Universität zu Köln

Boge, Florian (2016). On Probabilities in the Many Worlds Interpretation of Quantum Mechanics. Bachelor thesis, Universität zu Köln.

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Abstract

Quantum Mechanics notoriously faces a measurement problem, the problem that the unitary time evolution, encoded in its dynamical equations, together with the kinematical structure of the theory generally implies the non-existence of definite measurement outcomes. There have been multiple suggestions to solve this problem, among them the so called many worlds interpretation that originated with the work of Hugh Everett III. According to it, the quantum state and time evolution fully and accurately describe nature as it is, implying that under certain conditions multiple measurement outcomes that are seemingly mutually exclusive can be realized at the same time – but as different 'worlds' contained in a global, quantum mechanical structure, sometimes referred to as 'the multiverse'. The many worlds interpretation has, however, been confronted with serious difficulties over the course of its development, some of which were solved by the advent of decoherence theory. The present thesis critically investi- gates the state of play on a key remaining problem of the many worlds interpretation, the problem of the meaning and quantification of probabilities in a quantum multiverse. Recent attempts of deriving the pivotal statistical ingredient of quantum mechanics, Born’s rule, from either principles of decision theory or from quantum mechanics alone, supplemented with a few general premises about probability are analyzed and their premises are scrutinized. It will be argued that, though both approaches yield promising results, they both ultimately fail to clearly establish the validity of Born’s rule in the context of the many worlds interpretation. It is hence suggested that further research on this problem is indicated.

Item Type:	Thesis (Bachelor thesis)
Creators:	Creators Email ORCID ORCID Put Code Boge, Florian boge@phil.hhu.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-68892
Date:	4 April 2016
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	Philosophy Physics
Uncontrolled Keywords:	Keywords Language Quantum Theory, Everett, Many Worlds, Probability, Born's Rule, Deutsch, Wallace, Zurek UNSPECIFIED
Date of oral exam:	9 May 2016
Referee:	Name Academic Title Klesse, Rochus Dr. Kiefer, Claus Prof. Dr.
References:	[1] David Albert. Probability in the Everett Picture. In Simon Saunders, Jonathan Barrett, Adrian Kent, and David Wallace, editors, Many worlds?: Everett, quantum theory, & reality. OUP Oxford, 2010. [2] David Albert and Barry Loewer. Interpreting the many worlds interpretation. Synthese, 77(2):195–213, 1988. [3] M. Arndt, O. Nairz, J. Petschinka, and A. Zeilinger. High contrast interference with C 60 and C 70 . Comptes Rendus de l’Académie des Sciences-Series IV-Physics, 2(4):581–585, 2001. [4] Alain Aspect. Introduction: John Bell and the second quantum revolution. In J. S. Bell, editor, Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, second edition, 2004. [5] Alain Aspect, Jean Dalibard, and Gérard Roger. Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers. Physical Review Letters, 49(25):1804–1807, 1982. [6] Howard Barnum. No-signalling-based version of zurek’s derivation of quantum probabilities: A note on “environment-assisted invariance, entanglement, and probabilities in quantum physics”. arXiv preprint quant-ph / 0312150, 2003. [7] J.A. Barrett. The Quantum Mechanics of Minds and Worlds. OUP Oxford, 1999. [8] Jeffrey A. Barrett. On the Nature of Measurement Records in Relativistic Quantum Field Theory. In Meinard Kuhlmann, Holger Lyre, and Andrew Wayne, editors, Ontological Aspects of Quantum Field Theory, pages 165–180. New Jersey, London: World Scientific Publishing, 2002. [9] Jean-Louis Basdevant and Jean Dalibard. Quantum Mechanics. Berlin, Heidelberg: Springer, second edition, 2005. [10] J.S. Bell. Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press, second edition, 2004. [11] J. Binney and D. Skinner. The Physics of Quantum Mechanics. Oxford, New York: Oxford University Press, 2014. [12] F. Boge. On Modern Approaches to the Einsteinian View of Quantum States. philsci preprint 12013, 2016. [13] Michel Brune, E Hagley, J Dreyer, X Maitre, A Maali, C Wunderlich, JM Raimond, and S Haroche. Observing the progressive decoherence of the “meter” in a quantum measure- ment. Physical Review Letters, 77(24):4887, 1996. [14] J. Bub. Interpreting the Quantum World. Cambridge University Press, 1999. [15] Paul Busch, Pekka J. Lahti, and Peter Mittelstaedt. The Quantum Theory of Measurement. Lecture Notes in Physics. Berlin, Heidelberg: Springer, second revised edition, 1996. [16] Sean M Carroll and Charles T Sebens. Many worlds, the born rule, and self-locating uncertainty. In Quantum Theory: A Two-Time Success Story, pages 157–169. Springer, 2014. [17] C. M. Caves. Notes on Zurek’s derivation of the quantum probability rule. Online: info.phys.unm.edu / caves / reports / ZurekBornderivation.ps. Last modified 2005 July 29. [18] Richard Dawid and Karim PY Thébault. Many worlds: decoherent or incoherent? Synthese, 192(5):1559–1580, 2015. [19] Rafael de la Madrid. The role of the rigged Hilbert space in Quantum Mechanics. arXiv preprint quant-ph / 0502053, 2005. [20] Bernard d’Espagnat. Conceptual Foundations of Quantum Mechanics. Reading, Massachusttes: Perseus Books, second edition, 1999. [21] David Deutsch. Quantum theory of probability and decisions. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, volume 455, pages 3129–3137. The Royal Society, 1999. [22] Bryce S DeWitt. Quantum theory of gravity. i. the canonical theory. Physical Review, 160(5):1113, 1967. [23] Bryce S. DeWitt. Quantum Mechanics and Reality. In B.S. Dewitt and N. Graham, editors, The Many Worlds Interpretation of Quantum Mechanics, Princeton Series in Physics, pages 155–165. Princeton University Press, 1973. [24] B.S. Dewitt and N. Graham, editors. The Many Worlds Interpretation of Quantum Mechanics. Princeton Series in Physics. Princeton University Press, 1973. [25] P. A. M. Dirac. The Principles of Quantum Mechanics. Oxford: Clarendon Press, fourth(revised) edition, 1958. [26] D. Dürr, S. Goldstein, and N. Zanghì. Quantum Physics Without Quantum Philosophy. Springer Berlin Heidelberg, 2012. [27] Albert Einstein, Boris Podolsky, and Nathan Rosen. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47:777–780, 1935. [28] Hugh Everett III. “Relative state” formulation of quantum mechanics. Reviews of modern physics, 29(3):454, 1957. [29] C. A. Fuchs and A. Peres. Quantum theory needs no ‘interpretation’. Physics Today, 53(3):70–71, 2000. [30] Murray Gell-Mann and James B Hartle. Quantum mechanics in the light of quantum cosmology. Complexity, entropy and the physics of information, 8, 1990. [31] Gian Carlo Ghirardi, Alberto Rimini, and Tullio Weber. Unified dynamics for microscopic and macroscopic systems. Physical Review D, 34(2):470, 1986. [32] Domenico Giulini. Superselection Rules. In Daniel Greenberger, Klaus Hentschel, and Friedel Weinert, editors, Compendium of Quantum Physics. Concepts, Experiments, His- tory and Philosophy, pages 771–779. Berlin, Heidelberg: Springer, 2009. [33] H Greaves and D Wallace. Empirical consequences of symmetries. The British Journal for the Philosophy of Science, page axt005, 2013. [34] Hilary Greaves. Understanding Deutsch’s probability in a deterministic multiverse. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 35(3):423–456, 2004. [35] Hilary Greaves. Probability in the everett interpretation. Philosophy Compass, 2(1):109–128, 2007. [36] T. Heinosaari and M. Ziman. The Mathematical Language of Quantum Theory. From Uncertainty to Entanglement. Cambridge, New York: Cambridge University Press, 2012. [37] Werner Heisenberg. Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik, 43(3-4):172–198, 1927. [38] Werner Heisenberg. Physics and Philosophy. The Revolution in Modern Science. London: Allen & Unwin Ltd., third edition, 1971 [1958]. [39] Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki. Quantum entanglement. Reviews of modern physics, 81(2):865, 2009. [40] Don Howard. Who Invented the ‘Copenhagen Interpretation’? A Study in Mythology. Philosophy of Science, 71(5):669–682, 2002. [41] R. I. G. Hughes. The Structure and Interpretation of Quantum Mechanics. Cambridge: Harvard University Press, 1989. [42] Gregg Jaeger. Quantum Information. An Overview. New York: Springer Science + Business Media, LLC, 2007. [43] E. T. Jaynes. Probability Theory. The Logic of Science. Cambridge, New York: Cambridge University Press, 2003. [44] David Jennings and Matthew Leifer. No return to classical reality. Contemporary Physics, 57(1):60–82, 2015. [45] William Johnston. The Weighted Hermite Polynomials Form a Basis for L²(R). The American Mathematical Monthly, 121(3):249–253, 2014. [46] E. Joos, H.D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, and I.-O. Stamatescu. Decoherence and the Appearance of a Classical World in Quantum Theory. Berlin, Heidelberg: Springer, second edition, 2003. [47] Adrian Kent. Does it Make Sense to Speak of Self-Locating Uncertainty in the Universal Wave Function? Remarks on Sebens and Carroll. Foundations of Physics, 45(2):211–217, 2015. [48] Daniel Kleppner and Roman Jackiw. One Hundred Years of Quantum Physics. Science, 289(5481):893–898, 2000. [49] Peter J Lewis. Quantum sleeping beauty. Analysis, 67(293):59–65, 2007. [50] Michael Lockwood. ‘Many Minds’ Interpretations of Quantum Mechanics. The British journal for the philosophy of science, 47(2):159–188, 1996. [51] Gerhart Lüders. Über die Zustandsänderung durch den Messprozess. Annalen der Physik,443(5-8):322–328, 1951. [52] Tim Maudlin. Quantum Non-Locality and Relativity. Metaphysical Intimations of Modern Physics. Mladen, Oxford: Wiley-Blackwell, third edition, 2011. [53] Tim Maudlin. Critical Study: David Wallace, The Emergent Multiverse: Quantum Theory According to the Everett Interpretation. Noûs, 48(4):794–808, 2014. [54] N. David Mermin. What’s Wrong With This Pillow? Physics Today, 42(4):9, 1989. [55] N. David Mermin. Why QBism is not the Copenhagen interpretation and what John Bell might have thought of it. arXiv preprint 1409.2454v1, 2014. [56] Peter Mittelstaedt. The Interpretation of Quantum Mechanics and the Measurement Process. Cambridge, New York: Cambridge University Press, 1998. [57] Ulrich Mohrhoff. Probabilities from envariance? International Journal of Quantum Information, 2(02):221–229, 2004. [58] M. Nielsen and I. Chuang. Quantum Computation and Quantum Information. Cambridge, New York: Cambridge University Press, 10th anniversary edition, 2010. [59] Roger Penrose. On gravity’s role in quantum state reduction. General relativity and gravitation, 28(5):581–600, 1996. [60] Asher Peres. Quantum Theory: Concepts and Methods, volume 72 of Fundamental Theories of Physics. New York, Boston: Kluwer, 2002. [61] Alastair IM Rae. Everett and the Born rule. Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics, 40(3):243–250, 2009. [62] George G. Roussas. An Introduction to Measure-Theoretic Probability. Amsterdam, Boston: Elsevier, second edition, 2014. [63] G.G. Roussas. Introduction to Probability. Elsevier Academic Press, 2007. [64] Simon Saunders. Time, quantum mechanics, and probability. Synthese, 114(3):373–404, 1998. [65] L.J. Savage. The Foundations of Statistics. Dover Publications, second edition, 1972. [66] M. Schlosshauer. Decoherence and the Quantum to Classical Transition. Berlin, Heidelberg: Springer, second edition, 2007. [67] Maximilian Schlosshauer and Arthur Fine. On Zurek’s derivation of the Born rule. Foundations of Physics, 35(2):197–213, 2005. [68] Maximilian Schlosshauer, Johannes Kofler, and Anton Zeilinger. A snapshot of foundational attitudes toward quantum mechanics. Studies in History and Philosophy of Modern Physics, 44(3):222–230, 2013. [69] Erwin Schrödinger. The Present Situation in Quantum Mechanics. A Translation of Schrödinger’s “Cat Paradox” Paper. In John Archibald Wheeler and Wojciech Hubert Zurek, editors, Quantum Theory and Measurement. Princeton, New Jersey: Princeton University Press, 1983 [1935]. Translated by John D. Trimmer. [70] Gerhard Schurz. Philosophy of Science. A Unified Approach. New York, London: Routledge, 2014. [71] Franz Schwabl. Quantum Mechanics. Berlin, Heidelberg: Springer, fourth edition, 2007. [72] Max Tegmark. The Interpretation of Quantum Mechanics: Many Worlds or Many Words? Fortschritte der Physik, 46(6-8):855–862, 1998. [73] Paul Teller. An Interpretive Introduction to Quantum Field Theory. Princeton, New Jersey: Princeton University Press, 1995. [74] Lev Vaidman. Probability in the many-worlds interpretation of quantum mechanics. In Yemima Ben-Menahem and Meir Hemmo, editors, Probability in physics, pages 299–311. Springer, 2012. [75] R. von Mises. Mathematical Theory of Probability and Statistics. New York: Dover Publications Inc., second revised edition, 1981 [1957]. [76] J. von Neumann and O. Morgenstern. Theory of Games and Economic Behavior. Princeton University Press, third edition, 1953. [77] John von Neumann. Mathematical Foundations of Quantum Mechanics. Princeton: Princeton University Press, 1955 [1932]. Translated by Robert T. Beyer. [78] D. Wallace. Quantum probability and decision theory, revisited. arXiv preprint quantph / 0211104, 2002. [79] D. Wallace. Everettian rationality: defending deutsch’s approach to probability in the Everett interpretation. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 34(3):415–439, 2003. [80] D. Wallace. Quantum probability from subjective likelihood: improving on Deutsch’s proof of the probability rule. Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics, 38(2):311–332, 2007. [81] D. Wallace. The Emergent Multiverse: Quantum Theory According to the Everett Interpretation. OUP Oxford, 2012. [82] E. Wigner. Remarks on the mind-body question. In John Heil, editor, Philosophy of Mind: A Guide and Anthology, pages 866–877. Oxford, New York: Oxford University Press, 2004 [1967]. [83] H Dieter Zeh. On the interpretation of measurement in quantum theory. Foundations of Physics, 1(1):69–76, 1970. [84] Wojciech H Zurek. Environment-induced superselection rules. Physical Review D, 26(8):1862, 1982. [85] Wojciech H Zurek. Decoherence and the transition from quantum to classical-revisited. Los Alamos Science, 27:86–109, 2002. [86] Wojciech Hubert Zurek. Environment-assisted invariance, entanglement, and probabilities in quantum physics. Physical review letters, 90(12):120404, 2003. [87] Wojciech Hubert Zurek. Probabilities from entanglement, Born’s rule p k = | ψ k |² from envariance. Physical Review A, 71(5):052105, 2005.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/6889