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The Interpretation of Quantum Mechanics (Princeton Series in Physics) by Roland Omnes
The interpretation of quantum mechanics has been controversial since the introduction of quantum theory in the 1920s. Although the Copenhagen interpretation is commonly accepted, its usual formulation suffers from some serious drawbacks. Based mainly on Bohr's concepts, the formulation assumes an independent and essential validity of classical concepts running in parallel with quantum ones, and leaves open the possibility of their ultimate conflict. In this book, Roland Omn
- GenresPhysicsPhilosophyScience
Paperback
First published January 1, 1994
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About the author
Roland Omnès
17 books9 followersRoland Omnès is the author of several books which aim to close the gap between our common sense experience of the classical world and the complex, formal mathematics which is now required to accurately describe reality at its most fundamental level.
Omnès is currently Professor Emeritus of Theoretical Physics in the Faculté des sciences at Orsay, at the Université Paris-Sud XI. He has been instrumental in developing the consistent histories and quantum decoherence approaches in quantum mechanics.
http://en.wikipedia.org/wiki/Roland_O...
Omnès is currently Professor Emeritus of Theoretical Physics in the Faculté des sciences at Orsay, at the Université Paris-Sud XI. He has been instrumental in developing the consistent histories and quantum decoherence approaches in quantum mechanics.
http://en.wikipedia.org/wiki/Roland_O...
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October 28, 2022
A shortcoming of the conventional interpretive stance going back to John von Neumann and nowadays termed quantum logic is that it fails to address what would be the typical experimental situation in the laboratory, or in the world in general. Time does not come to a halt upon performing a measurement; rather, one normally conducts a series of measurements in order to get to know better the system with which one is dealing. But the elementary propositions in a von-Neumann-like quantum logic tell us something about a single instant in time only. If one expands the scope of the theory so as to contemplate the possibility of repeated measurements, it must lead to something resembling the so-called consistent histories formalism, first adumbrated in 1984 by Robert B. Griffiths [Journal of Statistical Physics 36, 219-272 (1984)].
The title of the contribution presently to be reviewed, The interpretation of quantum mechanics, somewhat oversells the contents of Roland Omnès’ textbook published by the Princeton University Press in 1994. For it would better be viewed as an extended review of an interpretation, viz., the consistent histories formalism. Clearly pitched in the style of an undergraduate-level textbook, not a research monograph – the author expressly disavows any scholarly intent! Consists in a mosaic alternating between wordy expositions and high-level derivations of the formulae. Nevertheless, Omnès’ penchant for verbosity can have its advantages for the inexpert reader. For instance, he dilates at length in a nice discussion of detection methods: retina, photographic emulsion, photomultipliers, bubble chambers, Stern-Gerlach magnets [pp. 63-72].
What are consistent histories? Omnès portrays them as a modernization of the Copenhagen interpretation that ought to command universal assent – for him the problems of quantum logic have all been satisfactorily solved! A consistent history is nothing but a record of observations of a system at a sequence of instants in time, separated by a large enough interval that the measurements do not interfere with one another. What’s strange is that the field of propositions in this quantum logic depends on the choice of sequence of observables to make up the putative consistent histories, whereas the conventional use of the word logic carries with it the connotation of universality. It does help to give an interpretation in terms of a Stern-Gerlach experiment pp. 158] so that definitions will not be so dry!
The following passage reveals well the author’s take on his subject:
The multiplicity of consistent logics is nothing but a rediscovery of the complementarity principle, though it has now lost its status of principle to become only a byproduct of logic. It will be seen more than once that this kind of occurrence is rather common when physics is approached from a logical standpoint and quite a few Copenhagen principles will be rediscovered so as to become a theorem, a side remark, or simply a convenience, not to mention the case when they can be disposed of. [p. 160]
An example of how Omnès thinks backwards! The conceit throughout that there is only one cogent interpretation of quantum mechanics – namely, his favored consistent-histories interpretation – gets to be a little bothersome. Re. complementarity [p. 88]: Omnès skates over issue that for Bohr complementarity exists only between conjugate pairs. A couple other apparent difficulties: he presumes properties are always sharply defined [p. 104], whereas one would suppose that a realistic instrument could measure only up to a certain precision. Thus, measurement theory as presented by Omnès always involves an idealization – which, this reviewer at least imagines, it could be profitable to ponder lifting? Another problem [p. 110]: ‘we assume that the Hilbert space framework and the Schrödinger dynamics are given’. This statement marks Omnès as an expositor of the views of others and not as an original researcher. In particular, the question of the realizability or not of an arbitrary so-called observable is subtler than Omnès lets on here [p. 114].
Chapter six describes how to recover classical mechanics from quantum mechanics [pp. 238-258]. Omnès’ presentation of a topic not ordinarily discussed in very much depth proves to be quite helpful. Appendices A and B are way too technical given the level of the rest of the book – here is definitely not the place to learn microlocal analysis!
Chapter seven discusses the important relation between decoherence and consistent histories. Roughly, decoherence justifies why we can take measurements of different observables at successive intervals and regard them as being independent of one another – if they weren’t thus independent, the whole edifice of quantum logic would have to be radically revised! NB: decoherence originates in dissipation [p. 277] and would not occur for superconductors and ordinary electromagnetic radiation (which obviously produces macroscopic interferences). The author rightly alludes to a point of principle in this connection that John Bell for one picked up on:
Although macroscopic interference effects disappear when a collective observable is measured, a pure quantum state remains a pure state under time evolution so that, in principle, interference might still be found if one were to measure a more clever or finer observable. [p. 270]
Decoherence is mainly due to the existence of a very large number of degrees of freedom in the environment. It also requires that the coupling between the collective subsystem and the environment should be somewhat disordered. [p. 282]
Bell’s argument went as follows: when one starts from a pure state, it will always remain in a pure state as long as it evolves according to the Schrödinger equation. Accordingly, even if the reduced density operator describing the collective observables becomes diagonalized, this is inessential: the full density operator still represents a pure state and it therefore contains the possibility of showing interference. True enough, no interference can be seen in a measurement of a collective observable, but there always exist more subtle observables that would be able to show it. By measuring such an observable, as was always assumed to be possible in principle, one will exhibit the existence of a surviving quantum superposition of macroscopically different states. The answer provided by decoherence is therefore valid ‘for all practical purposes’. [p. 305]
The consistent histories point of view on repeated measurements: reduction of wave function constitutes not an additional postulate but follows as a consequence of the theory of histories! [pp. 339-341, see especially third paragraph on p. 340]. This reviewer doesn’t follow immediately how decoherence allegedly explains the reduction of the wave packet [p. 353]. Doesn’t it lead only to a diagonal density matrix, not to a unique outcome? Nor is it not entirely clear to him yet how existence of facts in the present determines a unique past but leaves the future indeterminate [pp. 343-344]. Couldn’t one instead use projectors in the future to determine a history and leave the past indeterminate?
Chapter eight takes on other interpretations. The treatment of Everett’s many-worlds interpretation is too sketchy [pp. 345-348] and again, so too is his exposition of Ghirardi-Rimini-Weber stochastic collapse theory [pp. 349-350]: Omnès claims all that GRW try to explain has been already explained by decoherence. Re. criteria of truth: what justifies excluding inconsistent histories? [p. 355] Omnès says little on this crucial point.
Omnès resolution of the paradox [p. 391]: EPR’s elements of reality correspond only to reliable properties but not true properties, so that they are in fact arbitrary, depending upon a special choice in the description corresponding to a special choice of logic. They therefore have no objective character. NB, his quirky and limited notion of ‘truth’ as nothing more than a trace of a past measurement. In the final section of chapter nine, Omnès makes a good point after all: why prize determinism so highly (as hidden variable theorists do) when quantum mechanics has undermined determinism at the microphysical level? Isn’t it more natural to think of determinism as something that can hold only in a classical limit?
Chapter ten on non-classical macroscopic systems starts out with a high-level overview of the theory of superconductors but has nothing on how it connects with decoherence or quantum measurement theory [pp. 410-425]. The Aharanov-Bohm effect has in fact been entirely confirmed in SQUID’s and this was the first example of a macroscopic system showing quantum interference effects [p. 422]. A couple other topics are covered in this chapter: a too-abbreviated derivation of the exponential decay law [pp. 434-436] and why from the consistent histories point of view, the quantum Zeno effect is not evidence for collapse of the wave function [p. 441]. Omnès makes a big deal that consistent histories form an objective interpretation of quantum mechanics and that von Neumann was wrong to bring in the observer [pp. 510-511].
The final section of chapter twelve [pp. 506-531] offers a philosophical disquisition – somewhat disconnected, bringing in inter alia Kant, Wittgenstein, Heidegger etc, largely dependent on d’Espagnat. Omnès declares himself for realism as against nominalism which he attributes to Leibniz, viz., the hypothetico-deductive approach to science [p. 525]. In the last paragraph, he pluncks for a total realism as against veiled realism; in which human logic and mathematics explore an objective logos (shorn of religious connotations), and dismisses nominalism as too arbitrary [p. 527].
The consistent histories approach turns out to be nice in some respects (helpful in the study of the classical limit, i.e. collective modes as well as in certain systems showing macroscopic quantum behavior) but the basic problem with it is that it is premised on an uncritical reception of the underlying formalism of quantum mechanics rather than deriving this, and second: the supposedly overcome reduction of the wave packet is not after all truly eliminated but reappears under the guise of the problem of the existence of facts. Another problem the author recognizes is that, thus far, the rigorous theory of decoherence is based solely on toy models.
So: scan through Omnès’ textbook quickly as a warm-up to the original literature, but don’t expect much of an engagement with alternate points of view or any very trenchant criticisms of them.
The title of the contribution presently to be reviewed, The interpretation of quantum mechanics, somewhat oversells the contents of Roland Omnès’ textbook published by the Princeton University Press in 1994. For it would better be viewed as an extended review of an interpretation, viz., the consistent histories formalism. Clearly pitched in the style of an undergraduate-level textbook, not a research monograph – the author expressly disavows any scholarly intent! Consists in a mosaic alternating between wordy expositions and high-level derivations of the formulae. Nevertheless, Omnès’ penchant for verbosity can have its advantages for the inexpert reader. For instance, he dilates at length in a nice discussion of detection methods: retina, photographic emulsion, photomultipliers, bubble chambers, Stern-Gerlach magnets [pp. 63-72].
What are consistent histories? Omnès portrays them as a modernization of the Copenhagen interpretation that ought to command universal assent – for him the problems of quantum logic have all been satisfactorily solved! A consistent history is nothing but a record of observations of a system at a sequence of instants in time, separated by a large enough interval that the measurements do not interfere with one another. What’s strange is that the field of propositions in this quantum logic depends on the choice of sequence of observables to make up the putative consistent histories, whereas the conventional use of the word logic carries with it the connotation of universality. It does help to give an interpretation in terms of a Stern-Gerlach experiment pp. 158] so that definitions will not be so dry!
The following passage reveals well the author’s take on his subject:
The multiplicity of consistent logics is nothing but a rediscovery of the complementarity principle, though it has now lost its status of principle to become only a byproduct of logic. It will be seen more than once that this kind of occurrence is rather common when physics is approached from a logical standpoint and quite a few Copenhagen principles will be rediscovered so as to become a theorem, a side remark, or simply a convenience, not to mention the case when they can be disposed of. [p. 160]
An example of how Omnès thinks backwards! The conceit throughout that there is only one cogent interpretation of quantum mechanics – namely, his favored consistent-histories interpretation – gets to be a little bothersome. Re. complementarity [p. 88]: Omnès skates over issue that for Bohr complementarity exists only between conjugate pairs. A couple other apparent difficulties: he presumes properties are always sharply defined [p. 104], whereas one would suppose that a realistic instrument could measure only up to a certain precision. Thus, measurement theory as presented by Omnès always involves an idealization – which, this reviewer at least imagines, it could be profitable to ponder lifting? Another problem [p. 110]: ‘we assume that the Hilbert space framework and the Schrödinger dynamics are given’. This statement marks Omnès as an expositor of the views of others and not as an original researcher. In particular, the question of the realizability or not of an arbitrary so-called observable is subtler than Omnès lets on here [p. 114].
Chapter six describes how to recover classical mechanics from quantum mechanics [pp. 238-258]. Omnès’ presentation of a topic not ordinarily discussed in very much depth proves to be quite helpful. Appendices A and B are way too technical given the level of the rest of the book – here is definitely not the place to learn microlocal analysis!
Chapter seven discusses the important relation between decoherence and consistent histories. Roughly, decoherence justifies why we can take measurements of different observables at successive intervals and regard them as being independent of one another – if they weren’t thus independent, the whole edifice of quantum logic would have to be radically revised! NB: decoherence originates in dissipation [p. 277] and would not occur for superconductors and ordinary electromagnetic radiation (which obviously produces macroscopic interferences). The author rightly alludes to a point of principle in this connection that John Bell for one picked up on:
Although macroscopic interference effects disappear when a collective observable is measured, a pure quantum state remains a pure state under time evolution so that, in principle, interference might still be found if one were to measure a more clever or finer observable. [p. 270]
Decoherence is mainly due to the existence of a very large number of degrees of freedom in the environment. It also requires that the coupling between the collective subsystem and the environment should be somewhat disordered. [p. 282]
Bell’s argument went as follows: when one starts from a pure state, it will always remain in a pure state as long as it evolves according to the Schrödinger equation. Accordingly, even if the reduced density operator describing the collective observables becomes diagonalized, this is inessential: the full density operator still represents a pure state and it therefore contains the possibility of showing interference. True enough, no interference can be seen in a measurement of a collective observable, but there always exist more subtle observables that would be able to show it. By measuring such an observable, as was always assumed to be possible in principle, one will exhibit the existence of a surviving quantum superposition of macroscopically different states. The answer provided by decoherence is therefore valid ‘for all practical purposes’. [p. 305]
The consistent histories point of view on repeated measurements: reduction of wave function constitutes not an additional postulate but follows as a consequence of the theory of histories! [pp. 339-341, see especially third paragraph on p. 340]. This reviewer doesn’t follow immediately how decoherence allegedly explains the reduction of the wave packet [p. 353]. Doesn’t it lead only to a diagonal density matrix, not to a unique outcome? Nor is it not entirely clear to him yet how existence of facts in the present determines a unique past but leaves the future indeterminate [pp. 343-344]. Couldn’t one instead use projectors in the future to determine a history and leave the past indeterminate?
Chapter eight takes on other interpretations. The treatment of Everett’s many-worlds interpretation is too sketchy [pp. 345-348] and again, so too is his exposition of Ghirardi-Rimini-Weber stochastic collapse theory [pp. 349-350]: Omnès claims all that GRW try to explain has been already explained by decoherence. Re. criteria of truth: what justifies excluding inconsistent histories? [p. 355] Omnès says little on this crucial point.
Omnès resolution of the paradox [p. 391]: EPR’s elements of reality correspond only to reliable properties but not true properties, so that they are in fact arbitrary, depending upon a special choice in the description corresponding to a special choice of logic. They therefore have no objective character. NB, his quirky and limited notion of ‘truth’ as nothing more than a trace of a past measurement. In the final section of chapter nine, Omnès makes a good point after all: why prize determinism so highly (as hidden variable theorists do) when quantum mechanics has undermined determinism at the microphysical level? Isn’t it more natural to think of determinism as something that can hold only in a classical limit?
Chapter ten on non-classical macroscopic systems starts out with a high-level overview of the theory of superconductors but has nothing on how it connects with decoherence or quantum measurement theory [pp. 410-425]. The Aharanov-Bohm effect has in fact been entirely confirmed in SQUID’s and this was the first example of a macroscopic system showing quantum interference effects [p. 422]. A couple other topics are covered in this chapter: a too-abbreviated derivation of the exponential decay law [pp. 434-436] and why from the consistent histories point of view, the quantum Zeno effect is not evidence for collapse of the wave function [p. 441]. Omnès makes a big deal that consistent histories form an objective interpretation of quantum mechanics and that von Neumann was wrong to bring in the observer [pp. 510-511].
The final section of chapter twelve [pp. 506-531] offers a philosophical disquisition – somewhat disconnected, bringing in inter alia Kant, Wittgenstein, Heidegger etc, largely dependent on d’Espagnat. Omnès declares himself for realism as against nominalism which he attributes to Leibniz, viz., the hypothetico-deductive approach to science [p. 525]. In the last paragraph, he pluncks for a total realism as against veiled realism; in which human logic and mathematics explore an objective logos (shorn of religious connotations), and dismisses nominalism as too arbitrary [p. 527].
The consistent histories approach turns out to be nice in some respects (helpful in the study of the classical limit, i.e. collective modes as well as in certain systems showing macroscopic quantum behavior) but the basic problem with it is that it is premised on an uncritical reception of the underlying formalism of quantum mechanics rather than deriving this, and second: the supposedly overcome reduction of the wave packet is not after all truly eliminated but reappears under the guise of the problem of the existence of facts. Another problem the author recognizes is that, thus far, the rigorous theory of decoherence is based solely on toy models.
So: scan through Omnès’ textbook quickly as a warm-up to the original literature, but don’t expect much of an engagement with alternate points of view or any very trenchant criticisms of them.
August 3, 2014
I think this is a really excellent, pleasant read about QM (not every excellent read about QM is also a pleasant read!). For some reason, however, Goodreads deletes the author's name -- the book is written by Roland Omnes (Professor of Physics, University of Paris XI).
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January 27, 2019The interpretation of quantum mechanics
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