Time-symmetric quantum mechanics questioned and defended
Robert B. Griffiths
Readers of the article by Yakir Aharonov, Sandu Popescu, and Jeff Tollaksen might be interested in an alternative time-symmetric formulation of quantum mechanics, known as “consistent histories,” that was developed over roughly the same time period as Aharonov’s work (see the article by Robert Griffiths and Roland Omnès, PHYSICS TODAY, August 1999, page 26). Closely related is the “decoherent histories” approach of Murray Gell-Mann and James Hartle,11. M. Gell-Mann, J. B. Hartle, in Complexity, Entropy and the Physics of InformationW. H. Zurek,ed.,Addison-Wesley, Redwood City, CA (1990), p. 425. but as that is not usually formulated in a way that is transparently time-symmetric, the following remarks refer to the consistent histories approach; see reference 22. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); available online at http://quantum.phys.cmu.edu/CQT. for an up-to-date formulation.Both the consistent histories approach and that of Aharonov and coworkers pay attention to events at several different times, are formulated in a way that is time-symmetrical, and address a number of quantum paradoxes. Both are consistent with the calculational procedures taught to students in a typical quantum mechanics course, so they are “standard quantum mechanics,” without the additional variables of de Broglie–Bohm or the additional collapses of Ghirardi-Rimini-Weber. And both approaches do not accept the “shut up and calculate” mentality that alas continues to dominate much classroom instruction. So far as I can tell, all the results mentioned by Aharonov and coauthors and in the earlier work they cite are fairly readily translated into the language of consistent histories, though the reverse is not true (see below); therefore, the consistent histories view is more general.In the treatment by Aharonov and coauthors, measurement, as in textbook quantum theory, remains a black box: It collapses the wavefunction, but nothing more can be said. And for good reason: The textbook approach of introducing probabilities by reference to measurement yields what appear to be insoluble difficulties if one attempts to apply quantum theory to the measurement process itself—that is, to actual apparatus constructed out of entities that are quantum mechanical. In the consistent histories approach, that difficulty does not arise, because it treats quantum dynamics as fundamentally probabilistic, not deterministic, and the same rules apply to measurements as to all other physical processes. Speaking metaphorically, the probabilistic approach used in consistent histories allows one to open the black measurement box and watch the quantum gears turn.The other major difference between the two approaches is their treatment of quantum paradoxes. We owe many of the most striking and delightful paradoxes of quantum theory to Aharonov and his coworkers, and he and Daniel Rohrlich have written a book on the topic.33. Y. Aharonov, D. Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed, Wiley, Weinheim, Germany (2005) . But he leaves the paradoxes largely unresolved; the reader is encouraged to study but not unravel them. The consistent histories approach is exactly opposite: Paradoxes should be—and a large number of them have been—resolved by the correct application of well-formulated and fully consistent quantum principles (see reference 22. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); available online at http://quantum.phys.cmu.edu/CQT. , chapters 19–25).Students new to quantum theory are often confused and deserve reasoned responses to their queries. Although paradoxes are valuable illustrations of how the quantum world differs from our everyday experience, I prefer to provide students with the conceptual tools needed to resolve and make sense of them. In particular, students benefit from learning a fully consistent approach to probabilities in the quantum domain, one not based on measurements but on general quantum principles. A colleague and I have just finished using that approach in teaching the first term of our introductory graduate quantum mechanics course. Although it requires extra time and effort to learn how to think about quantum processes rather than just do calculations, the reward comes in a deeper understanding of how the real (quantum) world works.REFERENCESSection:ChooseTop of pageREFERENCES <<1. M. Gell-Mann, J. B. Hartle, in Complexity, Entropy and the Physics of InformationW. H. Zurek,ed.,Addison-Wesley, Redwood City, CA (1990), p. 425. Google Scholar2. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press, New York (2002); available online at http://quantum.phys.cmu.edu/CQT. Google Scholar3. Y. Aharonov, D. Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed, Wiley, Weinheim, Germany (2005) . Google ScholarCrossref© 2011 American Institute of Physics.
Physics Today•May 1, 2011•1 citation