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Physics Today
Coming to terms with decoherence Erich Joos, H. D. Zeh
Published Jul 1, 2010 • 1 citation
Abstract 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.
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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.
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.
In the last decade decoherence has become a very popular topic mainly due to the progress in experimental techniques which allow monitoring of the process of decoherence for single microscopic or mesoscopic systems. The other motivation is the rapid development of quantum information and quantum computation theory where decoherence is the main obstacle in the implementation of bold theoretical ideas. All that makes the second improved and extended edition of this book very timely. Despite the enormous efforts of many authors decoherence with its consequences still remains a rather controversial subject. It touches on, namely, the notoriously confusing issues of quantum measurement theory and interpretation of quantum mechanics. The existence of different points of view is reflected by the structure and content of the book. The first three authors (Joos, Zeh and Kiefer) accept the standard formalism of quantum mechanics but seem to reject orthodox Copenhagen interpretation, Giulini and Kupsch stick to both while Stamatescu discusses models which go beyond the standard quantum theory. Fortunately, most of the presented results are independent of the interpretation and the mathematical formalism is common for the (meta)physically different approaches. After a short introduction by Joos followed by a more detailed review of the basic concepts by Zeh, chapter 3 (the longest chapter) by Joos is devoted to the environmental decoherence. Here the author considers mostly rather `down to earth' and well-motivated mechanisms of decoherence through collisions with atoms or molecules and the processes of emission, absorption and scattering of photons. The issues of decoherence induced superselection rules and localization of objects including the possible explanation of the molecular structure are discussed in details. Many other topics are also reviewed in this chapter, e.g., the so-called Zeno effect, relationships between quantum chaos and decoherence, the role of decoherence in quantum information processing and even decoherence in the brain. The next chapter, written by Kiefer, is devoted to decoherence in quantum field theory and quantum gravity which is a much more speculative and less explored topic. Two complementary aspects are studied in this approach: decoherence of particle states by the quantum fields and decoherence of field states by the particles. Cosmological issues related to decoherence are discussed, not only within the standard Friedmann cosmology, but also using the elements of the theory of black holes, wormholes and strings. The relations between the formalism of consistent histories defined in terms of decoherence functionals and the environmental decoherence are discussed in chapter 5, also written by Kiefer. The Feynman--Vernon influence functional for the quantum open system is presented in detail as the first example of decoherence functional. Then the general theory is outlined together with possible interpretations including cosmological aspects. The next chapter by Giulini presents an overview of the superselection rules arising from physical symmetries and gauge transformations both for nonrelativistic quantum mechanics and quantum field theory. Critical discussion of kinematical superselection rules versus dynamical ones is illustrated by numerous examples like Galilei invariant quantum mechanics, quantum electrodynamics and quantum gravity. The introduction to the theory of quantum open systems and its applications to decoherence models is given in chapter 7 by Kupsch. Generalized master equations, Markovian approximation and a few Hamiltonian models relevant for decoherence are discussed. Some mathematical tools, e.g., complete positivity and entropy inequalities are also presented. The last chapter by Stamatescu is devoted to stochastic collapse models which can be interpreted either as certain representations of the dynamics of open quantum systems or as fundamental modifications of the Schr\"odinger equation. The final part of the book consists of remarks by Zeh on related concepts and methods and seven appendices. The broad spectrum, mathematically-friendly presentation, inclusion of the very recent developments and the extensive bibliography (about 550 references) make this book a valuable reference for all researchers, graduate and PhD students interested in the foundations of quantum mechanics, quantum open systems and quantum information. The relative independence of the chapters and numerous redundancies allow for selective reading, which is very helpful for newcomers to this field.
One of the main goals of no-collapse interpretations of quantum mechanics is to show how results of measurements are objectified, or, in a more poignant terminology, how in a measurement situation facts arise. One needs to show how in their dynamical evolution the measured system and, perhaps more importantly, the measuring apparatus acquire, or at least appear to acquire, the definite properties that are otherwise explained by the collapse of the state. This can be seen as a special case of the problem whether quantum mechanics alone can account for the classical behaviour of macroscopic systems; in particular, the permanent definiteness of at least those properties of macroscopic systems that are directly observable, such as the position of the pointer of a measuring apparatus. In other words, whether quantum mechanics can account for macrofacts of the familiar kind.
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.
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.