Macroscopic observables and the born rule, I. Long run frequencies

Reviews in Mathematical Physics

Volumn 20, Issue 10, 2008, Pages 1173-1190

  Landsman, N P ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

algebras; Born rule; C; Quantum theory

Indexed keywords

EID: 56749178083     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X08003511     Document Type: Article

References (51)

1. N. Bohr, Discussion with Einstein on epistemological problems in atomic physics, in Albert Einstein: Philosopher-Scientist, ed. P. A. Schilpp (Open Court, La Salle, 1949), pp. 201-241.
2. M. Born, Quantenmechanik der Stolzvorgänge, Z. Phys. 38 (1926) 819-827.
3. O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics, Vol. II: Equilibrium States, Models in Statistical Mechanics (Springer,Berlin, 1981).
4. J. Bub, Interpreting the Quantum World. (Cambridge University Press, Cambridge, 1999).
5. S. Bugajski and Z. Motyka, Generalized Borel law and quantum probabilities, Int. J. Theor. Physics 20 (1981) 262-268.
6. A. Cassinello and J. L. Sánchez-Gòmez, On the probabilistic postulate of quantum mechanics, Found. Phys. 26 (1996) 1357-1374.
7. C. Caves and R. Schack, Properties of the frequency operator do not imply the quantum probability postulate, Ann. Phys. (N.Y.) 315 (2005) 123-146.
8. M. Dickson, Non-relativistic quantum mechanics, in Handbook of the Philosophy of Science, Vol. 2: Philosophy of Physics, eds. J. Butterfield and J. Earman (North-Holland, Elsevier, Amsterdam 2007), pp. 275-415.
9. P. A. M. Dirac, The Principles of Quantum Mechanics (Clarendon Press, Oxford, 1930).
10. J. Dixmier, C*-Algebras (North-Holland, Amsterdam, 1977).
11. N. G. Duffield and R. F. Werner, Local dynamics of mean-field quantum systems, Helv. Phys. Acta 65 (1992) 1016-1054.
12. A. Einstein and M. Born, Briefwechsel 1916-1955 (Langen Müllier, München, 2005).
13. E. M. R. A. Engel, A Road to Randomness in Physical Systems, Lecture Notes in Statistics, Vol. 71 (Springer-Verlag, Berlin, 1992).
14. D. E. Evans and Y. Kawahigashi, Quantum Symmetries on Operator Algebras (Oxford University Press, Oxford, 1998).
15. E. Farhi, J. Goldstone and S. Gutmann, How probability arises in quantum mechanics, Ann. Phys. (N.Y.) 192 (1989) 368-382.
16. T. L. Fine, Theories of Probability (Academic Press, New York, 1978).
17. D. Finkelstein, The logic of quantum physics, Trans. New York Acad. Sci. 25 (1965) 621-637.
18. D. Gillies, Philosophical Theories of Probability (Cambridge University Press, Cambridge, 2000).
19. R. Haag, Local, Quantum Physics: Fields, Particles, Algebras (Springer-Verlag, Heidelberg, 1992).
20. A, Hájek, Interpretations of probability, in The Stanford Encyclopedia of Philosophy, ed. E. N, Zalta (The Metaphysics Research Lab, summer 2003) (electronic); http://www.science.uva.nl/∼seop/ entries/ probability-interpret/.
21. J. B. Hartle, Quantum mechanics of individual systems, Am. J, Phys. 36 (1968) 704-712.
22. W. Heisenberg, Physics and Philosophy: The Revolution in Modern Science (Allen and Unwin, London, 1958).
23. K. Hepp, Quantum theory of measurement and macroscopic observables, Helv. Phys. Acta 45 (1972) 237-248.
24. C. Heunen, N. P. Landsman and B. Spitters, A topos for algebraic quantum theory, arXiv:Q7Q9.4364v2.
25. G. 't Hooft, The mathematical basis for deterministic quantum mechanics, arxiv: quant-ph/0604008,
26. D. Howard, What makes a classical concept classical? Towards a reconstruction of Niels Bohr's philosophy of physics, in Niels Bohr and Contemporary Philosophy, eds. J. Faye and H. Folse (Kluwer Academic Publishers, Dordrecht, 1994), pp. 201-229.
27. D. Howard, Who invented the Copenhagen Interpretation? Philos. Sci. 71 (2004) 669-682.
28. R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. 2: Advanced Theory (Academic Press, New York, 1986).
29. E. Kirchberg and S. Wassermann, Operations on continuous bundles of C*-algebras, Math. Ann. 303 (1995) 677-697.
30. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-R,elativistic Theory, 3rd edn. (Pergamon Press, Oxford, 1977).
31. N. P. Landsman, Mathematical Topics Between Classical and Quantum Mechanics (Springer-Verlag, New York, 1998).
32. N. P. Landsman, Between classical and quantum, in Handbook of the Philosophy of Science, Vol. 2: Philosophy of Physics, eds. J. Butterfield and J. Earman (North-Holland, Elsevier, Amsterdam 2007), pp. 417-554.
33. J. Mehra and H. Rechenberg, The Historical Development of Quantum Theory, Vol. 6: The Completion of Quantum Mechanics 1926-1941. Part 1: The Probabilistic Interpretation and the Empirical and Mathematical Foundation of Quantum Mechanics. 1926-1936 (Springer-Verlag, New York, 2000).
34. D. H. Mellor, Probability: A Philosophical Introduction (R.outledge, London, 2005).
35. G. Morchio and F. Strocchi, Mathematical structures for long-range dynamics and symmetry breaking, J. Math. Phys. 28(1987) 622-635.
36. J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer-Verlag, Berlin, 1932); English translation: Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, 1955).
37. J. von Neumann, On infinite direct products, Compos. Math. 6 (1938) 1-77.
38. W. Ochs, On the strong law of large numbers in quantum probability theory, J. Philos. Logic 6 (1977) 473-480.
39. W. Pauli, Über Gasentartung und Paramagnetismus, Z. Phys. 41 (1927) 81-102.
40. J. von Plato, Creating Modern Probability (Cambridge University Press, Cambridge, 1994).
41. G. A. Raggio and R, F. Werner, Quantum statistical mechanics of general mean field systems, Helv. Phys. Acta 62 (1989) 980-1003.
42. S. Saunders, Derivation of the Born rule from operational assumptions, Proc. Boy. Soc. Lond. A 460 (2004) 1771-1788.
43. E. Scheibe, The Logical Analysis of Quantum Mechanics (Pergamon Press, Oxford, 1973).
44. M. Schlosshauer and K. Camilleri, The quantum-to-classical transition: Bohr's doctrine of classical concepts, emergent classicality, and decoherence, arxiv:0804.1609v1.
45. G. L. Sewell, Quantum Mechanics and its Emergent Macrophysics (Princeton University Press, Princeton, 2002).
46. E. Størmer, Symmetric states of infinite tensor products of C*-algebras, J. Funct. Anal. 3 (1969) 48-68.
47. W. Thirring, A Course in Mathematical Physics. Vol. 4: Quantum Mechanics of Large Systems (Springer-Verlag, New York, 1983).
48. T. Unnerstall, Phase-spaces and dynamical descriptions of infinite mean-field quantum systems, J. Math. Phys. 31 (1990) 680-688.
49. T. Unnerstall, Schrödinger dynamics and physical folia of infinite mean-field quantum systems, Comm. Math. Phys. 130 (1990) 237-255.
50. R. A. Van Wesep, Many worlds and the appearance of probability in quantum mechanics, Ann. Phys. (N. Y.) 321 (2006) 2438-2452.
51. D. Wallace, Everettian Rationality: Defending Deutsch's approach to probability in the Everett interpretation, Stud. Hist. Phil. Mod. Phys. 34 (2003) 415-438.