Ensembles and experiments in classical and quantum physics

International Journal of Modern Physics B

Volumn 17, Issue 16, 2003, Pages 2937-2980

  Neumaier, Arnold ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Axiomatization of physics; Bell inequality; Bohmian mechanics; Complementarity; Consistent experiment; Correspondence principle; Deterministic; Effect; Elements of physical reality; Ensemble; Event; Expectation; Flow of truth; Foundations of quantum mechanics

Indexed keywords

CORRELATION ANALYSIS; CORRESPONDENCE ANALYSIS; COSMOS; MATHEMATICAL ANALYSIS; MOLECULAR DYNAMICS; PHYSICS; QUANTUM MECHANICS; QUANTUM THEORY; REVIEW; THEORY;

EID: 0041694229     PISSN: 02179792     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217979203018338     Document Type: Review

References (91)

1. A. Aspect, Proposed experiment to test the nonseparability of quantum mechanics, Phys. Rev. D14, 1944 (1976) (Reprinted in Ref. 82.)
2. J. S. Bell, On the Einstein Podolsky Rosen paradox, Physics 1, 195 (1964) (Reprinted in Ref. 82.)
3. J. S. Bell, On the problem of hidden variables in quantum mechanics, Rev. Mod. Phys. 38, 447 (1966) (Reprinted in Ref. 82.)
4. J. S. Bell, Speakable and unspeakable in quantum mechanics (Cambridge Univ. Press, Cambridge, 1987).
5. H. J. Bernstein, Simple version of the Greenberger-Horne-Zeilinger (GHZ) argument against local realism, Found. Phys. 29, 521 (1999).
6. G. Birkhoff and J. von Neumann, The logics of quantum mechanics, Ann. Math. 37, 823 (1936).
7. D. Bohm, A suggested interpretation of the quantum theory in terms of "hidden" variables, I and II, Phys. Rev. 85, 166 (1952) (Reprinted in Ref. 82).
8. N. Bohr, Discussion with Einstein on Epistemological Problems in Atomic Physics, in P. A. Schilpp (ed.), Albert Einstein: Philosopher-Scientist, The Library of Living Philosophers (Evanston 1949), pp. 200-241 (Reprinted in Ref. 82.)
9. V. B. Braginsky and F. Ya Khalili, Quantum Measurement (Cambridge Univ. Press, Cambridge, 1992).
10. P. Busch, M. Grabowski and P. J. Lahti, Operational Quantum Physics (Springer, Berlin, 1995).
11. P. Busch, P. J. Lahti and P. Mittelstaedt, The Quantum Theory of Measurement, 2nd. ed. (Springer, Berlin, 1996).
12. B. S. Cirel'son, Quantum generalizations of Bell's inequality, Lett. Math. Phys. 4, 93 (1980).
13. J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880 (1969) (Reprinted in Ref. 82).
14. J. F. Clauser and A. Shimony, Bell's theorem: Experimental tests and implications, Rep. Prog. Phys. 41, 1881 (1978).
15. R. Clifton and A. Kent, Simulating quantum mechanics by non-contextual hidden variables, Proc. Roy. Soc. Lond. A456, 2101 (2000) quant-ph/9908031.
16. E. B. Davies, Quantum Theory of Open Systems (Academic Press, London, 1976).
17. P. A. M. Dirac, Lectures on Quantum Field Theory. Belfer Grad. School of Sci. New York (1966).
18. M. Drieschner, Voraussage - Wahrscheinlichkeit - Objekt. Über die begrifflichen Grundlagen der Quantenmechanik. Lecture Notes in Physics (Springer, Berlin, 1979).
19. P. H. Eberhard, Bell's theorem without hidden variables, Il Nuovo Cimento 38B, 75 (1977).
20. A. Einstein, Conversation with Bohr and Ehrenfest at the Fifth Solvay conference in October, 1927; cf. http://www.mat.univie.ac.at/~neum/contrib/dice.txt The formulation used is from a letter of September 7, 1944, reprinted pp. 275-276 in: A. P. French (ed.), Einstein, A Centenary Volume (Harvard Univ. Press, Cambridge, Mass, 1979).
21. A. Einstein, Conversation with Bohr and Ehrenfest at the Fifth Solvay conference in October, 1927; cf. http://www.mat.univie.ac.at/~neum/contrib/dice.txt The formulation used is from a letter of September 7, 1944, reprinted pp. 275-276 in: A. P. French (ed.), Einstein, A Centenary Volume (Harvard Univ. Press, Cambridge, Mass, 1979).
22. A. Einstein, Einleitende Bemerkungen über Grundbegriffe, in: Louis de Broglie, Physicien et Penseur (A. George, ed.), Albin Michel, Paris 1953. Quoted after Ref. 23, p. 407.
23. A. Einstein, B. Podolsky and N. Rosen, Can the quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935). (Reprinted in Ref. 82.)
24. B. d'Espagnat, Veiled Reality. An Analysis of Present-Day Quantum Mechanical Concepts (Addison-Wesley, Reading, Mass. 1995).
25. T. L. Fine, Theory of Probability; An Examination of Foundations (Acad. Press, New York, 1973).
26. L. L. Foldy and S. A. Wouthuysen, On the Dirac theory of spin 1/2 particles and its non-relativistic limit, Phys. Rev. 78, 29 (1950).
27. D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin, 1996).
28. D. M. Greenberger, M. A. Horne, A. Shimony and A. Zeilinger, Bell's theorem without inequalities, Amer. J. Phys. 58, 1131 (1990).
29. D. M. Greenberger, M. A. Horne and A. Zeilinger, Going beyond Bell's theorem, in: M. Kafatos (ed.), Bell's Theorem, Quantum Theory, and Conceptions of the Universe (Kluwer, Dordrecht, 1989), pp. 73-76.
30. I. Hacking, The Emergence of Probability (Cambridge Univ. Press, Cambridge, 1975).
31. L. Hardy, Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories, Phys. Rev. Lett. 68, 2981 (1992).
32. L. Hardy, Nonlocality for two particles without inequalities for almost all entangled states, Phys. Rev. Lett. 71, 1665 (1993).
33. W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Zeitschrift f. Physik 43, 172 (1927), (Engl. translation: Section 1.3 in Ref. 82.)
34. N. J. Higham, Accuracy and stability of numerical algorithms, SIAM, Philadelphia 1996.
35. R. Hoffmann, V. I. Minkin and B. K. Carpenter, Ockham's Razor and Chemistry, HYLE Int. J. Phil. Chem. 3, 3 (1997) http://rz70.rz.uni-karlsruhe.de/ed01/Hyle/Hyle3/hoffman.htm
36. P. R. Holland, The quantum theory of motion (Cambridge Univ. Press, Cambridge, 1993).
37. D. Home and M. A. B. Whitaker, Ensemble interpretations of quantum mechanics. A modern perspective, Phys. Rep. 210, 223 (1992).
38. Isaiah 55:9, Holy Bible, New International Version (1984).
39. Isaiah 65:24, Holy Bible, New International Version (1984).
40. M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, 1966).
41. M. Jammer, The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective (Wiley, New York, 1974).
42. J. M. Jauch, Foundations of Quantum Mechanics (Addison-Wesley, Reading, MA, 1968).
43. B. D. Keister and W. N. Polyzou, Relativistic Hamiltonian dynamics in nuclear and particle physics, Advances in Nuclear Physics 20, 226 (1991).
44. J. R. Klauder, Coherent states in action (1997), quant-ph/9710029
45. S. Kochen and E.P. Specker, The problem of hidden variables in quantum mechanics, J. Math. Mech. 17, 59 (1967). (Reprinted in C.A. Hooker, ed. The logico-algebraic approach to quantum mechanics, Vol. I: Historical evolution (Reidel, Dordrecht, 1975.))
46. S. Kochen and E.P. Specker, The problem of hidden variables in quantum mechanics, J. Math. Mech. 17, 59 (1967). (Reprinted in C.A. Hooker, ed. The logico-algebraic approach to quantum mechanics, Vol. I: Historical evolution (Reidel, Dordrecht, 1975.))
47. Kohelet, Ecclesiastes 11:6, in: Holy Bible, New International Version (1984).
48. A. N. Kolmogorov, Foundations of the Theory of Probability (Chelsea, New York, 1950.) [German original: Grundbegriffe der Wahrscheinlichkeitsrechnung (Springer, Berlin 1933.)]
49. A. N. Kolmogorov, Foundations of the Theory of Probability (Chelsea, New York, 1950.) [German original: Grundbegriffe der Wahrscheinlichkeitsrechnung (Springer, Berlin 1933.)]
50. H. Margenau, The Nature of Physical Reality (McGraw-Hill, New York, 1950).
51. D. Marolf and C. Rovelli, Relativistic quantum measurement, Phys. Rev. D66, 023510 (2002). gr-qc/0203056
52. J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry (Springer, New York, 1994).
53. N. D. Mermin, Simple unified form for the major no-hidden-variables theorems, Phys. Rev. Lett. 65, 3373 (1990).
54. N. D. Mermin, What's wrong with these elements of reality? Physics Today (June 1990), 9-10.
55. A. Messiah, Quantum Mechanics, Vol. 1 (North-Holland, Amsterdam, 1991); Vol. 2 (North-Holland, Amsterdam, 1976).
56. A. Messiah, Quantum Mechanics, Vol. 1 (North-Holland, Amsterdam, 1991); Vol. 2 (North-Holland, Amsterdam, 1976).
57. P. Mittelstaedt, The Interpretation of Quantum Mechanics and the Measurement Process (Cambridge Univ. Press, Cambridge, 1998).
58. P.-A. Meyer, Quantum Probability for Probabilists, 2nd. ed. (Springer, Berlin, 1995).
59. A. Neumaier, Molecular modeling of proteins and mathematical prediction of protein structure, SIAM Rev. 39, 407 (1997).
60. A. Neumaier, Fuzzy modeling in terms of surprise, Fuzzy Sets and Systems, 135, 21 (2003)
61. A. Neumaier, Quantum Field Theory as Eigenvalue Problem, (2003), gr-gc/0303037
62. J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932).
63. T. D. Newton and E. P. Wigner, Localized states for elementary systems, Rev. Mod. Phys. 21, 400 (1949).
64. W. of Ockham, Philosophical Writings, ed. by P. Boehner (Nelson, Edinburgh, 1957).
65. K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus (Birkhäuser, Basel, 1992).
66. St. Paul, 1 Corinthian 13:8-10, in: The New Testament. This is my paraphrase of a famous quote by Paul; for other renderings, see e.g. http://www.mat.univie.ac.at/~neum/christ/contrib/1cor13.html
67. St. Paul, 1 Timothy 6:8, in: Holy Bible, New International Version (1984).
68. A. Peres, In compatible results of quantum measurements, Physics Lett. A151, 107 (1990).
69. A. Peres, Two simple proofs of the Kochen-Specker theorem, J. Phys. A: Math. Gen. 24, L175 (1991).
70. A. Peres, Quantum theory: Concepts and methods, (Kluwer, Dordrecht, 1993).
71. I. Pitowsky, Quantum Probability - Quantum Logic, Lecture Notes in Physics 321 (Springer, Berlin, 1989).
72. Plato, Timaeus, Hackett Publishing, Indianapolis 1999. The quotes (Tim. 28-29) are from the Project Gutenberg Etext at ftp://metalab.unc.edu/pub/docs/books/gutenberg/etext98/tmeus11.txt (the first half of the document is a commentary, then follows the original in English translation)
73. C. E. Rickart, General Theory of Banach Algebras (Van Nostrand, Princeton, 1960).
74. H. P. Robertson, The uncertainty principle, Phys. Rev. 34, 163 (1929) (Reprinted in Ref. 82.)
75. T. Roubicek, Relaxation in Optimization Theory and Variational Calculus (Walter de Gruyter, Berlin, 1997).
76. E. Schrödinger, Die gegenwärtige Situation in der Quantenmechanik, Naturwissenschaften 23, 807, 823, 844 (1935). (Engl. translation: Section 1.11 in Ref. 82.)
77. L. Sklar, Physics and Chance (Cambridge Univ. Press, Cambridge, 1993).
78. King Solomon, Proverbs 16:3, in: Holy Bible, New International Version, 1984.
79. M. H. Stone, The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40, 37 (1936).
80. K. Svozil, Quantum Logic (Springer, Berlin, 1998).
81. B. N. Taylor, Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 1995 edition http://physics.nist.gov/cuu/Uaits/introduction.html
82. W. Tittel, J. Brendel, B. Gisin, T. Herzog, H. Zbinden and N. Gisin, Experimental demonstration of quantum-correlations over more than 10 kilometers, Phys. Rev. A57, 3229 (1998).
83. L. Vaidman, Variations on the theme of the Greenberger-Horne-Zeilinger proof, Found. Phys. 29, 615 (1999).
84. I. Vaisman, Lectures on the Geometry of Poisson Manifolds (Birkhäuser, Basel, 1994).
85. J. A. Wheeler, Delayed-choice experiments and the Bohr-Einstein dialogue, reprinted in: Law Without Law, pp. 182-213 of Ref. 82.
86. J. A. Wheeler and W. H. Zurek, Quantum Theory and Measurement (Princeton Univ. Press, Princeton, 1983).
87. P. Whittle, Probability via expectation, 3rd ed. (Springer, New York, 1992). (1st ed.: Probability, Harmondsworth, 1970.)
88. E. P. Wigner, The unreasonable effectiveness of mathematics in the natural sciences, Comm. Pure Appl. Math. 13, 1 (1960).
89. Book of Wisdom 11:20, The Holy Bible, New Revised Standard Version, 1989.
90. W. K. Wootters and W. H. Zurek, Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr's principle, Phys. Rev. D19, 473 (1979). (Reprinted in Ref. 82.)
91. H.-J. Zimmermann, Fuzzy Set Theory - and its Applications, 3rd ed. (Kluwer, Dordrecht, 1996).