Physics Today
Anachrony in decoherence
Robert A. Harris, Leo Stodolsky
Published Feb 1, 2010• 0 citations
Abstract
In a Search and Discovery news item (Physics Today, September 2009, page 16), we are faulted for not couching our work of the early 1980s “in terms of the then-nascent decoherence theory.” Well, we’re sorry about that, and can only offer the excuse that the term “decoherence” hadn’t yet been coined. We called it “quantum damping” and “tunneling friction.” The reader may agree that those are perhaps not such bad descriptions.Anyone bothering to read the articles 1 , 2 2. R. A. Harris, R. Silbey, J. Chem. Phys. 78, 7330 (1983). 1. R. A. Harris, L. Stodolsky, J. Chem. Phys. 74, 2145 (1981) Phys. Lett. B 116, 464 (1982). or those we have written since 3 3. L. Stodolsky, in Quantum Coherence: University of South Carolina , Columbia, USA , 14-16 December 1989 J. S. Anandan, ed., World Scientific , Hackensack, NJ (1990), p. 320; in Time and Matter: Proceedings of the International Colloquium on the Science of Time, I. I. Bigi, M. Faessler, eds., World Scientific, Hackensack, NJ (2006), p. 117, also available at http://arxiv.org/abs/quant-ph/0303024v2. will find the solutions to Hund’s paradox and the ideas presently in circulation concerning decoherence, like “decoherence by the environment,” clearly and quantitatively explicated.The situation is amusingly reminiscent of the case of Ramses II. Apparently, some people claim the pharaoh couldn’t have died of tuberculosis 4 4. J. R. Searle, N. Y. Rev. Books 56(14), 88 (2009). because the disease wasn’t discovered until the 19th century.REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. A. Harris, L. Stodolsky, J. Chem. Phys. 74, 2145 (1981) Google ScholarCrossref, ISI Phys. Lett. B 116, 464 (1982). , Google ScholarCrossref, ISI2. R. A. Harris, R. Silbey, J. Chem. Phys. 78, 7330 (1983). Google ScholarCrossref, ISI3. L. Stodolsky, in Quantum Coherence: University of South Carolina , Columbia, USA , 14-16 December 1989 , Google Scholar J. S. Anandan, ed., World Scientific , Hackensack, NJ (1990), p. 320; Google Scholarin Time and Matter: Proceedings of the International Colloquium on the Science of Time, I. I. Bigi, M. Faessler, eds., World Scientific, Hackensack, NJ (2006), p. 117, also available at http://arxiv.org/abs/quant-ph/0303024v2. Google Scholar4. J. R. Searle, N. Y. Rev. Books 56(14), 88 (2009). Google Scholar© 2010 American Institute of Physics.
- DOI
- 10.1063/1.3326974
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Coming to terms with decoherence
Erich Joos, H. D. Zeh
In response to Charles Day’s item on the solution to Hund’s paradox (Physics Today, September 2009, page 16), Robert Harris and Leo Stodolsky write that their work 1 1. R. A. Harris, L. Stodolsky, J. Chem. Phys. 74, 2145 (1981); Phys. Lett. B. 116, 464 (1982); R. A. Harris, R. Silbey, J. Chem. Phys. 78, 7330 (1983). from the early 1980s could not yet refer to decoherence because the term was created more than five years later (Physics Today, February 2010, page 10). However, Day’s formulation that their results—which we used and cited in our 1985 paper 2 2. E. Joos, H. D. Zeh, Z. Phys. B: Condens. Matter 59, 223 (1985). when the term decoherence still did not exist—were not yet couched in “the then-nascent decoherence theory” referred not to the name but to the concept. Harris and Stodolsky’s insistence that their terms “quantum damping” and “tunneling friction” are just as appropriate indicates that they adhere to a widespread misunderstanding of the concept of decoherence.Decoherence and dissipation are described by different terms in the master equation, with decoherence usually acting on a far shorter time scale than dissipation. Although the explicit expression obtained by Harris and Stodolsky does contain decoherence terms, we do not remember that they ever mentioned the importance of those terms for the quantum-to-classical transition, superselection rules, or the measurement problem, connections one of us (Zeh) first discussed conceptually during the 1970s. 3 3. See, for example, H. D. Zeh, Found. Phys. 1 , 69 (1970). The term “decoherence” does not describe any fundamentally new physics; in a way the idea is already present in Nevill Mott’s 1929 analysis of alpha-particle tracks. 4 4. N. F. Mott, Proc. R. Soc. London, Ser. A 126, 79 (1929). The point is that this consequence of the entanglement that unavoidably arises between all systems as they interact had been overlooked since the discovery of quantum mechanics, particularly when physicists tried unsuccessfully to recover classical mechanics for isolated systems in the limit in which Planck’s constant h vanishes. Hund’s paradox was not concerned with the lifetimes of certain chiral states but with the absence of their superpositions. It may appear from the master equation that superpositions are destroyed by decoherence, but that is not so; they are only irreversibly “dislocalized.”REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. A. Harris, L. Stodolsky, J. Chem. Phys. 74, 2145 (1981); Google ScholarCrossref, ISI Phys. Lett. B. 116, 464 (1982); , Google ScholarCrossref, ISI R. A. Harris, R. Silbey, J. Chem. Phys. 78, 7330 (1983). , Google ScholarCrossref, ISI, CAS2. E. Joos, H. D. Zeh, Z. Phys. B: Condens. Matter 59, 223 (1985). Google ScholarCrossref3. See, for example, H. D. Zeh, Found. Phys. 1 , 69 (1970). Google Scholar4. N. F. Mott, Proc. R. Soc. London, Ser. A 126, 79 (1929). Google ScholarCrossref, CAS© 2010 American Institute of Physics.
Physics Today•Jul 1, 2010•1 citation
Consistent treatments of quantum mechanics
Robert B. Griffiths
The Letters reply by Yakir Aharonov, Sandu Popescu, and Jeff Tollaksen gives a misleading impression of the consistent histories interpretation of quantum mechanics. As I pointed out in the same issue, consistent histories is an alternative to their time-symmetric formulation. It resolves the “collapse problem” of quantum foundations, which Aharonov and coauthors admit they have failed to do. However, that is not its only or even its principal virtue. It also solves what I call the second quantum measurement problem: how to infer from the measurement outcome the state of the measured system at an earlier time before the measurement took place. Thus the consistent histories approach, without any fuzzy references to “ensembles,” provides a proper probabilistic framework for inferring that Sx for a spin-1⁄2 particle actually was −1⁄2 before the measurement took place. This approach evades the criticisms expressed by Michael Nauenberg and Art Hobson in their letters in the same issue.Furthermore, consistent histories, unlike certain aspects of the approach of Aharonov and coauthors, is fully consistent with the Hilbert-space structure of quantum mechanics introduced by John von Neumann and now taught to all students of the subject. Indeed, with a consistent histories analysis one can locate fairly precisely11. R. E. Kastner, Stud. Hist. Phil. Mod. Phys. 35, 57 (2004), http://arxiv.org/abs/quant-ph/0207182. https://doi.org/10.1016/j.shpsb.2003.02.001 the error in reasoning that leads to claims such as that the measured spin of a spin-1⁄2 particle can equal 100.22. Y. Aharonov, D. Z. Albert, L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988). https://doi.org/10.1103/PhysRevLett.60.1351 Claims about what weak measurements actually measure, when made by those who have not yet solved either the collapse problem or the second measurement problem, should be treated with great caution.The claim that the consistent histories approach is controversial was true back in the 1990s, and the controversy led to a clearer formulation of the interpretation. However, no significant problems have come to light in the decade since the publication of my book.33. R. B. Griffiths, Consistent Quantum Theory Cambridge U. Press, New York (2002), http://quantum.phys.cmu.edu/CQT/. The fact that something has been ignored does not imply it is controversial. Admirers of Richard Feynman, some of whose writings were cited by Aharonov and coauthors in their reply, may be interested to know that shortly before his death he was quite sympathetic to an early form of the consistent histories or decoherent histories approach to understanding quantum mechanics (see PHYSICS TODAY, February 1999, page 11)—an open-mindedness worth imitating.REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. E. Kastner, Stud. Hist. Phil. Mod. Phys. 35, 57 (2004), http://arxiv.org/abs/quant-ph/0207182. https://doi.org/10.1016/j.shpsb.2003.02.001 , Google ScholarCrossref, ISI2. Y. Aharonov, D. Z. Albert, L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988). https://doi.org/10.1103/PhysRevLett.60.1351 , Google ScholarCrossref, ISI3. R. B. Griffiths, Consistent Quantum Theory Cambridge U. Press, New York (2002), http://quantum.phys.cmu.edu/CQT/. Google Scholar© 2011 American Institute of Physics.
Physics Today•Oct 1, 2011•1 citation
Bohr’s molecular model and the melding of classical and quantum mechanics
Leonard D. Mlodinow
Permit me to add some information to the article entitled, “Bohr’s molecular model, a century later.” The authors discuss the idea of “dimensional scaling,” approximating the spectra of atoms and molecules by employing perturbation theory to expand around the infinite-dimension/classical limit. That technique of approximating the Schrödinger equation, originally called the 1/N expansion, was developed and applied to numerous problems in the 1980s, including simple atoms, quarkonium, and the hydrogen molecule.11. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0,22. C. M. Bender, L. D. Mlodinow, N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). https://doi.org/10.1103/PhysRevA.25.1305,33. T. Imbo, U. Sukhatme, Phys. Rev. D 31, 2655 (1985); https://doi.org/10.1103/PhysRevD.31.2655M. Kumar, A. Srivastava, J. K. Bhattacharjee, K. Banerjee, Phys. Lett. A 117, 226 (1986). https://doi.org/10.1016/0375-9601(86)90081-2 It grew out of attempts in the 1970s to formulate quantum chromodynamics in the limit of a large number of colors. The use of the 1/N expansion in atomic physics was discussed by Edward Witten (Physics Today, July 1980, page 38), who pointed out that his discussion was based on work that applied the method to hydrogen and helium atoms.11. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0The work in reference 11. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0 made use of algebraic methods for the analysis, but the coordinate space method was also developed and was initially used to treat the strong-field Zeeman effect.22. C. M. Bender, L. D. Mlodinow, N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). https://doi.org/10.1103/PhysRevA.25.1305 A nice description of the status of the field at the time was given by Laurence Yaffe (Physics Today, August 1983, page 50). Many additional applications of that method in the physics literature may be found in reference 44. A. Chatterjee, Phys. Rep. 186, 249 (1990). https://doi.org/10.1016/0370-1573(90)90048-7.REFERENCESSection:ChooseTop of pageREFERENCES <<1. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 , Google ScholarCrossref, ISIL. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0, , Google ScholarCrossref, ISI2. C. M. Bender, L. D. Mlodinow, N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). https://doi.org/10.1103/PhysRevA.25.1305, Google ScholarCrossref, ISI3. T. Imbo, U. Sukhatme, Phys. Rev. D 31, 2655 (1985); https://doi.org/10.1103/PhysRevD.31.2655, Google ScholarCrossref, ISIM. Kumar, A. Srivastava, J. K. Bhattacharjee, K. Banerjee, Phys. Lett. A 117, 226 (1986). https://doi.org/10.1016/0375-9601(86)90081-2, , Google ScholarCrossref, ISI4. A. Chatterjee, Phys. Rep. 186, 249 (1990). https://doi.org/10.1016/0370-1573(90)90048-7, Google ScholarCrossref, ISI© 2014 American Institute of Physics.
Physics Today•Aug 1, 2014•1 citation
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
In a Search and Discovery news item (Physics Today, September 2009, page 16), we are faulted for not couching our work of the early 1980s “in terms of the then-nascent decoherence theory.” Well, we’re sorry about that, and can only offer the excuse that the term “decoherence” hadn’t yet been coined. We called it “quantum damping” and “tunneling friction.” The reader may agree that those are perhaps not such bad descriptions.Anyone bothering to read the articles 1 , 2 2. R. A. Harris, R. Silbey, J. Chem. Phys. 78, 7330 (1983). 1. R. A. Harris, L. Stodolsky, J. Chem. Phys. 74, 2145 (1981) Phys. Lett. B 116, 464 (1982). or those we have written since 3 3. L. Stodolsky, in Quantum Coherence: University of South Carolina , Columbia, USA , 14-16 December 1989 J. S. Anandan, ed., World Scientific , Hackensack, NJ (1990), p. 320; in Time and Matter: Proceedings of the International Colloquium on the Science of Time, I. I. Bigi, M. Faessler, eds., World Scientific, Hackensack, NJ (2006), p. 117, also available at
http://arxiv.org/abs/quant-ph/0303024v2. will find the solutions to Hund’s paradox and the ideas presently in circulation concerning decoherence, like “decoherence by the environment,” clearly and quantitatively explicated.The situation is amusingly reminiscent of the case of Ramses II. Apparently, some people claim the pharaoh couldn’t have died of tuberculosis 4 4. J. R. Searle, N. Y. Rev. Books 56(14), 88 (2009). because the disease wasn’t discovered until the 19th century.REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. A. Harris, L. Stodolsky, J. Chem. Phys. 74, 2145 (1981) Google ScholarCrossref, ISI Phys. Lett. B 116, 464 (1982). , Google ScholarCrossref, ISI2. R. A. Harris, R. Silbey, J. Chem. Phys. 78, 7330 (1983). Google ScholarCrossref, ISI3. L. Stodolsky, in Quantum Coherence: University of South Carolina , Columbia, USA , 14-16 December 1989 , Google Scholar J. S. Anandan, ed., World Scientific , Hackensack, NJ (1990), p. 320; Google Scholarin Time and Matter: Proceedings of the International Colloquium on the Science of Time, I. I. Bigi, M. Faessler, eds., World Scientific, Hackensack, NJ (2006), p. 117, also available at
http://arxiv.org/abs/quant-ph/0303024v2. Google Scholar4. J. R. Searle, N. Y. Rev. Books 56(14), 88 (2009). Google Scholar© 2010 American Institute of Physics.
In response to Charles Day’s item on the solution to Hund’s paradox (Physics Today, September 2009, page 16), Robert Harris and Leo Stodolsky write that their work 1 1. R. A. Harris, L. Stodolsky, J. Chem. Phys. 74, 2145 (1981); Phys. Lett. B. 116, 464 (1982); R. A. Harris, R. Silbey, J. Chem. Phys. 78, 7330 (1983). from the early 1980s could not yet refer to decoherence because the term was created more than five years later (Physics Today, February 2010, page 10). However, Day’s formulation that their results—which we used and cited in our 1985 paper 2 2. E. Joos, H. D. Zeh, Z. Phys. B: Condens. Matter 59, 223 (1985). when the term decoherence still did not exist—were not yet couched in “the then-nascent decoherence theory” referred not to the name but to the concept. Harris and Stodolsky’s insistence that their terms “quantum damping” and “tunneling friction” are just as appropriate indicates that they adhere to a widespread misunderstanding of the concept of decoherence.Decoherence and dissipation are described by different terms in the master equation, with decoherence usually acting on a far shorter time scale than dissipation. Although the explicit expression obtained by Harris and Stodolsky does contain decoherence terms, we do not remember that they ever mentioned the importance of those terms for the quantum-to-classical transition, superselection rules, or the measurement problem, connections one of us (Zeh) first discussed conceptually during the 1970s. 3 3. See, for example, H. D. Zeh, Found. Phys. 1 , 69 (1970). The term “decoherence” does not describe any fundamentally new physics; in a way the idea is already present in Nevill Mott’s 1929 analysis of alpha-particle tracks. 4 4. N. F. Mott, Proc. R. Soc. London, Ser. A 126, 79 (1929). The point is that this consequence of the entanglement that unavoidably arises between all systems as they interact had been overlooked since the discovery of quantum mechanics, particularly when physicists tried unsuccessfully to recover classical mechanics for isolated systems in the limit in which Planck’s constant h vanishes. Hund’s paradox was not concerned with the lifetimes of certain chiral states but with the absence of their superpositions. It may appear from the master equation that superpositions are destroyed by decoherence, but that is not so; they are only irreversibly “dislocalized.”REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. A. Harris, L. Stodolsky, J. Chem. Phys. 74, 2145 (1981); Google ScholarCrossref, ISI Phys. Lett. B. 116, 464 (1982); , Google ScholarCrossref, ISI R. A. Harris, R. Silbey, J. Chem. Phys. 78, 7330 (1983). , Google ScholarCrossref, ISI, CAS2. E. Joos, H. D. Zeh, Z. Phys. B: Condens. Matter 59, 223 (1985). Google ScholarCrossref3. See, for example, H. D. Zeh, Found. Phys. 1 , 69 (1970). Google Scholar4. N. F. Mott, Proc. R. Soc. London, Ser. A 126, 79 (1929). Google ScholarCrossref, CAS© 2010 American Institute of Physics.
The Letters reply by Yakir Aharonov, Sandu Popescu, and Jeff Tollaksen gives a misleading impression of the consistent histories interpretation of quantum mechanics. As I pointed out in the same issue, consistent histories is an alternative to their time-symmetric formulation. It resolves the “collapse problem” of quantum foundations, which Aharonov and coauthors admit they have failed to do. However, that is not its only or even its principal virtue. It also solves what I call the second quantum measurement problem: how to infer from the measurement outcome the state of the measured system at an earlier time before the measurement took place. Thus the consistent histories approach, without any fuzzy references to “ensembles,” provides a proper probabilistic framework for inferring that Sx for a spin-1⁄2 particle actually was −1⁄2 before the measurement took place. This approach evades the criticisms expressed by Michael Nauenberg and Art Hobson in their letters in the same issue.Furthermore, consistent histories, unlike certain aspects of the approach of Aharonov and coauthors, is fully consistent with the Hilbert-space structure of quantum mechanics introduced by John von Neumann and now taught to all students of the subject. Indeed, with a consistent histories analysis one can locate fairly precisely11. R. E. Kastner, Stud. Hist. Phil. Mod. Phys. 35, 57 (2004), http://arxiv.org/abs/quant-ph/0207182. https://doi.org/10.1016/j.shpsb.2003.02.001 the error in reasoning that leads to claims such as that the measured spin of a spin-1⁄2 particle can equal 100.22. Y. Aharonov, D. Z. Albert, L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988). https://doi.org/10.1103/PhysRevLett.60.1351 Claims about what weak measurements actually measure, when made by those who have not yet solved either the collapse problem or the second measurement problem, should be treated with great caution.The claim that the consistent histories approach is controversial was true back in the 1990s, and the controversy led to a clearer formulation of the interpretation. However, no significant problems have come to light in the decade since the publication of my book.33. R. B. Griffiths, Consistent Quantum Theory Cambridge U. Press, New York (2002), http://quantum.phys.cmu.edu/CQT/. The fact that something has been ignored does not imply it is controversial. Admirers of Richard Feynman, some of whose writings were cited by Aharonov and coauthors in their reply, may be interested to know that shortly before his death he was quite sympathetic to an early form of the consistent histories or decoherent histories approach to understanding quantum mechanics (see PHYSICS TODAY, February 1999, page 11)—an open-mindedness worth imitating.REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. E. Kastner, Stud. Hist. Phil. Mod. Phys. 35, 57 (2004), http://arxiv.org/abs/quant-ph/0207182. https://doi.org/10.1016/j.shpsb.2003.02.001 , Google ScholarCrossref, ISI2. Y. Aharonov, D. Z. Albert, L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988). https://doi.org/10.1103/PhysRevLett.60.1351 , Google ScholarCrossref, ISI3. R. B. Griffiths, Consistent Quantum Theory Cambridge U. Press, New York (2002), http://quantum.phys.cmu.edu/CQT/. Google Scholar© 2011 American Institute of Physics.
Permit me to add some information to the article entitled, “Bohr’s molecular model, a century later.” The authors discuss the idea of “dimensional scaling,” approximating the spectra of atoms and molecules by employing perturbation theory to expand around the infinite-dimension/classical limit. That technique of approximating the Schrödinger equation, originally called the 1/N expansion, was developed and applied to numerous problems in the 1980s, including simple atoms, quarkonium, and the hydrogen molecule.11. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0,22. C. M. Bender, L. D. Mlodinow, N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). https://doi.org/10.1103/PhysRevA.25.1305,33. T. Imbo, U. Sukhatme, Phys. Rev. D 31, 2655 (1985); https://doi.org/10.1103/PhysRevD.31.2655M. Kumar, A. Srivastava, J. K. Bhattacharjee, K. Banerjee, Phys. Lett. A 117, 226 (1986). https://doi.org/10.1016/0375-9601(86)90081-2 It grew out of attempts in the 1970s to formulate quantum chromodynamics in the limit of a large number of colors. The use of the 1/N expansion in atomic physics was discussed by Edward Witten (Physics Today, July 1980, page 38), who pointed out that his discussion was based on work that applied the method to hydrogen and helium atoms.11. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0The work in reference 11. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0 made use of algebraic methods for the analysis, but the coordinate space method was also developed and was initially used to treat the strong-field Zeeman effect.22. C. M. Bender, L. D. Mlodinow, N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). https://doi.org/10.1103/PhysRevA.25.1305 A nice description of the status of the field at the time was given by Laurence Yaffe (Physics Today, August 1983, page 50). Many additional applications of that method in the physics literature may be found in reference 44. A. Chatterjee, Phys. Rep. 186, 249 (1990). https://doi.org/10.1016/0370-1573(90)90048-7.REFERENCESSection:ChooseTop of pageREFERENCES <<1. L. D. Mlodinow, N. Papanicolaou, Ann. Phys. 128, 314 (1980); https://doi.org/10.1016/0003-4916(80)90323-1 , Google ScholarCrossref, ISIL. D. Mlodinow, N. Papanicolaou, Ann. Phys. 131, 1 (1981). https://doi.org/10.1016/0003-4916(81)90181-0, , Google ScholarCrossref, ISI2. C. M. Bender, L. D. Mlodinow, N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). https://doi.org/10.1103/PhysRevA.25.1305, Google ScholarCrossref, ISI3. T. Imbo, U. Sukhatme, Phys. Rev. D 31, 2655 (1985); https://doi.org/10.1103/PhysRevD.31.2655, Google ScholarCrossref, ISIM. Kumar, A. Srivastava, J. K. Bhattacharjee, K. Banerjee, Phys. Lett. A 117, 226 (1986). https://doi.org/10.1016/0375-9601(86)90081-2, , Google ScholarCrossref, ISI4. A. Chatterjee, Phys. Rep. 186, 249 (1990). https://doi.org/10.1016/0370-1573(90)90048-7, Google ScholarCrossref, ISI© 2014 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.