What is quantum mechanics trying to tell us?

American Journal of Physics

Volumn 66, Issue 9, 1998, Pages 753-767

  Mermin, N David ^a  

^a Laboratory of Atomic and Solid State Physics and Sibley School of Mechanical and Aerospace Engineering   (United States)

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EID: 0032347964     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18955     Document Type: Article

References (60)

1. Notes for a lecture given at the Symposium in Honor of Edward M. Purcell, Harvard University, October 18, 1997.
2. Introductory Survey to Atomic Theory and the Description of Nature (Cambridge U.P., Cambridge, 1934), p. 18. Reprinted in Niels Bohr, Collected Works (North-Holland, Amsterdam, 1985), Vol. 6, p. 296.
3. Introductory Survey to Atomic Theory and the Description of Nature (Cambridge U.P., Cambridge, 1934), p. 18. Reprinted in Niels Bohr, Collected Works (North-Holland, Amsterdam, 1985), Vol. 6, p. 296.
4. N. David Mermin, "The Ithaca Interpretation of Quantum Mechanics," Pramana (to be published); a version can be found in quant-ph 9609013, Los Alamos e-Print archive at xxx.lanl.gov (1996). The nomenclature was intended to indicate a resemblance to the body of interpretational lore named after a grander city in northern Europe, and also, by its geographic modesty and lack of descriptive content, to suggest that what was being promulgated was not so much a logical foundation for the subject as a philosophical perspective or pedagogical approach. It does not imply that others in Ithaca share these views, or that others outside of Ithaca have not expressed similar thoughts. None of the ingredients of the IIQM are novel, but I have cooked them together into a somewhat different stew.
5. These are examples of the kinds of terms or distinctions that have a special character in the IIQM, and are collected together in Appendix C.
6. D. Bohm and D. J. Hiley, The Undivided Universe (Routledge, New York, 1993).
7. For a recent review and a set of references, see for example Philip Pearle, "Wavefunction Collapse Models With Nonwhite Noise," in Perspectives on Quantum Reality, edited by Rob Clifton (Kluwer, Dordrecht, 1996), pp. 93-109.
8. A technical point: In taking the state space of the system to be a product of subsystem state spaces I am restricting the discussion to cases where the significant manifestations of quantum mechanical indistinguishability of particles - the symmetry or antisymmetry of many-particle wave functions - are limited to the constituents of the individual subsystems. This is conventional (though rarely noted) in discussions of the foundations of quantum mechanics. Thus in discussing the measurement of the spin of an atom, one does not antisymmetrize the combined wave function for the atom-apparatus system over, for example, the electronic variables occurring in both subsystems. The overlap between atomic and apparatus electronic wave functions is taken to be zero. Since the major conceptual problems posed by quantum mechanics - nonlocality and the measurement problem - are present even in the quantum mechanics of distinguishable particles, this simplification does not appear to evade essential features. A more rigorous approach will probably require a field-theoretic formulation. There seems no point in trying to cross that bridge unless one can first cross the simpler one attempted here. In a similar vein, I also consider here only nonrelativistic quantum mechanics, because the conceptual problems are already present in the nonrelativistic theory. A treatment of relativistic quantum mechanics will also require a field theoretic reformulation.
9. This is spelled out more explicitly at the beginning of Sec. IX.
10. For example, the joint distribution for electron position and proton position in a hydrogen atom exists simultaneously with the joint distribution for electron momentum and proton position, even though the position and momentum of the electron do not have joint physical reality or a meaningful joint distribution of their own. And both the position-position and momentum-position distributions return the same distribution for the proton position, when the electronic variables are integrated out.
11. The essential role of objective probability in the quantum mechanical description of an individual system was stressed by Popper, who used the term "propensity." See Karl Popper, Quantum Theory and the Schism in Physics (Rowman and Littlefield, Totowa, NJ, 1982). Heisenberg may have had something similar in mind with his term "potentia." While I agree with Popper that quantum mechanics requires us to adopt a view of probability as a fundamental feature of an individual system, I do not believe that he gives anything like an adequate account of how this clears up what he called the "quantum mysteries and horrors." See N. David Mermin, "The Great Quantum Muddle," Philos. Sci. 50, 651-656 (1983); reprinted in Boojums All the Way Through (Cambridge U.P., Cambridge, 1990), pp. 190-197.
12. The essential role of objective probability in the quantum mechanical description of an individual system was stressed by Popper, who used the term "propensity." See Karl Popper, Quantum Theory and the Schism in Physics (Rowman and Littlefield, Totowa, NJ, 1982). Heisenberg may have had something similar in mind with his term "potentia." While I agree with Popper that quantum mechanics requires us to adopt a view of probability as a fundamental feature of an individual system, I do not believe that he gives anything like an adequate account of how this clears up what he called the "quantum mysteries and horrors." See N. David Mermin, "The Great Quantum Muddle," Philos. Sci. 50, 651-656 (1983); reprinted in Boojums All the Way Through (Cambridge U.P., Cambridge, 1990), pp. 190-197.
13. The essential role of objective probability in the quantum mechanical description of an individual system was stressed by Popper, who used the term "propensity." See Karl Popper, Quantum Theory and the Schism in Physics (Rowman and Littlefield, Totowa, NJ, 1982). Heisenberg may have had something similar in mind with his term "potentia." While I agree with Popper that quantum mechanics requires us to adopt a view of probability as a fundamental feature of an individual system, I do not believe that he gives anything like an adequate account of how this clears up what he called the "quantum mysteries and horrors." See N. David Mermin, "The Great Quantum Muddle," Philos. Sci. 50, 651-656 (1983); reprinted in Boojums All the Way Through (Cambridge U.P., Cambridge, 1990), pp. 190-197.
14. Wolfgang Pauli, "Probability and physics," in Writings on Physics and Philosophy (Springer-Verlag, New York, 1994), pp. 43-48.
15. I comment further on the Everett interpretation, which was subsequently transformed into the many worlds interpretation, in Sec. XI.
16. Einstein was apparently resigned to the inaccessibility of now to physics. According to Carnap ["Intellectual Autobiography," in The Philosophy of Rudolf Carnap, edited by P. A. Schilpp (Open Court, LaSalle, IL, 1963), pp. 37-38] in a conversation in the early 1950's "Einstein said that the problem of the Now worried him seriously. He explained that the experience of the Now means something special for man, something essentially different from the past and the future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation." This is particularly interesting in view of Einstein's notorious unwillingness to extend his resignation over the inability of physics to deal with the special character of now, to its inability to deal with the special character of correlata underlying the quantum correlations.
17. To my surprise, this point - a banality among philosophers, who speak of qualia - is extremely hard, if not impossible, to put across to some physicists. I have sometimes managed to do it by citing a theory I had as a child to account for the fact that different people have different favorite colors. My idea - a kind of chromo-aesthetic absolutism - was that there was, in fact, only one most pleasurable color sensation, but the reason your favorite color was blue while mine was red was that the sensation you experienced looking at blue objects was identical to the sensation I experienced looking at red ones. I recently found precisely this example (complete to the choice of colors - only "you" and "me" are interchanged) on a list of possibly meaningless questions in P. W. Bridgman, The Logic of Modern Physics (Macmillan, New York, 1927), p. 30.
18. For an example see the discussion of quantum nonlocality in Sec. X.
19. For an engaging discussion of these issues and many references, see Euan Squires, Conscious Mind in the Physical World (Hilger, Bristol and New York, 1990).
20. S. Bergia, F. Cannata, A. Cornia, and R. Livi, "On the actual measurability of the density matrix of a decaying system by means of measurements on the decay products," Found. Phys. 10, 723-730 (1980). See also W. K. Wootters, in Complexity, Entropy and the Physics of Information, edited by W. H. Zurek (Addison-Wesley, Redwood City, CA, 1990), pp. 39-46.
21. S. Bergia, F. Cannata, A. Cornia, and R. Livi, "On the actual measurability of the density matrix of a decaying system by means of measurements on the decay products," Found. Phys. 10, 723-730 (1980). See also W. K. Wootters, in Complexity, Entropy and the Physics of Information, edited by W. H. Zurek (Addison-Wesley, Redwood City, CA, 1990), pp. 39-46.
22. J. S. Bell, "Against measurement," Phys. World 33-40 (August, 1990). This critique elicited interesting rejoinders from Rudolf Peierls ["In defense of measurement," Phys. World 19-20 (January, 1991)] and Kurt Gottfried ["Does quantum mechanics carry the seeds of its own destruction?" 31-40 (October, 1991)]. Bell's death deprived us of his response.
23. J. S. Bell, "Against measurement," Phys. World 33-40 (August, 1990). This critique elicited interesting rejoinders from Rudolf Peierls ["In defense of measurement," Phys. World 19-20 (January, 1991)] and Kurt Gottfried ["Does quantum mechanics carry the seeds of its own destruction?" 31-40 (October, 1991)]. Bell's death deprived us of his response.
24. J. S. Bell, "Against measurement," Phys. World 33-40 (August, 1990). This critique elicited interesting rejoinders from Rudolf Peierls ["In defense of measurement," Phys. World 19-20 (January, 1991)] and Kurt Gottfried ["Does quantum mechanics carry the seeds of its own destruction?" 31-40 (October, 1991)]. Bell's death deprived us of his response.
25. I defer to Sec. VIII any discussion of "the measurement problem" - the constellation of issues arising in the context of "wave-packet collapse."
26. FAPP=For all practical purposes. See J. S. Bell, in Ref. 18.
27. i still appear.
28. Hugh Everett III, "Relative-State Formulation of Quantum Mechanics," Rev. Mod. Phys. 29, 454-462 (1957). Everett says virtually nothing about many worlds except, perhaps, in a note added in proof. I discuss the relation of the IIQM to Everett's relative-state formulation in Sec. XI.
29. See N. David Mermin, "Hidden Variables and the Two Theorems of John Bell," Rev. Mod. Phys. 65, 803-815 (1993), especially Sec. VII.
30. Lucien Hardy, "Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories," Phys. Rev. Lett. 68, 2981-2984 (1992). The version of Hardy's argument given here uses the notation in N. David Mermin, "Quantum mysteries refined," Am. J. Phys. 62, 880-897 (1994).
31. Lucien Hardy, "Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories," Phys. Rev. Lett. 68, 2981-2984 (1992). The version of Hardy's argument given here uses the notation in N. David Mermin, "Quantum mysteries refined," Am. J. Phys. 62, 880-897 (1994).
32. 2 (unless the individual subsystem probabilities are completely random - i.e., unless the individual subsystem density matrices are proportional to the unit matrix). See Lucien Hardy, "Nonlocality for two particles without inequalities for almost all entangled states," Phys. Rev. Lett. 71, 1665-1668 (1993).
33. John S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics 1, 195-200 (1964).
34. Most recently in Henry P. Stapp, "Nonlocal character of quantum theory," Am. J. Phys. 65, 300-304 (1997).
35. I have given a detailed analysis of how Stapp's carefully constructed derivation of nonlocality from the Hardy state can be used to illuminate Bohr's reply to Einstein, Podolsky, and Rosen. See N. David Mermin, "Nonlocal character of quantum theory?" Am. J. Phys. (to be published). Stapp responds in "Quantum nonlocality," ibid. (to be published).
36. I have given a detailed analysis of how Stapp's carefully constructed derivation of nonlocality from the Hardy state can be used to illuminate Bohr's reply to Einstein, Podolsky, and Rosen. See N. David Mermin, "Nonlocal character of quantum theory?" Am. J. Phys. (to be published). Stapp responds in "Quantum nonlocality," ibid. (to be published).
37. Paul Teller, in Philosophical Consequences of Quantum Theory, edited by James T. Cushing and Ernan McMullin (Notre Dame U.P., Notre Dame, IN, 1989), pp. 208-223.
38. Arthur Fine, in Ref. 29, pp. 175-194.
39. Niels Bohr, "Can Quantum Mechanical Description of Physical Reality Be Considered Complete?" Phys. Rev. 48, 696-702 (1935). One of Bohr's points is that there is nothing new or unusual about EPR correlations: Precisely the same kinds of correlations are set up in the measurement process, and therefore there is no cause for alarm because he has already straightened out that problem.
40. Albert Einstein, Boris Podolsky, and Nathan Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" Phys. Rev. 47, 777-780 (1935).
41. This point of view is expressed in Lee Smolin, The Life of the Cosmos (Oxford U.P., New York, 1997).
42. Carlo Rovelli, "Relational Quantum Mechanics," Int. J. Theoret. Phys. 35, 1637-78 (1996). See also quant-ph 9609002, Los Alamos e-Print archive at xxx.lanl.gov (1996).
43. Gyula Bene, "Quantum Reference systems: a new framework for quantum mechanics," quant-ph/9703021, Los Alamos e-Print archive at xxx.lanl.gov (1996); "Quantum phenomena do not violate the principle of locality - a new interpretation with physical consequences," Physica A (to be published); quant-ph/9706043, Los Alamos e-Print archive at xxx.lanl.gov (1996), Am. J. Phys. (submitted).
44. Gyula Bene, "Quantum Reference systems: a new framework for quantum mechanics," quant-ph/9703021, Los Alamos e-Print archive at xxx.lanl.gov (1996); "Quantum phenomena do not violate the principle of locality - a new interpretation with physical consequences," Physica A (to be published); quant-ph/9706043, Los Alamos e-Print archive at xxx.lanl.gov (1996), Am. J. Phys. (submitted).
45. Gyula Bene, "Quantum Reference systems: a new framework for quantum mechanics," quant-ph/9703021, Los Alamos e-Print archive at xxx.lanl.gov (1996); "Quantum phenomena do not violate the principle of locality - a new interpretation with physical consequences," Physica A (to be published); quant-ph/9706043, Los Alamos e-Print archive at xxx.lanl.gov (1996), Am. J. Phys. (submitted).
46. Gyula Bene, "Quantum Reference systems: a new framework for quantum mechanics," quant-ph/9703021, Los Alamos e-Print archive at xxx.lanl.gov (1996); "Quantum phenomena do not violate the principle of locality - a new interpretation with physical consequences," Physica A (to be published); quant-ph/9706043, Los Alamos e-Print archive at xxx.lanl.gov (1996), Am. J. Phys. (submitted).
47. H. Everett, III, in Ref. 22. It was later swept off into the many worlds interpretation.
48. Christopher Fuchs (private communication).
49. A similar attitude has been expressed by Rudolf Peierls, Surprises in Theoretical Physics (Princeton U.P., Princeton, NJ, 1979), p. 33: "We are confident today that, if we could solve the Schrödinger equation for all the electrons in a large molecule, it would give us all the knowledge that chemists are able to discover about it... . Many people take it for granted that the same must be true of the science of life. The difficulty about how to formulate the acquisition of information, which we have met, is a strong reason for doubting this assumption." Even closer is the view of Robert Geroch, "The Everett interpretation," Nous 18, 617-633 (1984), p. 629: "[W]hat must be accounted for... is, not the specific classical outcomes deemed to have occurred for a specific experiment, but rather the general human impression that classical outcomes do occur. This problem may well be soluble, but is probably beyond our present abilities; and, in any case, is basically not a problem in quantum mechanics."
50. A similar attitude has been expressed by Rudolf Peierls, Surprises in Theoretical Physics (Princeton U.P., Princeton, NJ, 1979), p. 33: "We are confident today that, if we could solve the Schrödinger equation for all the electrons in a large molecule, it would give us all the knowledge that chemists are able to discover about it... . Many people take it for granted that the same must be true of the science of life. The difficulty about how to formulate the acquisition of information, which we have met, is a strong reason for doubting this assumption." Even closer is the view of Robert Geroch, "The Everett interpretation," Nous 18, 617-633 (1984), p. 629: "[W]hat must be accounted for... is, not the specific classical outcomes deemed to have occurred for a specific experiment, but rather the general human impression that classical outcomes do occur. This problem may well be soluble, but is probably beyond our present abilities; and, in any case, is basically not a problem in quantum mechanics."
51. See, for example, Roger Penrose, The Emperor's New Mind (Oxford U.P., New York, 1989), and Shadows of the Mind (Oxford U.P., New York, 1994); Henry Stapp, Mind, Matter, and Quantum Mechanics (Springer-Verlag, New York, 1993).
52. See, for example, Roger Penrose, The Emperor's New Mind (Oxford U.P., New York, 1989), and Shadows of the Mind (Oxford U.P., New York, 1994); Henry Stapp, Mind, Matter, and Quantum Mechanics (Springer-Verlag, New York, 1993).
53. See, for example, Roger Penrose, The Emperor's New Mind (Oxford U.P., New York, 1989), and Shadows of the Mind (Oxford U.P., New York, 1994); Henry Stapp, Mind, Matter, and Quantum Mechanics (Springer-Verlag, New York, 1993).
54. See, for example, Jeffrey Bub, Interpreting the Quantum World (Cambridge U.P., Cambridge, 1997) and Bas C. Van Fraassen, Quantum Mechanics: An Empiricist View (Clarendon, Oxford, 1991), and references cited therein.
55. See, for example, Jeffrey Bub, Interpreting the Quantum World (Cambridge U.P., Cambridge, 1997) and Bas C. Van Fraassen, Quantum Mechanics: An Empiricist View (Clarendon, Oxford, 1991), and references cited therein.
56. For a recent formulation and references see Robert B. Griffiths, "Consistent Histories and Quantum Reasoning," Phys. Rev. A 54, 2759-2774 (1996).
57. See, for example, Asher Peres, Quantum Theory: Concepts and Methods (Kluwer, Dodrecht, 1993), pp. 123-126.
58. Indeed, I believe its character would be clarified if consistent historians were to characterize mutually exclusive families of correlations and correlata not as inconsistent or incompatible but as complementary. This terminology is suggested on p. 162 of Roland Omnès, The Interpretation of Quantum Mechanics (Princeton U.P., Princeton, 1994).
59. J. S. Bell, Physics World, in Ref. 18.
60. A. M. Gleason, "Measures on the Closed Subspaces of a Hilbert Space," J. Math. Mech. 6, 885-893 (1957).