Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
[1] Ghirardi, G.C., Rimini, A., and Weber, T. Unified dynamics for microscopic and macroscopic systems. Physical Review D 34, 470 (1984).
[2] Bohm, D. and Hiley, B.J. The Undivided Universe: An ontological interpretation of quantum theory. London: Routledge (1993).
[3] Bell, J. S. Speakable and Unspeakable in Quantum Mechanics Cambridge: Cambridge University Press.
[4] Ramsey, F.P. Truth and Probability. (1926) reprinted In D. H. Mellor (ed) F. P. Ramsey: Philosophical Papers. Cambridge: Cambridge University Press (1990).
[5] Savage, L.J. The Foundations of Statistics. London: John Wiley and Sons (1954).
[6] Feynman, R. P. The concept of probability in quantum mechanics. Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, Berkeley: University of California Press, 553 (1951).
[7] Feynman, R. P. and Hibbs, A. R. Quantum Mechanics and Path Integrals New York: McGraw-Hill (1965).
[8] Pitowsky , I. George Boole’s “conditions of possible experience” and the quantum puzzle. British Journal for the Philosophy of Science 45, 95–125 (1994).
[9] Weinberg, S. Gravitation and cosmology: Principles and Applications of the General Theory of Relativity, New York: John Wiley & Sons (1972).
[10] Pitowsky, I. Unified field theory and the conventionality of geometry. Philosophy of Science 51, 685–689 (1984).
[11] Ben Menahem Conventionalism, Cambridge: Cambridge University Press (2005).
[12] Bub, J. The Interpretation of Quantum Mechanics. Dordrecht: Reidel (1974).
[13] Bub, J. Quantum Mechanics is About Quantum Information, Foundations of Physics 35, 541 (2005).
[14] Barnum, H. Caves, C. M. Finkelstein, J. Fuchs, C. A., and Schack, R. Quantum probability from decision theory? Proceedings of the Royal Society of London A 456, 1175 (2000).
[15] Pitowsky, I. Betting on the outcomes of measurements: A Bayesian theory of quantum probability Studies in the History and Philosophy of Modern Physics 34, 395 (2003).
[16] Stairs, A. Kipske, Tupman and quantum logic: the quantum logician’s conundrum. This volume.
[17] Deutsch, D. Quantum theory of probability and decisions, Proceedings of the Royal Society of London A455, 3129 (1999).
[18] Wallace, D. Everettian Rationality: defending Deutsch’s approach to probability in the Everett interpretation. Studies in the History and Philosophy of Modern Physics 34, 415 (2003).
[19] Birkhoff, G. and von Neumann, J. The logic of quantum mechanics. Annals of Mathematics 37, 823 (1936).
[20] Finkelstein, D. Logic of quantum physics. Transactions of the New York Academy of Science 25, 621 (1963).
[21] Putnam. H., The logic of quantum mechanics. (1968) reprinted inMathematics Matter and Method — Philosophical Papers Volume1. Cambridge: Cambridge University Press (1975).
[22] Pitowsky, I. Quantum Probability, Quantum Logic, Lecture Notes in Physics 321, Heidelberg: Springer (1989).
[23] Rédei, M. Why John von Neumann did not like the Hilbert space formalism of quantum mechanics (and what he liked instead). Studies in the History and Philosophy of Modern Physics 27, 493 (1996).
[24] Solovay, R. M. A model of set-theory in which every set of reals is Lebesgue measurable. Annals of Mathematics 92, 1 (1970).
[25] Young, W. J. Projective Geometry Chicago: Open Court (1930).
[26] Artin, E. Geometric Algebra New York: John Wiley & Sons (1957).
[27] Solèr, M. P. Characterization of Hilbert spaces with orthomodular spaces Communications in Algebra 23, 219 (1995).
[28] Holland, S. S. Orthomodularity in infinite dimensions; a theorem of M. Solèr. Bulletin of the American Mathematical Society 32, 205 (1995).
[29] Gleason, A. M. Measures on the closed subspaces of a Hilbert space. Journal of Mathematics and Mechanics 6, 885–893 (1957).
[30] Gödel, K. What is Cantor’s continuum problem? in Feferman, S. (ed.) Kurt Gödel’s collected Papers, Vol II Oxford: Oxford University Press (1990).
[31] Kochen, S. and Specker, E. P. The problem of hidden variables in muantum Mechanics. Journal of Mathematics and Mechanics 17, 59–87 (1967).
[32] Pitowsky, I. Infinite and finite Gleason’s theorems and the logic of indeterminacy. Journal of Mathematical Physics 39, 218 (1998).
[33] Hrushovski, E. and Pitowsky, I. Generalizations of Kochen and Specker’s Theorem and the Effectiveness of Gleason’s Theorem. Studies in the History and Philosophy of Modern Physics 35, 177 (2004).
[34] Clauser, J.F., Horne, M. A., Shimony, A., and Holt, R. A. Proposed experiment to test local hiddenvariable theories. Physical Review Letters 23, 880 (1969).
[35] Fine, A. Hidden variables, joint probability and Bell inequalities. Physical Review Letters 48, 291 (1982).
[36] Pitowsky, I. and Svozil, K. New Optimal tests of quantum nonlocality. Physical Review A 64, 4102 (2001).
[37] Boole, G. On the theory of probabilities. Philosophical Transactions of the Royal Society of London 152, 225 (1862).
[38] Boole, G. The laws of Thought New York: Dover, 1958 (first published in 1854).
[39] Wigner, E. P. Group Theory and its Applications to Quantum Mechanics of Atomic Spectra. New York: Academic Press (1959).
[40] Uhlhorn, U. Representation of symmetry transformations in quantum mechanics. Arkiv Fysik 23, 307 (1963).
[41] Mermin, N. D. Extreme quantum entanglement in a superposition of macroscopically distinct states Physical Review Letters. 65, 1838 (1990).
[42] Werner, R. F. and Wolf, M. All multipartite Bell correlation inequalities for two dichotomic observables per site. Physical Review A 64, 032112 (2001).
[43] Zukowski M. and Brukner C. Bell’s theorem for general N-qubit states. Physical Review. Letters 88, 210401 (2002).
[44] Pitowsky, I. Macroscopic objects in quantum mechanics-A combinatorial approach. Physical Review A 70, 022103 (2004).
[45] Brukner, C. and Vedral, V. Macroscopic thermodynamical witnesses of quantum entanglement quant-ph/0406040 (2004).
[46] Ben Menahem, Y. Realism and quantum mechanics in A. van der Merve (ed): Microphysical Reality and Quantum Formalism Dordrecht: Kluwer, (1988).
[47] Demopoulos, W. Elementary propositions and essentially incomplete knowledge: A framework for the interpretation of quantum mechanics Noûs 38, 86 (2004).
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this chapter
Cite this chapter
Pitowsky, I. (2006). Quantum Mechanics as a Theory of Probability. In: Demopoulos, W., Pitowsky, I. (eds) Physical Theory and its Interpretation. The Western Ontario Series in Philosophy of Science, vol 72. Springer, Dordrecht . https://doi.org/10.1007/1-4020-4876-9_10
Download citation
DOI: https://doi.org/10.1007/1-4020-4876-9_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4875-3
Online ISBN: 978-1-4020-4876-0
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)