Relative frequency and probability in the Everett interpretation of Heisenberg-picture quantum mechanics

Foundations of Physics

Volumn 33, Issue 3, 2003, Pages 379-405

  Rubin, Mark A ^a  

^a MIT LINCOLN LABORATORY   (United States)

Author keywords

Born rule; Everett interpretation; Heisenberg picture; Probability; Relative frequency

Indexed keywords

EID: 0037500342     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023765114419     Document Type: Article

References (45)

1. H. Everett III, "'Relative state' formulation of quantum mechanics," Rev. Mod. Phys. 29, 454-462 (1957); reprinted in B. S. DeWitt and N. Graham, eds., The Many Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1973).
2. H. Everett III, "'Relative state' formulation of quantum mechanics," Rev. Mod. Phys. 29, 454-462 (1957); reprinted in B. S. DeWitt and N. Graham, eds., The Many Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1973).
3. B. d'Espagnat, Conceptual Foundations of Quantum Mechanics, 2nd edn. (Benjamin, Reading, MA, 1976).
4. H. Cramér, Mathematical Methods of Statistics (Princeton University Press, Princeton, NJ, 1946).
5. L. Vaidman, "Many-worlds interpretation of quantum mechanics," in Stanford Encyclopedia of Philosophy (Summer 2002 Edition), E. N. Zalta, ed., http://plato.stanford.edu/archives/sum2002/entries/qm-manyworlds (2002).
6. G. Pólya, Mathematics and Plausible Reasoning, Vol. II, 2nd ed. (Princeton University Press, Princeton, NJ, 1968).
7. J. Hartle, "Quantum mechanics of individual systems," Amer. J. Phys. 36, 704-712 (1968).
8. D. Finkelstein, "The logic of quantum mechanics," Trans. N. Y. Aca. Sci. 25, 621-637 (1965).
9. N. Graham, "The measurement of relative frequency," in The Many Worlds Interpretation of Quantum Mechanics, B. S. DeWitt and N. Graham, eds. (Princeton University Press, Princeton, NJ, 1973).
10. E. Farhi, J. Goldstone, and S. Gutmann, "How probability arises in quantum mechanics," Ann. Phys. (NY) 192, 368-382 (1989).
11. A. Kent, "Against many-worlds interpretations," Internat. J. Modern Phys. A 5, 1745-1762 (1990); gr-qc/9703089.
12. W. H. Zurek, "Decoherence, einselection and the existential interpretation (the rough guide)," Philos. Trans. Roy. Soc. London Ser. A 356, 1793-1820 (1998); quant-ph/9805065.
13. D. Deutsch, The Fabric of Reality (The Penguin Press, New York, 1997).
14. B. S. DeWitt, "The many-universes interpretation of quantum mechanics," in Proceedings of the International School of Physics "Enrico Fermi" Course IL: Foundations of Quantum Mechanics (Academic Press, New York, 1972); reprinted in B. S. DeWitt and N. Graham, eds., The Many Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1973).
15. B. S. DeWitt, "The many-universes interpretation of quantum mechanics," in Proceedings of the International School of Physics "Enrico Fermi" Course IL: Foundations of Quantum Mechanics (Academic Press, New York, 1972); reprinted in B. S. DeWitt and N. Graham, eds., The Many Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1973).
16. Y. Okhuwa, "Decoherence functional and probability interpretation," Phys. Rev. D 48, 1781-1784 (1993).
17. D. Deutsch and P. Hayden, "Information flow in entangled quantum systems," Proc. Roy. Soc. London Ser. A 456, 1759-1774, (2000); quant-ph/9906007.
18. M. A. Rubin, "Locality in the Everett interpretation of Heisenberg-picture quantum mechanics," Found. Phys. Lett. 14, 301-322 (2001); quant-ph/0103079.
19. M. A. Rubin, "Locality in the Everett interpretation of quantum field theory," Found. Phys. 32, 1495-1523 (2002); quant-ph/0204024.
20. L. Vaidman, "On schizophrenic experiences of the neutron or why we should believe in the many-worlds interpretation of quantum theory," Internat. Stud. Philos. Sci. 12, 245-261 (1998); quant-ph/9609006.
21. D. Deustsch, "Quantum theory of probability and decisions," Proc. Roy. Soc. London Ser. A 455, 3129-3137 (1999); quant-ph/9906015.
22. B. DeWitt, "The quantum mechanics of isolated systems," Internat. J. Modern Phys. A 13, 1881-1916 (1998).
23. L. Polley, "Quantum-mechanical probability from the symmetries of two-state systems," quant-ph/9906124.
24. L. Polley, "Position eigenstates and the statistical axiom of quantum mechanics," quant-ph/0102113.
25. C. M. Caves, C. A. Fuchs, and R. Schack, "Quantum probabilities as Bayesian probabilities," Phys. Rev. A 65, 022305 (2002); quant-ph/0106133.
26. J. D. Beckenstein, "Limitations on quantum information from black hole physics," Acta Phys. Polon. B 32, 3555-3570 (2001); quant-ph/0110005.
27. A. Rényi, Foundations of Probability (Holden-Day, San Francisco, 1970).
28. W. Rudin, Principles of Mathematical Analysis, 3d edn. (McGraw-Hill, New York, 1976).
29. R. B. Griffiths, "Consistent histories and the interpretation of quantum mechanics," J. Statist. Phys. 36, 219-272 (1984).
30. J. B. Hartle, "Spacetime quantum mechanics and the quantum mechanics of space-time," in Les Houches, Session LVII, 1992, Gravitation and Quantizations, B. Julia and J. Zinn-Justin, eds. (Elsevier Science B.V., 1995).
31. D. N. Page, "Probabilities don't matter," in Proceedings of the 7th Marcel Grossmann Meeting on General Relativity, M. Keiser and R. T. Jantsen, eds. (World Scientific, Singapore, 1995); gr-qc/9411004.
32. D. N. Page, "Sensible quantum mechanics: Are only perceptions probabilistic?," quant-ph/9506010.
33. D. N. Page, "Sensible quantum mechanics: Are probabilities only in the mind?," Internat. J. Modern Phys. D 5, 583-596 (1996); gr-qc/9507042.
34. R. Landauer, "Information is physical," Physics Today 44, May 23-29 (1991).
35. W. H. Zurek, "Decoherence and the transition from quantum to classical," Physics Today 44, 36-44 (October 1991).
36. D. Deutsch, "The structure of the multiverse," Proc. Roy. Soc. London Ser. A 458, 2911-2923 (2002); quant-ph/0104033.
37. H. Stein, "The Everett interpretation of quantum mechanics: Many worlds or none?," Noûs 18, 635-652 (1984).
38. R. Geroch, "The Everett interpretation," Noûs 18, 617-633 (1984).
39. E. R. Kandel, J. H. Schwartz, and T. M. Jessell, Principles of Neural Science, 3d. edn. (Appelton & Lange, Norwalk, CT, 1991).
40. M. Tegmark, "The importance of quantum decoherence in brain processes," Phys. Rev. E 61, 4194-4206 (2000); quant-ph/9907009.
41. D. Deutsch, "Quantum theory as a universal physical theory," Internat. J. Theoret. Phys. 24, 1-41 (1985).
42. D. Albert and B. Loewer, "Interpreting the many worlds interpretation," Synthese 77, 195-213 (1988).
43. D. Z. Albert, Quantum Mechanics and Experience (Harvard University Press, Cambridge, MA, 1992).
44. M. B. Weissman, "Emergent measure-dependent probabilities from modified quantum dynamics without state-vector reduction," Found. Phys. Lett. 12, 407-426 (1999); quant-ph/9906127.
45. K. Gottfried, Quantum Mechanics, Vol. 1: Fundamentals (Benjamin, Reading, MA, 1966).