in practice and in theory.
Quantum measurement theory addresses several problems. All of them arise from applying a microscopically valid theory to the macroscopic domain. The most famous is the Schrödinger cat example in which the ordinary use of quantum rules suggests a superposition of macroscopically different states, something we do not seem to experience. Another problem is the Einstein-Podolsky-Rosen (EPR) paradox in which a fundamental quantum concept, entanglement, creates subtle and non-classical correlations among remote sets of measurements. Although it seems mere word play to observe that such an apparent micro-macro conflict ought to be viewed as a problem in statistical mechanics—by virtue of the way that discipline is defined—until recently the importance of this observation was seldom recognized. The founders, Bohr, Schrödinger, Heisenberg, Einstein did not emphasize this direction, but over the years the realization that measurement necessarily involves macroscopic objects—objects with potentially mischievous degrees of freedom of their own—began to be felt. For me this was brought home by the now classic fourth chapter of Gottfried's text on quantum mechanics. He takes up the following problem. The density matrix ρ 0 for a normalized pure state is ρ 0 = |ψ〉 〈ψ|. It follows that Tr ρ 0 = Tr ρ 0 2 = 1. After a non-trivial measurement, the density matrix ρ is supposed to be diagonal in the basis denned by the measured observable, with Tr ρ = 1 but Tr ρ 2 < 1.
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.
SCHUCKING AND VON MEYENN REPLY: Yes, indeed, it was at the Solvay Conference in 1930 that Bohr reminded Einstein of his elevator. How the wrong date crept into our manuscript baffles us still.Kurt Gottfried is surprised that Pauli thought of Dirac as a formalist. Dirac was a formalist. He wrote in 1931: “The most powerful method of advance that can be suggested at present is to employ all the resources of pure mathematics in attempts to perfect and generalize the mathematical formalism that forms the existing basis of theoretical physics, and after each success in this direction, to try to interpret the new mathematical features in terms of physical entities.” 1 1. P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931) https://doi.org/10.1098/rspa.1931.0130. We disagree with Gottfried’s characterization of the Pauli equation for the electron as merely an elegant restatement of a Heisenberg–Jordan paper. Paul Ehrenfest wrote on 25 March 1931 about the Pauli equation: “This work has become very important. It has opened the way to Dirac’s ingenious work on the spin-electrons and probably also to Heisenberg’s famous work about the helium spectrum.” 2 2. W. Pauli, Scientific Correspondence, Vol. 2, K. von Meyenn, ed., Springer-Verlag, New York (1985) p. 71. Pauli introduced spinors into quantum mechanics and thus—in hindsight—made the step from two to four components not such a giant leap.We agree with Gottfried that the golden rule 3 3. K. Gottfried, Quantum Mechanics, Addison-Wesley, Redwood City, Calif. (1989), eq. 35, p. 444. is due to Dirac. When Pauli derived this equation using Dirac’s time-dependent perturbation theory, he analyzed its domain of validity using the uncertainty relation for time and energy that he had first pointed out in a letter to Heisenberg. Apparently, Pauli and Heisenberg 4 4. W. Pauli, Scientific Correspondence, Vol. 1, A. Hermann, ed., Springer-Verlag, New York (1979), p. 460. had first thought that Dirac had “gemogelt” (cheated) in its derivation.We both cherish Dirac’s beautiful physics, but his approach to theory was different from Pauli’s or Heisenberg’s. By praising Galileo, one does not demean Kepler.On Dirac’s comment about Schrödinger, we stand corrected. Luis Boya also may have a point on vacuum degeneracy. But Pauli’s crucial role in the Heisenberg theory still needs clarification. There are 144 letters from the correspondence between Pauli and Heisenberg in 1957 and 1958, up to 30 pages in length, which still await analysis.With regard to the early history of quantum field theory, we agree that much more could be said about it, and we refer Boya to Tian Yu Cao. 5 5. T. Y. Cao, Conceptual Developments of 20th Century Field Theories, Cambridge U. Press, New York (1997) https://doi.org/10.1017/CBO9780511563997. For the history of nuclear magnetism, we suggest that Boya might consult Hendrik Casimir. 6 6. H. Casimir, Haphazard Reality, Harper & Row, New York (1983); appendix B, p. 322. Boya remarks that Heisenberg “never tried using his newborn matrix mechanics to solve for the hydrogen spectrum.” On 3 November 1925 Heisenberg wrote to Pauli: “After your first letter, I had also tried at once the calculation in three dimensions and was busy just this afternoon with the evaluation of the last equations and the elimination of the many possible mistakes in calculation when the postman entered and made my work superfluous.” 7 7. See ref. 4, p. 252. The postman had brought Pauli’s three-dimensional calculation for the H-atom. We believe that Boya underrates the role Pauli played in the dialogue with Heisenberg and that a careful reading of their correspondence supports our view. Freeman Dyson, with his unique insight into physics and the ways of physicists seems to agree with our assessment.Finally, we thank Gottfried, Boya, and Dyson for their comments.REFERENCESSection:ChooseTop of pageREFERENCES <<1. P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931) https://doi.org/10.1098/rspa.1931.0130. Google ScholarCrossref, CAS2. W. Pauli, Scientific Correspondence, Vol. 2, K. von Meyenn, ed., Springer-Verlag, New York (1985) p. 71. Google Scholar3. K. Gottfried, Quantum Mechanics, Addison-Wesley, Redwood City, Calif. (1989), eq. 35, p. 444. Google Scholar4. W. Pauli, Scientific Correspondence, Vol. 1, A. Hermann, ed., Springer-Verlag, New York (1979), p. 460. Google Scholar5. T. Y. Cao, Conceptual Developments of 20th Century Field Theories, Cambridge U. Press, New York (1997) https://doi.org/10.1017/CBO9780511563997. Google ScholarCrossref6. H. Casimir, Haphazard Reality, Harper & Row, New York (1983); appendix B, p. 322. Google Scholar7. See ref. 4, p. 252. Google Scholar© 2001 American Institute of Physics.