×

Everettian probabilities, the Deutsch-Wallace theorem and the principal principle. (English) Zbl 1498.81045

Hemmo, Meir (ed.) et al., Quantum, probability, logic. The work and influence of Itamar Pitowsky. Cham: Springer. Jerus. Stud. Philos. Hist. Sci., 165-198 (2020).
Summary: This paper is concerned with the nature of probability in physics, and in quantum mechanics in particular. It starts with a brief discussion of the evolution of Itamar Pitowsky’s thinking about probability in quantum theory from 1994 to 2008, and the role of Gleason’s 1957 theorem in his derivation of the Born Rule. Pitowsky’s defence of probability therein as a logic of partial belief leads us into a broader discussion of probability in physics, in which the existence of objective “chances” is questioned, and the status of David Lewis influential Principal Principle is critically examined. This is followed by a sketch of the work by David Deutsch and David Wallace which resulted in the Deutsch-Wallace (DW) theorem in Everettian quantum mechanics. It is noteworthy that the authors of this important decision-theoretic derivation of the Born Rule have different views concerning the meaning of probability. The theorem, which was the subject of a 2007 critique by Meir Hemmo and Pitowsky, is critically examined, along with recent related work by John Earman. Here our main argument is that the DW theorem does not provide a justification of the Principal Principle, contrary to the claims by Wallace and Simon Saunders. A final section analyses recent claims to the effect that the DW theorem is redundant, a conclusion that seems to be reinforced by consideration of probabilities in “deviant” branches of the Everettian multiverse.
For the entire collection see [Zbl 1445.00001].

MSC:

81P16 Quantum state spaces, operational and probabilistic concepts
60A05 Axioms; other general questions in probability
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Albrecht, A., & Phillips D. (2014). Origin of probabilities and their application to the multiverse. Physical Review D, 90, 123514. · doi:10.1103/PhysRevD.90.123514
[2] Bacciagaluppi, G., & Ismael, J. (2015). Essay review: The emergent multiverse. Philosophy of Science, 82, 1-20. · doi:10.1086/679037
[3] Bacciagaluppi, G. (2020). Unscrambling subjective and epistemic probabilities. This volume, http://philsci-archive.pitt.edu/16393/1/probability · Zbl 1498.81013 · doi:10.1007/978-3-030-34316-3_3
[4] Barnum, H. (2003). No-signalling-based version of Zurek’s derivation of quantum probabilities: A note on “environment-assisted invariance, entanglement, and probabilities in quantum physics”. quant-ph/0312150.
[5] Bé, M. M., & Chechev, V. P. (2012).^14C - Comments on evaluation of decay data. www.nucleide.org/DDEP_WG/Nucleides/C-14_com.pdf. Accessed 01 June 2019.
[6] Bell, J. S. (1966). On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics, 38, 447-452. · Zbl 0152.23605 · doi:10.1103/RevModPhys.38.447
[7] Bricmont, J. (2001). Bayes, Boltzmann and Bohm: Probabilities in physics. In J. Bricmont, D. Dürr, M. C. Galavotti, G. Ghirardi, F. Petruccione, & N. Zangi (Eds.), Chance in physics. Foundations and perspectives. Berlin/Heidelberg/New York: Springer.
[8] Brown, H. R. (2011). Curious and sublime: The connection between uncertainty and probability in physics. Philosophical Transactions of the Royal Society, 369, 1-15. https://doi.org/10.1098/rsta.2011.0075 · doi:10.1098/rsta.2011.0075
[9] Brown, H. R. (2017). Once and for all; The curious role of probability in the Past Hypothesis. http://philsci-archive.pitt.edu/id/eprint/13008. Forthcoming In D. Bedingham, O. Maroney, & C. Timpson (Eds.). (2020). The quantum foundations of statistical mechanics. Oxford: Oxford University Press.
[10] Brown, H. R. (2019). The reality of the wavefunction: Old arguments and new. In A. Cordero (Ed.), Philosophers look at quantum mechanics (Synthese Library 406, pp. 63-86). Springer. http://philsci-archive.pitt.edu/id/eprint/12978
[11] Brown, H. R., & Svetlichny, G. (1990). Nonlocality and Gleason’s Lemma. Part I. Deterministic theories. Foundations of Physics, 20, 1379-1387. · doi:10.1007/BF01883492
[12] Busch, P. (2003). Quantum states and generalized observables: A simple proof of Gleasons theorem. Physical Review Letters, 91, 120403. · doi:10.1103/PhysRevLett.91.120403
[13] Dawid, R., & Thébault, K. (2014). Against the empirical viability of the Deutsch-Wallace-Everett approach to quantum mechanics. Studies in History and Philosophy of Modern Physics, 47, 55-61. · Zbl 1294.81014 · doi:10.1016/j.shpsb.2014.05.005
[14] de Finetti, B. (1964). Foresight: Its logical laws, its subjective sources. English translation. In: J. E. Kyburg & H. E. Smokler (Eds.), Studies in subjective probability (pp. 93-158). New York: Wiley.
[15] Deutsch, D. (1999). Quantum theory of probability and decisions. Proceedings of the Royal Society of London, A455, 3129-3137. · Zbl 0964.81003
[16] Deutsch, D. (2016). The logic of experimental tests, particularly of Everettian quantum theory. Studies in History and Philosophy of Modern Physics, 55, 24-33. · Zbl 1348.81038 · doi:10.1016/j.shpsb.2016.06.001
[17] Earman, J. (2018) The relation between credence and chance: Lewis’ “Principal Principle” is a theorem of quantum probability theory. http://philsci-archive.pitt.edu/14822/
[18] Feynman, R. P., Leighton, R. B., & Matthew Sands, M. (1965). The Feynman lectures on physics (Vol. 1). Reading: Addison-Wesley. · Zbl 0131.38703
[19] Gillies, D. (1972). The subjective theory of probability. British Journal for the Philosophy of Science, 23(2), 138-157. · doi:10.1093/bjps/23.2.138
[20] Gillies, D. (1973). An objective theory of probability. London: Methuen & Co.
[21] Gillies, D. (2000). Philosophical theories of probability. London: Routledge.
[22] Galavotti, M. C. (1989). Anti-realism in the philosophy of probability: Bruno de Finetti’s Subjectivism. Erkenntnis, 31, 239-261. · doi:10.1007/BF01236565
[23] Gleason, A. (1957). Measures on the closed subspaces of a Hilbert space. Journal of Mathematics and Mechanics, 6, 885-894. · Zbl 0078.28803
[24] Greaves, H., & Myrvold, W. (2010). Everett and evidence. In S. Saunders, J. Barrett, A. Kent, & D. Wallace (Eds.), Many worlds? Everett, quantum theory, and reality (pp. 264-304). Oxford: Oxford University Press. http://philsci-archive.pitt.edu/archive/0004222 · doi:10.1093/acprof:oso/9780199560561.003.0011
[25] Hacking, I. (1984). The emergence of probability. Cambridge: Cambridge University Press. · Zbl 1067.01544
[26] Hall, N. (2004). Two mistakes about credence and chance. Australasian Journal of Philosophy, 82, 93-111. · doi:10.1080/713659806
[27] Handfield, T. (2012). A philosophical guide to chance. Cambridge: Cambridge University Press. · doi:10.1017/CBO9781139012096
[28] Harari, Y. N. (2014). Sapiens. A brief history of humankind. London: Harvill-Secker.
[29] Hemmo, M., & Pitowsky, I. (2007). Quantum probability and many worlds. Studies in History and Philosophy of Modern Physics, 38, 333-350. · Zbl 1223.81031 · doi:10.1016/j.shpsb.2006.04.005
[30] Hoefer, C. (2019). Chance in the world: A Humean guide to objective chance. (Oxford Studies in Philosophy of Science). Oxford, Oxford University Press, 2019. · Zbl 1430.00001
[31] Hume, D. (2008). An enquiry concerning human understanding. Oxford: Oxford University Press.
[32] Ismael, J. (1996). What chances could not be. British Journal for the Philosophy of Science, 47(1), 79-91. · doi:10.1093/bjps/47.1.79
[33] Ismael, J. (2019, forthcoming). On Chance (or, Why I am only Half-Humean). In S. Dasgupta (Ed.), Current controversies in philosophy of science. London: Routledge.
[34] Jaynes, E. T. (1963). Information theory and statistical mechanics. In: G. E. Uhlenbeck et al. (Eds.), Statistical physics. (1962 Brandeis lectures in theoretical physics, Vol. 3, pp. 181-218). New York: W.A. Benjamin.
[35] Kochen, S., & Specker, E. P. (1967). The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 17, 59-87. · Zbl 0156.23302
[36] Lewis, D. (1980). A subjectivist’s guide to objective chance. In: R. C. Jeffrey (Ed.), Studies in inductive logic and probability (Vol. 2, pp. 263-293). University of California Press (1980). Reprinted in: Lewis, D. Philosophical papers (Vol. 2, pp. 83-132). Oxford: Oxford University Press.
[37] Maris, J. P, Navrátil, P., Ormand, W. E., Nam, H., & Dean, D. J. (2011). Origin of the anomalous long lifetime of^14C. Physical Review Letters, 106, 202502. · doi:10.1103/PhysRevLett.106.202502
[38] Maudlin, T. (2007). What could be objective about probabilities? Studies in History and Philosophy of Modern Physics, 38, 275-291. · Zbl 1223.60004 · doi:10.1016/j.shpsb.2006.04.006
[39] McQueen, K. J., & Vaidman, L. (2019). In defence of the self-location uncertainty account of probability in the many-worlds interpretation. Studies in History and Philosophy of Modern Physics, 66, 14-23. · Zbl 1414.81030 · doi:10.1016/j.shpsb.2018.10.003
[40] Myrvold, W. C. (2016). Probabilities in statistical mechanics, In C. Hitchcock & A. Hájek (Eds.), Oxford handbook of probability and philosophy. Oxford: Oxford University Press. Available at http://philsci-archive.pitt.edu/9957/ · Zbl 1345.60001
[41] Page, D. N. (1994). Clock time and entropy. In J. J. Halliwell, J. Pérez-Mercader, & W. H. Zurek (Eds.), The physical origins of time asymmetry, (pp. 287-298). Cambridge: Cambridge University Press.
[42] Page, D. N. (1995). Sensible quantum mechanics: Are probabilities only in the mind? arXiv:gr-qc/950702v1.
[43] Papineau, D. (1996). Many minds are no worse than one. British Journal for the Philosophy of Science, 47(2), 233-241. · doi:10.1093/bjps/47.2.233
[44] Pattie, R. W. Jr., et al. (2018). Measurement of the neutron lifetime using a magneto-gravitational trap and in situ detection. Science, 360, 627-632. · doi:10.1126/science.aan8895
[45] Pitowsky, I. (1994). George Boole’s ‘conditions of possible experience’ and the quantum puzzle. British Journal for the Philosophy of Science, 45(1), 95-125. · doi:10.1093/bjps/45.1.95
[46] Pitowsky, I. (2006). Quantum mechanics as a theory of probability. In W. Demopoulos & I. Pitowsky (Eds.), Physical theory and its interpretation (pp. 213-240). Springer. arXiv:quant-phys/0510095v1.
[47] Read, J. (2018). In defence of Everettian decision theory. Studies in History and Philosophy of Modern Physics, 63, 136-140. · Zbl 1395.81014 · doi:10.1016/j.shpsb.2018.01.005
[48] Saunders, S. (2005). What is probability? In A. Elitzur, S. Dolev, & N. Kolenda (Eds.), Quo vadis quantum mechanics? (pp. 209-238). Berlin: Springer. · Zbl 1092.81003 · doi:10.1007/3-540-26669-0_12
[49] Saunders, S. (2010). Chance in the Everett interpretation. In S. Saunders, J. Barrett, A. Kent, & D. Wallace (Eds.), Many worlds? Everett, quantum theory, and reality (pp. 181-205). Oxford: Oxford University Press. · doi:10.1093/acprof:oso/9780199560561.003.0008
[50] Saunders, S. (2020), The Everett interpretation: Probability. To appear in E. Knox & A. Wilson (Eds.), Routledge Companion to the Philosophy of Physics. London: Routledge.
[51] Skyrms, B. (1984). Pragmatism and empiricism. New Haven: Yale University Press.
[52] Strevens, M. (1999). Objective probability as a guide to the world, philosophical studies. An International Journal for Philosophy in the Analytic Tradition, 95(3), 243-275. · doi:10.1023/A:1004256510606
[53] Svetlichny, G. (1998). Quantum formalism with state-collapse and superluminal communication. Foundations of Physics, 28(2), 131-155. · doi:10.1023/A:1018726717481
[54] Timpson, C. (2011). Probabilities in realist views of quantum mechanics, chapter 6. In C. Beisbart & S. Hartmann (Eds.), Probabilities in physics. Oxford: Oxford University Press.
[55] Tipler, F. J. (2014). Quantum nonlocality does not exist. Proceedings of the National Academy of Sciences, 111(31), 11281-11286. · Zbl 1355.81019 · doi:10.1073/pnas.1324238111
[56] Vaidman, L. (2020). Derivations of the Born Rule. This volume, http://philsci-archive.pitt.edu/15943/1/BornRule24-4-19.pdf · Zbl 1498.81047 · doi:10.1007/978-3-030-34316-3_26
[57] Wallace, D. (2002). Quantum probability and decision theory, Revisited, arXiv:quant-ph/0211104v1.
[58] Wallace, D. (2003). Everettian rationality: Defending Deutsch’s approach to probability in the Everett interpretation. Studies in History and Philosophy of Modern Physics, 34, 415-439. · Zbl 1222.81090 · doi:10.1016/S1355-2198(03)00036-4
[59] Wallace, D. (2010). How to prove the born rule. In: S. Saunders, J. Barrett, A. Kent, & D. Wallace (Eds.), Many worlds? Everett, quantum theory, and reality (pp. 227-263). Oxford: Oxford University Press. · doi:10.1093/acprof:oso/9780199560561.003.0010
[60] Wallace, D. (2012). The emergent universe. Quantum theory according to the Everett interpretation. Oxford: Oxford University Press. · Zbl 1272.81003
[61] Wallace, D. (2014). Probability in physics: Statistical, stochastic, quantum. In A. Wilson (Ed.), Chance and temporal asymmetry (pp. 194-220). Oxford: Oxford University Press. http://philsci-archive.pitt.edu/9815/1/wilson.pdf
[62] Wright, V. · Zbl 1422.81024 · doi:10.1088/1751-8121/aaf93d
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.