Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems

American Journal of Physics

Volumn 69, Issue 6, 2001, Pages 655-701

  Laloe F ^a  

^a LABORATOIRE KASTLER BROSSEL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035606734     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1356698     Document Type: Article

References (223)

1. N. Bohr, "The Solvay meetings and the development of quantum mechanics," Essays 1958-62 on Atomic Physics and Human Knowledge (Vintage, New York, 1966); Atomic Physics and the Description of Nature (Cambridge U.P., Cambridge, 1930).
2. N. Bohr, "The Solvay meetings and the development of quantum mechanics," Essays 1958-62 on Atomic Physics and Human Knowledge (Vintage, New York, 1966); Atomic Physics and the Description of Nature (Cambridge U.P., Cambridge, 1930).
3. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton U.P., Princeton, 1955).
4. J. S. Bell, "On the problem of hidden variables in quantum mechanics," Rev. Mod. Phys. 38, 447-452 (1966); reprinted in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 396-402.
5. J. S. Bell, "On the problem of hidden variables in quantum mechanics," Rev. Mod. Phys. 38, 447-452 (1966); reprinted in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 396-402.
6. D. Bohm and J. Bub, "A proposed solution of the measurement problem in quantum mechanics by a hidden variable theory," Rev. Mod. Phys. 38, 453-469 (1966).
7. D. Bohm and J. Bub, "A refutation of the proof by Jauch and Piron that hidden variables can be excluded in quantum mechanics," Rev. Mod. Phys. 38, 470-475 (1966).
8. N. D. Mermin, "Hidden variables and the two theorems of John Bell," Rev. Mod. Phys. 65, 803-815 (1993); in particular see Sec. III.
9. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge U.P., Cambridge, 1987); this lovely little book contains the complete set of J. Bell's articles on quantum mechanics.
10. A. Shimony, "Role of the observer in quantum theory," Am. J. Phys. 31, 755-773 (1963).
11. D. Bohm, "A suggested interpretation of the quantum theory in terms of "hidden" variables," Phys. Rev. 85, 166-179 (1952); 85, 180-193 (1952;); see also Quantum Theory (Constable, London, 1954), although this book does not discuss theories with additional variables.
12. D. Bohm, "A suggested interpretation of the quantum theory in terms of "hidden" variables," Phys. Rev. 85, 166-179 (1952); 85, 180-193 (1952;); see also Quantum Theory (Constable, London, 1954), although this book does not discuss theories with additional variables.
13. D. Bohm, "A suggested interpretation of the quantum theory in terms of "hidden" variables," Phys. Rev. 85, 166-179 (1952); 85, 180-193 (1952;); see also Quantum Theory (Constable, London, 1954), although this book does not discuss theories with additional variables.
14. N. Wiener and A. Siegel, "A new form for the statistical postulate of quantum mechanics." Phys. Rev. 91, 1551-1560 (1953); A. Siegel and N. Wiener, "Theory of measurement in differential space quantum theory," ibid. 101, 429-432 (1956).
15. N. Wiener and A. Siegel, "A new form for the statistical postulate of quantum mechanics." Phys. Rev. 91, 1551-1560 (1953); A. Siegel and N. Wiener, "Theory of measurement in differential space quantum theory," ibid. 101, 429-432 (1956).
16. P. Pearle, "Reduction of the state vector by a non-linear Schrödinger equation," Phys. Rev. D 13, 857-868 (1976).
17. P. Pearle, "Toward explaining why events occur," Int. J. Theor. Phys. 18, 489-518 (1979).
18. G. C. Ghirardi, A. Rimini, and T. Weber, "Unified dynamics for microscopic and macroscopic systems." Phys. Rev. D 34, 470-491 (1986); "Disentanglement of quantum wave functions," 36, 3287-3289 (1987).
19. G. C. Ghirardi, A. Rimini, and T. Weber, "Unified dynamics for microscopic and macroscopic systems." Phys. Rev. D 34, 470-491 (1986); "Disentanglement of quantum wave functions," 36, 3287-3289 (1987).
20. B. S. de Witt, "Quantum mechanics and reality," Phys. Today 23, 30-35 (September 1970).
21. R. B. Griffiths, "Consistent histories and the interpretation of quantum mechanics," J. Stat. Phys. 36, 219-272 (1984).
22. S. Goldstein, "Quantum Theory without observers," Phys. Today 51, 42-46 (March 1998); 51, 38-41 (April 1998).
23. S. Goldstein, "Quantum Theory without observers," Phys. Today 51, 42-46 (March 1998); 51, 38-41 (April 1998).
24. "Quantum mechanics debate," Phys. Today 24, 36-44 (April 1971); "Still more quantum mechanics," 24, 11-15 (October 1971).
25. "Quantum mechanics debate," Phys. Today 24, 36-44 (April 1971); "Still more quantum mechanics," 24, 11-15 (October 1971).
26. B. S. de Witt and R. N. Graham. "Resource letter IQM-I on the interpretation of quantum mechanics." Am. J. Phys. 39, 724-738 (1971).
27. M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, 1966); second edition (1989). The same author has written another interesting book on a similar subject: The Philosophy of Quantum Mechanics (Wiley, New York, 1974).
28. M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, 1966); second edition (1989). The same author has written another interesting book on a similar subject: The Philosophy of Quantum Mechanics (Wiley, New York, 1974).
29. O. Darrigol, From c-numbers to q-numbers; the Classical Analogy in the History of Quantum Theory (University of California Press, 1992).
30. B. d'Espagnat, Conceptual Foundations of Quantum Mechanics (Benjamin, New York, 1971).
31. B. d'Espagnat, Veiled Reality: an Analysis of Present Day Quantum Mechanics Concepts (Addison-Wesley, Reading, MA, 1995); Le Réel Voilé, Analyse des Concepts Quantiques (Fayard, Paris, 1994); Une Incertaine Réalité, la Connaissance et la Durée (Gauthier-Villars, Paris, 1985); A la Recherche du Réel (Gauthier-Villars, Bordas, 1979).
32. B. d'Espagnat, Veiled Reality: an Analysis of Present Day Quantum Mechanics Concepts (Addison-Wesley, Reading, MA, 1995); Le Réel Voilé, Analyse des Concepts Quantiques (Fayard, Paris, 1994); Une Incertaine Réalité, la Connaissance et la Durée (Gauthier-Villars, Paris, 1985); A la Recherche du Réel (Gauthier-Villars, Bordas, 1979).
33. B. d'Espagnat, Veiled Reality: an Analysis of Present Day Quantum Mechanics Concepts (Addison-Wesley, Reading, MA, 1995); Le Réel Voilé, Analyse des Concepts Quantiques (Fayard, Paris, 1994); Une Incertaine Réalité, la Connaissance et la Durée (Gauthier-Villars, Paris, 1985); A la Recherche du Réel (Gauthier-Villars, Bordas, 1979).
34. B. d'Espagnat, Veiled Reality: an Analysis of Present Day Quantum Mechanics Concepts (Addison-Wesley, Reading, MA, 1995); Le Réel Voilé, Analyse des Concepts Quantiques (Fayard, Paris, 1994); Une Incertaine Réalité, la Connaissance et la Durée (Gauthier-Villars, Paris, 1985); A la Recherche du Réel (Gauthier-Villars, Bordas, 1979).
35. A. Pais, "Einstein and the quantum theory," Rev. Mod. Phys. 51, 863-911 (1979).
36. O. Darrigol, "Strangeness and soundness in Louis de Broglie's early works," Physis 30, 303-372 (1993).
37. E. A. Cornell and C. E. Wieman, "The Bose-Einstein condensate," Sci. Am. 278, 26-31 (March 1998).
38. W. Heisenberg, The Physical Principles of the Quantum Theory (University of Chicago Press, Chicago, 1930).
39. P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford U.P., Oxford, 1958).
40. H. P. Stapp, "S-matrix interpretation of quantum theory," Phys. Rev. D 3, 1303-1320 (1971).
41. A. Peres, "What is a state vector?," Am. J. Phys. 52, 644-650 (1984).
42. B. G. Englert, M. O. Scully, and H. Walther, "Quantum erasure in double-slit interferometers with which-way detectors," Am. J. Phys. 67, 325-329 (1999); see the first few lines of Sec. IV.
43. C. A. Fuchs and A. Peres, "Quantum theory needs no "interpretation," " Phys. Today 53, 70-71 (March 2000); see also various reactions to this text in the letters of the September 2000 issue.
44. C. Chevalley, "Niels Bohr's words and the Atlantis of Kantianismin," in Niels Bohr and Contemporary Philosophy, edited by J. Faye and H. Folse (Kluwer, Dordrecht, 1994), pp. 33-57.
45. J. S. Bell, "Bertlmann's socks and the nature of reality," J. Phys. C 2, 41-62 (1981).
46. J. S. Bell, Quantum Mechanics for Cosmologists, edited by C. Isham, R. Penrose, and D. Sciama in Quantum Gravity Vol. 2 (Clarendon, Oxford, 1981), pp. 611-637; p. 117 of Ref. 7.
47. L. Rosenfeld, "The measuring process in quantum mechanics," Suppl. Prog. Theor. Phys. 222, Extra Number "Commemoration issue for the thirtieth anniversary of the meson theory by Dr. H. Yukawa" (1965).
48. M. Brune, E. Hagley, J. Dreyer, W. Maître, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, "Observing the progressive decoherence of the "meter" in a quantum measurement," Phys. Rev. Lett. 77, 4887-4890 (1996).
49. E. P. Wigner, "Remarks on the mind-body question," in The Scientist Speculates, edited by I. J. Good (Heinemann, London, 1961), pp. 284-302; reprinted in E. P. Wigner, Symmetries and Reflections (Indiana U.P., Bloomington, 1967), pp. 171-184.
50. E. P. Wigner, "Remarks on the mind-body question," in The Scientist Speculates, edited by I. J. Good (Heinemann, London, 1961), pp. 284-302; reprinted in E. P. Wigner, Symmetries and Reflections (Indiana U.P., Bloomington, 1967), pp. 171-184.
51. E. P. Wigner, "The problem of measurement," Am. J. Phys. 31, 6-15 (1963); reprinted in Symmetries and Reflections (Indiana U.P., Bloomington, 1967), pp. 153-170; or again in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 324-341.
52. E. P. Wigner, "The problem of measurement," Am. J. Phys. 31, 6-15 (1963); reprinted in Symmetries and Reflections (Indiana U.P., Bloomington, 1967), pp. 153-170; or again in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 324-341.
53. E. P. Wigner, "The problem of measurement," Am. J. Phys. 31, 6-15 (1963); reprinted in Symmetries and Reflections (Indiana U.P., Bloomington, 1967), pp. 153-170; or again in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 324-341.
54. E. Schrödinger, "Die gegenwärtige situation in der quantenmechanik," Naturwissenschaften 23, 807-812 (1935); 23, 823-828 (1935); 23, 844-849 (1935). English translation: "The present situation in quantum mechanics," Proc. Am. Philos. Soc. 124, 323-338 (1980); or pp. 152-167 in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983).
55. E. Schrödinger, "Die gegenwärtige situation in der quantenmechanik," Naturwissenschaften 23, 807-812 (1935); 23, 823-828 (1935); 23, 844-849 (1935). English translation: "The present situation in quantum mechanics," Proc. Am. Philos. Soc. 124, 323-338 (1980); or pp. 152-167 in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983).
56. E. Schrödinger, "Die gegenwärtige situation in der quantenmechanik," Naturwissenschaften 23, 807-812 (1935); 23, 823-828 (1935); 23, 844-849 (1935). English translation: "The present situation in quantum mechanics," Proc. Am. Philos. Soc. 124, 323-338 (1980); or pp. 152-167 in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983).
57. E. Schrödinger, "Die gegenwärtige situation in der quantenmechanik," Naturwissenschaften 23, 807-812 (1935); 23, 823-828 (1935); 23, 844-849 (1935). English translation: "The present situation in quantum mechanics," Proc. Am. Philos. Soc. 124, 323-338 (1980); or pp. 152-167 in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983).
58. E. Schrödinger, "Die gegenwärtige situation in der quantenmechanik," Naturwissenschaften 23, 807-812 (1935); 23, 823-828 (1935); 23, 844-849 (1935). English translation: "The present situation in quantum mechanics," Proc. Am. Philos. Soc. 124, 323-338 (1980); or pp. 152-167 in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983).
59. E. Schrödinger, Proc. Cambridge Philos. Soc. 31, 555 (1935); 32, 446 (1936).
60. E. Schrödinger, Proc. Cambridge Philos. Soc. 31, 555 (1935); 32, 446 (1936).
61. A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777-780 (1935); or in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 138-141.
62. A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777-780 (1935); or in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 138-141.
63. M. Born ed., The Einstein-Born Letters (1916-1955) (MacMillan, London, 1971).
64. N. Bohr, "Quantum mechanics and physical reality," Nature (London) 136, 65 (1935); "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 48, 696-702 (1935).
65. N. Bohr, "Quantum mechanics and physical reality," Nature (London) 136, 65 (1935); "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 48, 696-702 (1935).
66. D. Mermin, "Is the moon there when nobody looks? Reality and the quantum theory," Phys. Today 38, 38-47 (April 1985).
67. D. Home and F. Selleri, "Bell's theorem and EPR paradox," Riv. Nuovo Cimento 14, 1-95 (1991).
68. P. Pearle, "Alternative to the orthodox interpretation of quantum theory," Am. J. Phys. 35, 742-753 (1967).
69. J. S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics (Long Island City, N.Y.) 1, 195-200 (1964).
70. F. Laloë, "Les surprenantes prédictions de la mécanique quantique," Recherche 182, 1358-1367 (November 1986).
71. F. Laloë, "Cadre général de la mécanique quantique; les objections de Einstein, Podolsky et Rosen," J. Phys. Colloq. C-2, 1-40 (1981). See also the following articles, especially that by J. Bell on Bertlmann socks, which is a classics!
72. D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs. NJ, 1951).
73. P. Eberhard, "Bell's theorem and the different concepts of locality," Nuovo Cimento B 46, 392-419 (1978).
74. J. F. Clauser, M. A. Home, A. Shimony, and R. A. Holt, "Proposed experiment to test local hidden-variables theories," Phys. Rev. Lett. 23, 880-884 (1969).
75. A. Peres, "Unperformed experiments have no results," Am. J. Phys. 46, 745-747 (1978).
76. J. A. Wheeler, "Niels Bohr in Today's Words" in Quantum Theory and Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983).
77. E. P. Wigner, "On hidden variables and quantum mechanical probabilities," Am. J. Phys. 38, 1005-1009 (1970).
78. S. J. Freedman and J. F. Clauser, "Experimental test of local hidden variable theories," Phys. Rev. Lett. 28, 938-941 (1972); S. J. Freedman, thesis, University of California, Berkeley; J. F. Clauser, "Experimental investigations of a polarization correlation anomaly," Phys. Rev. Lett. 36, 1223 (1976).
79. S. J. Freedman and J. F. Clauser, "Experimental test of local hidden variable theories," Phys. Rev. Lett. 28, 938-941 (1972); S. J. Freedman, thesis, University of California, Berkeley; J. F. Clauser, "Experimental investigations of a polarization correlation anomaly," Phys. Rev. Lett. 36, 1223 (1976).
80. S. J. Freedman and J. F. Clauser, "Experimental test of local hidden variable theories," Phys. Rev. Lett. 28, 938-941 (1972); S. J. Freedman, thesis, University of California, Berkeley; J. F. Clauser, "Experimental investigations of a polarization correlation anomaly," Phys. Rev. Lett. 36, 1223 (1976).
81. E. S. Fry and R. C. Thompson, "Experimental test of local hidden variable theories," Phys. Rev. Lett. 37, 465-468 (1976).
82. M. Lamehi-Rachti and W. Mittig, "Quantum mechanics and hidden variables: A test of Bell's inequality by the measurement of spin correlation in low energy proton-proton scattering," Phys. Rev. D 14, 2543-2555 (1976).
83. A. Aspect, P. Grangier, and G. Roger, "Experimental tests of realistic local theories via Bell's theorem," Phys. Rev. Lett. 47, 460-463 (1981); "Experimental realization of Einstein-Podolsky-Bohm gedankenexperiment: A new violation of Bell's inequalities," 49, 91-94 (1982).
84. A. Aspect, P. Grangier, and G. Roger, "Experimental tests of realistic local theories via Bell's theorem," Phys. Rev. Lett. 47, 460-463 (1981); "Experimental realization of Einstein-Podolsky-Bohm gedankenexperiment: A new violation of Bell's inequalities," 49, 91-94 (1982).
85. W. Perrie, A. J. Duncan, H. J. Beyer, and H. Kleinpoppen, "Polarization correlations of the two photons emitted by metastable atomic deuterium: A test of Bell's inequality," Phys. Rev. Lett. 54, 1790-1793 (1985).
86. T. E. Kiess, Y. E. Shih, A. V. Sergienko, and C. O. Alley. "Einstein-Podolsky-Rosen-Bohm experiments using light quanta produced by type-II parametric conversion," Phys. Rev. Lett. 71, 3893-3897 (1993).
87. J. S. Bell, contribution to "Foundations of quantum mechanics," Proceedings of the International School of Physics Enrico Fermi (Academic, New York, 1971), course II, p. 171.
88. J. P. Jarrett, "On the Physical Significance of the Locality Conditions in the Bell Arguments," Nöus 18, 569-589 (1984).
89. L. E. Ballentine and J. P. Jarrett, "Bell's theorem: Does quantum mechanics contradict relativity?," Am. J. Phys. 55, 696-701 (1987).
90. A. Shimony, "Events and processes in the quantum world," Quantum concepts in Space and Time, edited by R. Penrose and C. J. Isham (Oxford U.P., Oxford, 1986), pp. 182-203.
91. J. D. Franson, "Bell inequality for position and time," Phys. Rev. Lett. 62, 2205-2208 (1989).
92. J. Brendel, E. Mohler, and W. Martienssen, "Experimental test of Bell's inequality for energy and time," Eur. Phys. Lett. 20, 575-580 (1993).
93. N. Gisin, "Bell's inequality holds for all non-product states," Phys. Lett. A 154, 201-202 (1991).
94. S. Popescu and D. Rohrlich, "Generic quantum non locality," Phys. Lett. A 166, 293-297 (1992).
95. L. Hardy, "Quantum mechanics, local realistic theories, and Lorentz invariant realistic theories," Phys. Rev. Lett. 68, 2981-2984 (1992).
96. N. D. Mermin, "What's wrong with this temptation?," Phys. Today 47, 9-11 (June 1994); "Quantum mysteries refined," Am. J. Phys. 62, 880-887 (1994).
97. N. D. Mermin, "What's wrong with this temptation?," Phys. Today 47, 9-11 (June 1994); "Quantum mysteries refined," Am. J. Phys. 62, 880-887 (1994).
98. D. Boschi, S. Branca, F. De Martini, and L. Hardy, "Ladder proof of nonlocality without inequalities: Theoretical and experimental results," Phys. Rev. Lett. 79, 2755-2758 (1997).
99. S. Goldstein, "Nonlocality without inequalities for almost all entangled states for two particles," Phys. Rev. Lett. 72, 1951-1954 (1994).
100. D. M. Greenberger, M. A. Home, and A. Zeilinger, Bell's Theorem, Quantum Theory, and Conceptions of the Universe, edited by M. Kafatos (Kluwer, Dordrecht, 1989), pp. 69-72; this reference is not always easy to find, but one can also read the following article, published one year later.
101. D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, "Bell's theorem without inequalities," Am. J. Phys. 58, 1131-1143 (1990).
102. F. Laloë, "Correlating more than two particles in quantum mechanics," Curr. Sci. 68, 1026-1035 (1995).
103. N. D. Mermin, "Quantum mysteries revisited," Am. J. Phys. 58, 731-733 (1990).
104. R. Lafiamme, E. Knill, W. H. Zurek, P. Catasi, and S. V. S. Mariappan, "NMR GHZ," quant-ph/9709025; Philos. Trans. R. Soc. London, Ser. A 356, 1941-1948 (1998).
105. Seth Lloyd, "Microscopic analogs of the Greenberger-Horne-Zeilinger experiment," Phys. Rev. A 57, R1473-1476 (1998).
106. U. Sakaguchi, H. Ozawa, C. Amano, and T. Fokumi, "Microscopic analogs of the Greenberger-Horne-Zeilinger experiment on an NMR quantum computer," Phys. Rev. A 60, 1906-1911 (1999).
107. Jian-Wei Pan, Dik Bouwmeester, H. Weinfurter, and A. Zeilinger, "Experimental entanglement swapping: Entangling photons that never interacted," Phys. Rev. Lett. 80, 3891-3894 (1998).
108. Jian-Wei Pan, Dik Bouwmeester, H. Weinfurter, A. Zeilinger, and M. Daniell, "Observation of three-photon Greenberger-Horne-Zeilinger entanglement," Phys. Rev. Lett. 82, 1345-1349 (1999).
109. N. D. Mermin, "Extreme quantum entanglement in a superposition of macroscopically distinct states," Phys. Rev. Lett. 65, 1838-1841 (1990).
110. S. Kochen and E. P. Specker, "The problem of hidden variables in quantum mechanics," J. Math. Mech. 17, 59-87 (1967).
111. F. Belifante, Survey of Hidden Variables Theories (Pergamon, New York, 1973).
112. A. Peres, "Incompatible results of quantum measurements," Phys. Lett. A 151, 107-108 (1990).
113. J. S. Bell, oral presentation to the EGAS conference in Paris, July 1979 (published in an abridged version in the next reference).
114. J. S. Bell, "Atomic cascade photons and quantum mechanical nonlocality," Comments At. Mol. Phys. 9, 121 (1980); CERN preprint TH.2053 and TH 2252.
115. P. G. Kwiat, P. H. Eberhard, A. M. Steinberg, and R. Chiao, "Proposal for a loophole-free Bell inequality experiment," Phys. Rev. A 49, 3209-3220 (1994).
116. E. S. Fry, T. Walther, and S. Li, "Proposal for a loophole-free test of the Bell inequalities," Phys. Rev. A 52, 4381-4395 (1995).
117. A. Aspect, J. Dalibard, and G. Roger, "Experimental tests of Bell's inequalities using time varying analyzers," Phys. Rev. Lett. 49, 1804-1807 (1982).
118. G. Weihs, T. Jennenwein, C. Simon, H. Weinfurter, and A. Zeilinger, "Violation of Bell's inequality under strict Einstein locality conditions," Phys. Rev. Lett. 81, 5039-5043 (1998).
119. J. S. Bell, "Free variables and local causality," pp. 100-104 in Ref. 7.
120. H. P. Stapp, "Whiteheadian approach to quantum theory and the generalized Bell's theorem," Found. Phys. 9, 1-25 (1979); "Bell's theorem and the foundations of quantum physics," Am. J. Phys. 53, 306-317 (1985).
121. H. P. Stapp, "Whiteheadian approach to quantum theory and the generalized Bell's theorem," Found. Phys. 9, 1-25 (1979); "Bell's theorem and the foundations of quantum physics," Am. J. Phys. 53, 306-317 (1985).
122. H. P. Stapp, "Nonlocal character of quantum theory," Am. J. Phys. 65, 300-304 (1997); "Meaning of counterfactual statements in quantum physics," 66, 924-926 (1998).
123. H. P. Stapp, "Nonlocal character of quantum theory," Am. J. Phys. 65, 300-304 (1997); "Meaning of counterfactual statements in quantum physics," 66, 924-926 (1998).
124. D. Mermin, "Nonlocal character of quantum theory?," Am. J. Phys. 66, 920-924 (1998).
125. M. Redhead, Incompleteness, Nonlocality and Realism (Clarendon, Oxford, 1988), Chap. 4.
126. J. F. Clauser and A. Shimony, "Bell's theorem: Experimental tests and implications," Rep. Prog. Phys. 41, 1881-1927 (1978).
127. B. d'Espagnat, "Nonseparability and the tentative descriptions of reality," Phys. Rep. 110, 201-264 (1984).
128. B. d'Espagnat, Reality and the Physicist (Cambridge U.P., Cambridge, 1989).
129. R. B. Griffiths, "Consistent quantum counterfactuals," Phys. Rev. A 60, R5-R8 (1999).
130. J. J Bollinger, W. M. Itano, and D. J. Wineland, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-4652 (1996).
131. E. Hagley, X. Maître, G. Nogues, C. Wunderlich, M. Brune, J. M. Raimond, and S. Haroche, "Generation of EPR pairs of atoms," Phys. Rev. A 79, 1-5 (1997).
132. K. Molmer and A. Sorensen, "Multiple particle entanglement of hot trapped ions," Phys. Rev. Lett. 82, 1835-1838 (1999).
133. C. A. Sackett, D. Klepinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, O. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
134. A. Ekert, "Quantum cryptography based on Bell's theorem," Phys. Rev. A 67, 661-663 (1991).
135. C. H. Bennett, G. Brassard, and N. D. Mermin, "Quantum cryptography without Bell's theorem," Phys. Rev. Lett. 68, 557-559 (1992)
136. W. K. Wooters and W. H. Zurek, "A single quantum cannot be cloned," Nature (London) 299, 802-803 (1982).
137. D. Dieks, "Communication by EPR devices, " Phys. Lett. A 92, 271-272 (1982).
138. N. Gisin and S. Massar, "Optimal quantum cloning machines," Phys. Rev. Lett. 79, 2153-2156 (1997).
139. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. L. Wooters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895-1898 (1993).
140. D. Bouwmeister, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature (London) 390, 575-579 (1997).
141. S. Massar and S. Popescu, "Optimal extraction of information from finite quantum ensembles," Phys. Rev. Lett. 74, 1259-1263 (1995).
142. S. Popescu, "Bell's inequalities versus teleportation: What is nonlocality?," Phys. Rev. Lett. 72, 797-800 (1994); quant-ph/9501020.
143. T. Sudbury, "The fastest way from A to B," Nature (London) 390, 551-552 (1997).
144. G. P. Collins, "Quantum teleportation channels opened in Rome and Innsbruck," Phys. Today 51, 18-21 (February 1998).
145. C. H. Bennett, "Quantum information and computation," Phys. Today 48, 24-30 (October 1995).
146. D. P. DiVicenzo, "Quantum computation," Science 270, 255-261 (October 1995).
147. C. H. Bennett and D. P. DiVicenzo, "Quantum information and computation," Science 404, 247-255 (2000).
148. D. Deutsch, "Quantum theory, the Church-Turing principle and the universal quantum computer," Proc. R. Soc. London, Ser. A 400, 97-117 (1985).
149. P. Shor, Proceedings of the 55th Annual Symposium on the Foundations of Computer Science (IEEE Computer Society Press, Los Alamitos, CA, 1994), pp. 124-133.
150. D. S. Abrams and S. Lloyd, "Simulation of many-body Fermi systems on a universal quantum computer," Phys. Rev. Lett. 79, 2586-2589 (1997).
151. J. I Cirac and P. Zoller, "Quantum computation with cold trapped ions," Phys. Rev. Lett. 74, 4091-4094 (1995).
152. P. Shor, "Scheme for reducing decoherence in quantum computer memory," Phys. Rev. A 52, 2493-2496 (1995).
153. A. M. Steane, "Error correcting codes in quantum theory," Phys. Rev. Lett. 77, 793-796 (1996).
154. J. Preskill, "Battling decoherence: The fault-tolerant quantum computer," Phys. Today 52, 24-30 (June 1999).
155. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wooters, "Purification of noisy entanglement and faithful teleportation via noisy channels," Phys. Rev. Lett. 76, 722-725 (1996).
156. C. H. Bennett, D. P. DiVicenzo, J. A. Smolin, and W. A. Wooters, "Mixed-state entanglement and quantum error correction," Phys. Rev. A 54, 3824-3851 (1996).
157. H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, "Quantum repeaters: The role of imperfect local operations in quantum communication," Phys. Rev. Lett. 81, 5932-5935 (1998).
158. R. B. Griffiths and Chi-Sheng Niu, "Semiclassical Fourier transform for quantum computation," Phys. Rev. Lett. 76, 3228-3231 (1996).
159. S. Haroche and J. M. Raimond, "Quantum computing: Dream or nightmare?," Phys. Today 49, 51-52 (August 1996).
160. F. London and E. Bauer, La Théorie de l'observation en Mécanique Quantique, No. 775 of Actualités Scientifiques et Industrielles, Exposés de Physique Générale (Hermann. Paris, 1939); translated into English as "The theory of observation in quantum mechanics," in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 217-259; sec in particular Sec. 11, but also Secs. 13 and 14.
161. F. London and E. Bauer, La Théorie de l'observation en Mécanique Quantique, No. 775 of Actualités Scientifiques et Industrielles, Exposés de Physique Générale (Hermann. Paris, 1939); translated into English as "The theory of observation in quantum mechanics," in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 217-259; sec in particular Sec. 11, but also Secs. 13 and 14.
162. E. P. Wigner, "Interpretation of quantum mechanics," lectures given in 1976 at Princeton University: later published in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 260-314; see also Wigner's contribution in "Foundations of quantum mechanics," Proceedings of the Enrico Fermi Int. Summer School, edited by B. d'Espagnat (Academic, New York, 1971).
163. E. P. Wigner, "Interpretation of quantum mechanics," lectures given in 1976 at Princeton University: later published in Quantum Theory of Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 260-314; see also Wigner's contribution in "Foundations of quantum mechanics," Proceedings of the Enrico Fermi Int. Summer School, edited by B. d'Espagnat (Academic, New York, 1971).
164. N. D. Mermin, "What is quantum mechanics trying to tell us?," Am. J. Phys. 66, 753-767 (1998).
165. B. Misra and E. C. G. Sudarshan, "The Zeno's paradox in quantum theory," J. Math. Phys. 18, 756-763 (1977).
166. L. de Broglie, Tentative D'interprétation Causale et Non-linéaire de la Mécanique Ondulatoire (Gauthier-Villars, Paris, 1956).
167. 2 in causal interpretation of quantum theory," Phys. Rev. 108, 1070-1076 (1957).
168. L. E. Ballentine, "The statistical interpretation of quantum mechanics," Rev. Mod. Phys. 42, 358-381 (1970).
169. E. Madelung, "Quantentheorie in hydrodynamische Form," Z. Phys. 40, 322-326 (1927).
170. E. Nelson, "Derivation of the Schrödinger equation from Newtonian mechanics," Phys. Rev. 150, 1079-1085 (1966).
171. R. Werner, "A generalization of stochastic mechanics and its relation to quantum mechanics," Phys. Rev. D 34, 463-469 (1986).
172. C. Philippidis, C. Dewdney, and B. J. Hiley, "Quantum interference and the quantum potential," Nuovo Cimento Soc. Ital. Fis., B 52B, 15-23 (1979).
173. J. S. Bell, "De Broglie-Bohm, delayed choice, double slit experiment, and density matrix," Int. J. Quantum Chem., Symp. 14, 155-159 (1980).
174. B. G. Englert, M. O. Scully, G. Süssmann, and H. Walther, "Surrealistic Bohm trajectories," Z. Naturforsch., A: Phys. Sci. 47a, 1175-1186 (1992).
175. J. S. Bell, Sec. 4 of Ref. 34 or p. 128 of Ref. 7.
176. R. B. Griffiths, "Bohmian mechanics and consistent histories," Phys. Lett. A 261, 227-234 (1999).
177. N. Gisin, "Quantum measurements and stochastic processes," Phys. Rev. Lett. 52, 1657-1660 (1984); "Stochastic quantum dynamics and relativity," Helv. Phys. Acta 62, 363-371 (1989).
178. N. Gisin, "Quantum measurements and stochastic processes," Phys. Rev. Lett. 52, 1657-1660 (1984); "Stochastic quantum dynamics and relativity," Helv. Phys. Acta 62, 363-371 (1989).
179. L. Diosi, "Quantum stochastic processes as models for state vector reduction," J. Phys. A 21, 2885-2898 (1988).
180. P. Pearle, "On the time it takes a state vector to reduce," J. Stat. Phys. 41, 719-727 (1985).
181. A. Barchielli, L. Lanz, and G. M. Prosperi, "A model for the macroscopic description and continual observations in quantum mechanics," Nuovo Cimento Soc. Ital. Fis., B 42B, 79-121 (1982).
182. A. Barchielli, "Continual measurements for quantum open systems," Nuovo Cimento Soc. Ital. Fis., B 74B, 113-138 (1983); "Measurement theory and stochastic differential equations in quantum mechanics," Phys. Rev. A 34, 1642-1648 (1986).
183. A. Barchielli, "Continual measurements for quantum open systems," Nuovo Cimento Soc. Ital. Fis., B 74B, 113-138 (1983); "Measurement theory and stochastic differential equations in quantum mechanics," Phys. Rev. A 34, 1642-1648 (1986).
184. F. Benatti, G. C. Ghirardi, A. Rimini, and T. Weber, "Quantum mechanics with spontaneous localization and the quantum theory of measurement," Nuovo Cimento Soc. Ital. Fis., B 100B, 27-41 (1987).
185. P. Pearle, "Combining stochastic dynamical state-vector reduction with spontaneous localization," Phys. Rev. A 39, 2277-2289 (1989).
186. G. C. Ghirardi, P. Pearle, and A. Rimini, "Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles," Phys. Rev. A 42, 78-89 (1990).
187. L. Diosi, "Continuous quantum measurement and Ito formalism," Phys. Lett. A 129, 419-423 (1988).
188. L. Diosi, "Models for universal reduction of macroscopic quantum fluctuations," Phys. Rev. A 40, 1165-1174 (1989).
189. G. Ghirardi, R. Grassi, and A. Rimini, "Continuous-spontaneous-reduction model involving gravity," Phys. Rev. A 42, 1057-1064 (1990).
190. Experimental Metaphysics, Quantum Mechanical Studies for Abner Shimony, Festschrift Vols. 1 and 2, edited by Robert S. Cohen, Michael Horne, and John J. Stachel, Boston Studies in the Philosophy of Science Vols. 193 and 194 (Kluwer Academic, Dordrecht, 1997).
191. Experimental Metaphysics, Quantum Mechanical Studies for Abner Shimony, Festschrift Vols. 1 and 2, edited by Robert S. Cohen, Michael Horne, and John J. Stachel, Boston Studies in the Philosophy of Science Vols. 193 and 194 (Kluwer Academic, Dordrecht, 1997).
192. F. Benatti, G. C. Ghirardi, A. Rimini, and T. Weber, "Operations involving momentum variables in non-Hamiltonian evolution equations," Nuovo Cimento Soc. Ital. Fis., B 101B, 333-355 (1988).
193. S. Weinberg, "Precision tests of quantum mechanics," PRL 62, 485-488 (1989).
194. K. Wodkiewicz and M. O. Scully, "Weinberg's nonlinear wave mechanics," Phys. Rev. A 42, 5111-5116 (1990).
195. N. Gisin, "Weinberg's non-linear quantum mechanics and supraluminal communications," Phys. Lett. A 143, 1-2 (1990).
196. G. C. Ghirardi, "Quantum superpositions and definite perceptions: Envisaging new feasible tests," Phys. Lett. A 262, 1-14 (1999).
197. N. Gisin and I. Percival, "The quantum-state diffusion model applied to open systems," J. Phys. A 25, 5677-5691 (1992); "Quantum state diffusion, localization and quantum dispersion entropy," 26, 2233-2243 (1993); "The quantum state diffusion picture of physical processes," 26, 2245-2260 (1993).
198. N. Gisin and I. Percival, "The quantum-state diffusion model applied to open systems," J. Phys. A 25, 5677-5691 (1992); "Quantum state diffusion, localization and quantum dispersion entropy," 26, 2233-2243 (1993); "The quantum state diffusion picture of physical processes," 26, 2245-2260 (1993).
199. N. Gisin and I. Percival, "The quantum-state diffusion model applied to open systems," J. Phys. A 25, 5677-5691 (1992); "Quantum state diffusion, localization and quantum dispersion entropy," 26, 2233-2243 (1993); "The quantum state diffusion picture of physical processes," 26, 2245-2260 (1993).
200. I. Percival, Quantum State Diffusion (Cambridge U.P., Cambridge, 1998).
201. M. B. Plenio and P. Knight, "The quantum-jump approach to dissipative dynamics in quantum optics," Rev. Mod. Phys. 70, 101-141 (1998).
202. J. G. Cramer, "The transactional interpretation of quantum mechanics," Rev. Mod. Phys. 58, 647-687 (1986); in an appendix, this article contains a review of the various interpretations of quantum mechanics.
203. R. Omnès, "Logical reformulation of quantum mechanics. I. Foundation," J. Stat. Phys. 53, 893-932 (1988); "Logical reformulation of quantum mechanics. II. Interferences and the EPR experiments," 53, 933-955 (1988); "Logical reformulation of quantum mechanics. III. Classical limit and irreversibility," 53, 957-975 (1988).
204. R. Omnès, "Logical reformulation of quantum mechanics. I. Foundation," J. Stat. Phys. 53, 893-932 (1988); "Logical reformulation of quantum mechanics. II. Interferences and the EPR experiments," 53, 933-955 (1988); "Logical reformulation of quantum mechanics. III. Classical limit and irreversibility," 53, 957-975 (1988).
205. R. Omnès, "Logical reformulation of quantum mechanics. I. Foundation," J. Stat. Phys. 53, 893-932 (1988); "Logical reformulation of quantum mechanics. II. Interferences and the EPR experiments," 53, 933-955 (1988); "Logical reformulation of quantum mechanics. III. Classical limit and irreversibility," 53, 957-975 (1988).
206. M. Gell-Mann and J. Hartle, "Classical equations for quantum systems," Phys. Rev. D 47, 3345-3382 (1993).
207. R. Omnès, The Interpretation of Quantum Mechanics (Princeton U.P., Princeton, 1994); Understanding Quantum Mechanics (Princeton U.P., Princeton, 1999).
208. R. Omnès, The Interpretation of Quantum Mechanics (Princeton U.P., Princeton, 1994); Understanding Quantum Mechanics (Princeton U.P., Princeton, 1999).
209. R. B. Griffiths and R. Omnès, "Consistent histories and quantum measurements," Phys. Today 52, 26-31 (August 1999).
210. Y. Aharonov, P. G. Bergmann, and J. L. Lebowitz, "Time symmetry in the quantum process of measurement," Phys. Rev. B 134, 1410-1416 (1964).
211. R. B. Griffiths, "Consistent histories and quantum reasoning," Phys. Rev. A 54, 2759-2774 (1996).
212. R. B. Griffiths, "Choice of consistent family, and quantum incompatibility," Phys. Rev. A 57, 1604-1618 (1998).
213. Phys. Today "Observant readers take the measure of novel approaches to quantum theory; some get Bohmed," 52, 11-15 (February 1999); 52, 89-92 (February 1999).
214. Phys. Today "Observant readers take the measure of novel approaches to quantum theory; some get Bohmed," 52, 11-15 (February 1999); 52, 89-92 (February 1999).
215. W. H. Zurek, "Preferred states, predictability, classicality and the
216. R. B. Griffiths, "Correlations in separated quantum systems: A consistent history analysis of the EPR problem," Am. J. Phys. 55, 11-17 (1987).
217. F. Dowker and A. Kent, "Properties of consistent histories," Phys. Rev. Lett. 75, 3038-3041 (1995); "On the consistent histories approach to quantum mechanics," J. Stat. Phys. 82, 1575-1646 (1996).
218. F. Dowker and A. Kent, "Properties of consistent histories," Phys. Rev. Lett. 75, 3038-3041 (1995); "On the consistent histories approach to quantum mechanics," J. Stat. Phys. 82, 1575-1646 (1996).
219. A. Kent, "Quasiclassical dynamics in a closed quantum system," Phys. Rev. A 54, 4670-4675 (1996).
220. H. Everett III, "Relative state formulation of quantum mechanics," Rev. Mod. Phys. 29, 454-462 (1957); reprinted in Quantum Theory and Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 315-323.
221. H. Everett III, "Relative state formulation of quantum mechanics," Rev. Mod. Phys. 29, 454-462 (1957); reprinted in Quantum Theory and Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton U.P., Princeton, 1983), pp. 315-323.
222. H. D. Zeh, "On the interpretation of measurement in quantum theory," Found. Phys. 1, 69-76 (1970).
223. H. Hertz, Miscellaneous Papers, translated from first German edition (1895) by D. E. Jones and J. A. Schott (MacMillan, London, 1896), Vol. 1, p. 318.