Choice of consistent family, and quantum incompatibility

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 57, Issue 3, 1998, Pages 1604-1618

  Griffiths, Robert B ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001419241     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.57.1604     Document Type: Article

References (35)

1. R. B. Griffiths, J. Stat. Phys. 36, 219 (1984).JSTPBS
2. R. B. Griffiths, Am. J. Phys. 55, 11 (1987).AJPIAS
3. M. Gell-Mann and J. B. Hartle, in Complexity, Entropy, and the Physics of Information, edited by W. Zurek (Addison-Wesley, Reading, 1990); in Proceedings of the 25th International Conference on High Energy Physics, Singapore, 1990, edited by K. K. Phua and Y. Yamaguchi (World Scientific, Singapore, 1990).
4. R. Omnès, Rev. Mod. Phys. 64, 339 (1992).RMPHAT
5. R. B. Griffiths, Found. Phys. 23, 1601 (1993).FNDPA4
6. R. Omnès, The Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1994).
7. R. B. Griffiths, Phys. Rev. A 54, 2759 (1996). PLRAANThis is referred to in the text as CHQR. (Note the following errata: in (4.1) and later in the same paragraph, (Formula presented) should be (Formula presented); in the third paragraph of Sec. VI A, replace “(Formula presented) and (Formula presented)” with “(Formula presented) and (Formula presented)”)
8. R. B. Griffiths, in Symposium on the Foundations of Modern Physics 1994, edited by K. V. Laurikainen, C. Montonen, and K. Sunnarborg (Editions Frontières, Gif-sur-Yvette, France, 1994), p. 85.
9. T. A. Brun, Phys. Rev. Lett. 78, 1833 (1997).PRLTAO
10. R. B. Griffiths and C-S. Niu, Phys. Rev. Lett. 76, 3228 (1996).PRLTAO
11. R. B. Griffiths and C-S. Niu, Phys. Rev. A 56, 1173 (1997).PLRAAN
12. B. d’Espagnat, Phys. Lett. A 124, 204 (1987).PYLAAG
13. B. d’Espagnat, J. Stat. Phys. 56, 747 (1989).JSTPBS
14. B. d’Espagnat, Found. Phys. 20, 1147 (1990).FNDPA4
15. B. d’Espagnat, Veiled Reality (Addison-Wesley, Reading, 1995), Sec. 11.4.
16. F. Dowker and A. Kent, Phys. Rev. Lett. 75, 3038 (1995).PRLTAO
17. F. Dowker and A. Kent, J. Stat. Phys. 82, 1575 (1966).JSTPBS
18. A. Kent, Phys. Rev. A 54, 4670 (1996).PLRAAN
19. A. Kent, Phys. Rev. Lett. 78, 2874 (1997). PRLTAO(A preprint of this paper available when 7 was prepared did not employ the term “contrary” used in the published version.)
20. A. Kent, e-print gr-qc/9607073.
21. See Griffiths (Ref. 1), Sec. 6.1.
22. For example, in Refs. 2456.
23. J. S. Bell, in Sixty-Two Years of Uncertainty, edited by A. I. Miller (Plenum Press, New York, 1990), p. 17.
24. G. Birkhoff and J. von Neumann, Ann. Math. 37, 823 (1936).ANMAAH
25. One sometimes encounters discussions of how one can “measure” whether (Formula presented) or (Formula presented). From the consistent history perspective, this is somewhat careless terminology; what the writers have in mind is, typically, a situation in which a macroscopic apparatus can be set to produce a spin half particle either in the state (Formula presented) or in the state (Formula presented). Because the settings represent macroscopically distinct situations, the two apparatus states (viewed as quantum states) are orthogonal, and the measurement on the spin half particle is then used to try and infer something about the apparatus states.
26. Even in a classical world it would be impossible for a physical system to contain a complete description of itself. Consequently, it is always simplest to imagine that a quantum description is being constructed outside the system which it purports to describe. Sometimes the question is asked as to how we can describe, in a scientific sense, the universe in which we live. This is a nontrivial philosophical issue, but it does not seem implausible to assume that some sort of analogy will work: we can imagine simple model systems inside a closed box, check that they have some features that we find in our everyday experience, and then extrapolate by imagining ourselves in a large box, etc.
27. See The Interpretation of Quantum Mechanics (Ref. 6), p. 499.
28. See Veiled Reality (Ref. 15), p. 238.
29. R. Omnès (private communication).
30. See Veiled Reality (Ref. 15), p. 239.
31. R. B. Griffiths and J. B. Hartle, e-print gr-qc/9710025.
32. Y. Aharonov and L. Vaidman, J. Phys. A 24, 2315 (1991).JPHAC5
33. See, for example, M. R. Cohen and E. Nagel, An Introduction to Logic (Hackett Publishing Co., Indianapolis, 1992), 2nd ed., p. 55.
34. Rule 4 on p. 163 of The Interpretation of Quantum Mechanics (Ref. 6).
35. One way to avoid confusion would be to introduce a new term, say “perp,” to denote the relationship (A5) between two projectors. If (Formula presented) and (Formula presented) are “perp” and belong to the same consistent family, this means that the corresponding propositions are “contrary” in the logical sense. But if (Formula presented) and (Formula presented) are not in the same consistent family, “perp” says nothing about a logical relationship.