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  • Cited by 16
Publisher:
Cambridge University Press
Online publication date:
February 2021
Print publication year:
2021
Online ISBN:
9781108885515

Book description

Quantum mechanics is an extraordinarily successful scientific theory. But more than 100 years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them. Topics covered include nonlocality, contextuality, the reality of the wavefunction and the measurement problem. The discussion is supplemented with descriptions of some of the most important mathematical results from recent work in quantum foundations, including Bell's theorem, the Kochen-Specker theorem and the PBR theorem.

Reviews

'… what the author accomplishes is remarkable … she manages to introduce the formalism of the theory and to provide a discussion of quantum non­ locality, quantum contextuality, the reality of the quantum state, and the main interpretations of quantum mechanics, among other topics. In addition, she offers proof of the principal theorems involved. The whole tour does not result in an anodyne summary of well-known things. On the contrary, it incorporates original views and arguments, reflecting the novel perspective of the author on the field.'

Albert Solé and Antonio Vassallo Source: Metascience

References

Aaronson, S., and Gottesman, D. (2004). Improved simulation of stabilizer circuits. Physical Review A, 70:052328.
Abramsky, S., and Heunen, C. (2012). Operational theories and categorical quantum mechanics. In Logic and Algebraic Structures in Quantum Computing. Cambridge University Press.
Adlam, E. (2014). The problem of confirmation in the Everett interpretation. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 47:2132.
Adlam, E. (2018a). Quantum mechanics and global determinism. Quanta, 7(1):4053.
Adlam, E. (2018b). Spooky action at a temporal distance. Entropy, 20(1):41.
Adler, S. L. (2006). Lower and upper bounds on CSL parameters from latent image formation and IGM heating. Journal of Physics A: Mathematical and Theoretical, 40:29352957.
Aharonov, Y., Cohen, E., Gruss, E., and Landsberger, T. (2014). Measurement and collapse within the two-state vector formalism. Quantum Studies: Mathematics and Foundations, 1(1–2):133146.
Aharonov, Y., and Gruss, E. Y. (2005). Two-time interpretation of quantum mechanics. eprint arXiv:quant-ph/0507269.
Albert, D. (2010). Probability in the Everett picture. In Saunders, S., Barrett, J., Kent, A., and Wallace, D., editors, Many Worlds?: Everett, Quantum Theory & Reality. Oxford University Press.
Allori, V., Goldstein, S., Tumulka, R., and Zanghì, N. (2008). On the common structure of Bohmian mechanics and the Ghirardi-Rimini-Weber theory. British Journal for the Philosophy of Science, 59(3):353389.
Allori, V., Goldstein, S., Tumulka, R., and Zanghi, N. (2013). Predictions and primitive ontology in quantum foundations: A study of examples. British Journal for the Philosophy of Science, 65(2):323352.
Arntzenius, F. (1994). Spacelike connections. British Journal for the Philosophy of Science, 45(1):201217.
Aspect, A., Grangier, P., and Roger, G. (1981). Experimental tests of realistic local theories via Bell’s theorem. Physical Review Letters, 47:460463.
Barrau, A. (2014). Testing the Everett interpretation of quantum mechanics with cosmology. Electronic Journal of Theoretical Physics, 33:127134.
Barrett, J. (2007). Information processing in generalized probabilistic theories. Physical Review A, 75:032304.
Bell, J. (1987). Free variables and local causality. In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press.
Bell, J. (2004). Are there quantum jumps? In Speakable and Unspeakable in Quantum Mechanics, 2nd edition. Cambridge University Press.
Bell, J. S. (1985). Free variables and local causality. In John S. Bell on the Foundations of Quantum Mechanics. World Scientific.
Bell, J. S. (1964). On the Einstein Podolsky Rosen paradox. Physics Physique Fizika, 1(3):195.
Bell, J. S. (1966). On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics, 38(3):447.
Bell, J. S., and Aspect, A. (2004). Are there quantum jumps? In Speakable and Unspeakable in Quantum Mechanics, 2nd edition. Cambridge University Press.
Beltrametti, E., and Bujaski, S. (1995). A classical extension of quantum mechanics. Journal of Physics A: Mathematics and General, 37(28):33293343.
Berkovitz, J. (2002). On causal loops in the quantum realm. In Placek, T. and Butterfield, J., editors, Non-locality and Modality. Kluwer.
Black, M. (1956). Why cannot an effect precede its cause? Analysis, 16(3):4958.
Bondy, J., and Murty, U. (1976). Graph Theory with Applications. Elsevier Science Publishing.
Bravyi, S., and Kitaev, A. (2005). Universal quantum computation with ideal Clifford gates and noisy ancillas. Physical Review A., 71(2):022316.
Brizard, A. (2008). An Introduction to Lagrangian Mechanics. World Scientific.
Brown, H. R., and Lehmkuhl, D. (2016). Einstein, the reality of space, and the action-reaction principle. In Einstein, Tagore and the Nature of Reality, Routledge Studies in the Philosophy of Mathematics and Physics. Taylor & Francis.
Bruschi, D. E., Sabín, C., Kok, P., Johansson, G., Delsing, P., and Fuentes, I. (2016). Towards universal quantum computation through relativistic motion. Scientific Reports, 6(1):18349.
Busch, P., Lahti, J., and Mittelstaedt, P. (1996). The Quantum Theory of Measurement. Springer-Verlag.
Butterfield, J. (1992). Bell’s theorem: What it takes. British Journal for the Philosophy of Science, 43(1):4183.
Cabello, A., Estebaranz, J., and García-Alcaine, G. (1996). Bell-Kochen-Specker theorem: A proof with 18 vectors. Physics Letters A, 212(4):183187.
Cabello, A., Severini, S., and Winter, A. (2014). Graph-theoretic approach to quantum correlations. Physical Review Letters, 112(4):040401.
Chen, E. K. (2019). Realism about the wave function. Philosophy Compass, 14(7):e12611.
Clauser, J. F., Horne, M. A., Shimony, A., and Holt, R. A. (1969). Proposed experiment to test local hidden-variable theories. Physical Review Letters, 23:880884.
Coffman, V., Kundu, J., and Wootters, W. K. (2000). Distributed entanglement. Physical Review A, 61(5):052306.
Cramer, J. G. (1986). The transactional interpretation of quantum mechanics. Reviews of Modern Physics, 58:647687.
Cuffaro, M. E. (2015). On the significance of the Gottesman–Knill theorem. British Journal for the Philosophy of Science, 68(1):91121.
d’ Espagnat, B. (1971). Conceptual Foundations of Quantum Mechanics. Addison-Wesley.
de Muynck, W. M. (2007). POVMs: A small but important step beyond standard quantum mechanics. In Nieuwenhuizen, T. M., Mehmani, B., Špička, V., Aghdami, M. J., and Khrennikov, A. Y., editors, Beyond the Quantum. World Scientific.
Deutsch, D. (2011). The Fabric of Reality. Penguin Books.
Deutsch, D. (2016). The logic of experimental tests, particularly of Everettian quantum theory. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 55:2433.
Dürr, D., Goldstein, S., and Zanghi, N. (1992). Quantum equilibrium and the origin of absolute uncertainty. Journal of Statistical Physics, 67(56).
Dürr, D., Goldstein, S., and Zanghì, N. (1995). Bohmian mechanics and the meaning of the wave function. In Experimental Metaphysics: Quantum Mechanical Studies in Honor of Abner Shimony. Springer.
Dürr, D., Goldstein, S., and Zanghì, N. (2004). Quantum equilibrium and the role of operators as observables in quantum theory. Journal of Statistical Physics, 116(1-4):9591055.
Dürr, D., Goldstein, S., Norsen, T., Struyve, W., and Zanghì, N. (2014). Can Bohmian mechanics be made relativistic? Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470(2162):20130699.
Dürr, D., Goldstein, S., Tumulka, R., and Zanghi, N. (2005). On the role of density matrices in Bohmian mechanics. Foundations of Physics, 35(3):449467.
Eastin, B., and Knill, E. (2009). Restrictions on transversal encoded quantum gate sets. Physical Review Letters, 102(11):110502.
Edward Bruschi, D., Sabín, C., White, A., Baccetti, V., Oi, D. K. L., and Fuentes, I. (2014). Testing the effects of gravity and motion on quantum entanglement in space-based experiments. New Journal of Physics, 16(5):053041.
Einstein, A. (1905). On the electrodynamics of moving bodies. Annalen der Physik, 17:891921.
Einstein, A. (1920). Relativity: The Special and General Theory. Henry Holt.
Einstein, A. (1948). Quantum mechanics and reality. Dialectica 2(3–4):320324.
Einstein, A., Podolsky, B., and Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47:777780.
Emerson, J., Serbin, D., Sutherland, C., and Veitch, V. (2013). The whole is greater than the sum of the parts: On the possibility of purely statistical interpretations of quantum theory. ArXiv eprints.
Esfeld, M., and Gisin, N. (2013). The GRW flash theory: A relativistic quantum ontology of matter in space-time? ArXiv eprints.
Everett, H. (2016). ‘Relative state’ formulation of quantum mechanics. In The Many-Worlds Interpretation of Quantum Mechanics. Princeton University Press.
Faye, J. (2019). Copenhagen interpretation of quantum mechanics. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy, winter 2019 edition. Metaphysics Research Lab, Stanford University.
Frauchiger, D., and Renner, R. (2018). Quantum theory cannot consistently describe the use of itself. Nature Communications, 9(1):3711.
Friederich, S., and Evans, P. W. (2019). Retrocausality in quantum mechanics. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy, summer 2019 edition. Metaphysics Research Lab, Stanford University.
Fuchs, C. A. (2010). QBism, the perimeter of quantum Bayesianism. ArXiv eprints.
Gell-Mann, M. (1980). Questions for the future. In Wolfson College Lectures. Oxford University Press.
Ghirardi, G. C., Rimini, A., and Weber, T. (1986a). Unified dynamics for microscopic and macroscopic systems. Physical Review D, 34:470491.
Ghirardi, G. C., Rimini, A., and Weber, T. (1986b). Unified dynamics for microscopic and macroscopic systems. Physical Review D, 34:470491.
Goldstein, S., and Teufel, S. (1999). Quantum spacetime without observers: Ontological clarity and the conceptual foundations of quantum gravity. In Quantum Physics Without Quantum Philosophy. Springer.
Goldstein, S., and Tumulka, R. (2003). Opposite arrows of time can reconcile relativity and nonlocality. Classical and Quantum Gravity, 20(3):557564.
Gottesman, D. (1998). The Heisenberg representation of quantum computers. Speech at the 1998 International Conference on Group Theoretic Methods in Physics.
Greaves, H. (2007). Probability in the Everett interpretation. Philosophy Compass, 2(1):109128.
Halpern, J. Y., and Tuttle, M. R. (1993). Knowledge, probability, and adversaries. Journal of the ACM, 40(4):917960.
Hardy, L., and Spekkens, R. (2010). Why physics needs quantum foundations. Physics in Canada, 66(2):7376.
Harrigan, N., and Spekkens, R. W. (2010). Einstein, incompleteness, and the epistemic view of quantum states. Foundations of Physics, 40:125157.
Held, C. (2014). The Kochen-Specker theorem. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy, winter 2014 edition. Metaphysics Research Lab, Stanford University.
Hensen, B., Bernien, H., Dréau, A. E., Reiserer, A., Kalb, N., Blok, M. S., Ruitenberg, J., Vermeulen, R. F. L., Schouten, R. N., Abellán, C., Amaya, W., Pruneri, V., Mitchell, M. W., Markham, M., Twitchen, D. J., Elkouss, D., Wehner, S., Taminiau, T. H., and Hanson, R. (2015). Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km. Nature, 526:682686.
Hesse, M. B. (1955). Action at a distance in classical physics. Isis, 46(4):337353.
Hoefer, C. (2016). Causal determinism. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy, spring 2016 edition. Metaphysics Research Lab, Stanford University.
Holland, P. (1995). The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics. Cambridge University Press.
Horne, M. A., Clauser, J. F., and Shimony, A. (1993). An Exchange on Local Beables, volume 2. Cambridge University Press.
Hossenfelder, S. (2018). Lost in Math: How Beauty Leads Physics Astray. Basic Books.
Hossenfelder, S., and Palmer, T. (2020). Rethinking superdeterminism. Frontiers in Physics, 8:139.
Howard, M., Wallman, J., Veitch, V., and Emerson, J. (2014). Contextuality supplies the ‘magic’ for quantum computation. Nature, 510:351355.
Kent, A. (2009). One world versus many: The inadequacy of Everettian accounts of evolution, probability, and scientific confirmation. In Many Worlds? Everett, Quantum Theory and Reality. Oxford University Press.
Kent, A. (2010). One world versus many: The inadequacy of Everettian accounts of evolution, probability, and scientific confirmation. In Saunders, S., Barrett, J., Kent, A., and Wallace, D., editors, Many Worlds?: Everett, Quantum Theory & Reality. Oxford University Press.
Kent, A. (2013). A no-summoning theorem in relativistic quantum theory. Quantum Information Processing, 12(2):10231032.
Kielpinski, D., Meyer, V., Sackett, C. A., Itano, W. M., Monroe, C., and Wineland, D. J. (2001). Experimental violation of a Bell’s inequality with efficient detection. Nature, 409:791794.
Koashi, M., and Winter, A. (2004). Monogamy of quantum entanglement and other correlations. Physical Review A, 69(2):022309.
Kochen, S., and Specker, E. (1975). The problem of hidden variables in quantum mechanics. In Hooker, C., editor, The Logico-Algebraic Approach to Quantum Mechanics, volume 5a of The University of Western Ontario Series in Philosophy of Science. Springer.
Kuhlmann, M. (2018). Quantum field theory. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy, winter 2018 edition. Metaphysics Research Lab, Stanford University.
Lancaster, T., and Blundell, S. (2014). Quantum Field Theory for the Gifted Amateur. Oxford University Press.
Landau, L., and Lifshitz, E. (2013). Quantum Mechanics: Non-Relativistic Theory. Elsevier Science.
Leifer, M. (2014). Is the quantum state real? An extended review of -ontology theorems. Quanta, 3(1):67155.
Leifer, M., and Pusey, M. (2017). Is a time symmetric interpretation of quantum theory possible without retrocausality? Proceedings of the Royal Society A.
Lewis, D. K. (1980). A subjectivist’s guide to objective chance. In Jeffrey, R. C., editor, Studies in Inductive Logic and Probability, volume 2. University of California Press.
Lewis, P. J. (2004). Interpreting spontaneous collapse theories. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 36(1):165180.
Lindkvist, J., Sabín, C., Johansson, G., and Fuentes, I. (2015). Motion and gravity effects in the precision of quantum clocks. Scientific Reports, 5(1):10070.
Lindley, D. (2008). Uncertainty. Knopf Doubleday.
MacKenzie, R. (2000). Path integral methods and applications. Lectures given at Rencontres du Vietnam, 6. Vietnam School of Physics.
Mari, A., and Eisert, J. (2012). Positive Wigner functions render classical simulation of quantum computation efficient. Physical Review Letters, 109:230503.
Masanes, L., and Müller, M. P. (2011). A derivation of quantum theory from physical requirements. New Journal of Physics, 13(6):063001.
Maudlin, T. (2011). Quantum Non-locality and Relativity: Metaphysical Intimations of Modern Physics. Wiley.
Maudlin, T. (2012). Philosophy of Physics: Space and Time. Princeton University Press.
Meacham, C. J. G. (2008). Sleeping beauty and the dynamics of de se beliefs. Philosophical Studies, 138(2):245269.
Navascués, M., Guryanova, Y., Hoban, M. J., and Acín, A. (2015). Almost quantum correlations. Nature Communications, 6(1):6288.
Nielsen, M. A., and Chuang, I. L. (2011). Quantum Computation and Quantum Information, 10th edition. Cambridge University Press.
Oreshkov, O., and Cerf, N. J. (2016). Operational quantum theory without predefined time. New Journal of Physics, 18(7):073037.
Paris, M. G. A. (2012). The modern tools of quantum mechanics. A tutorial on quantum states, measurements, and operations. European Physical Journal Special Topics, 203:6186.
Pawlowski, M., Paterek, T., Kaszlikowski, D., Scarani, V., Winter, A., and Żukowski, M. (2009). Information causality as a physical principle. Nature, 461:11011104.
Peskin, M., and Schroeder, D. (1995). An Introduction to Quantum Field Theory. Westview Press.
Price, H. (1994). A neglected route to realism about quantum mechanics. Mind, 103(411):303336.
Price, H. (2008). Decisions, decisions, decisions: Can Savage salvage Everettian probability? Presented at the Many Worlds at 50 conference. Perimeter Institute.
Price, H. (2010). Does Time-Symmetry Imply Retrocausality? How the Quantum World Says ‘Maybe’. Studies in History and Philosophy of Modern Physics, 43:7583.
Pusey, M. F., Barrett, J., and Rudolph, T. (2012). On the reality of the quantum state. Nature Physics, 8:476479.
Robinson, H. (2017). Dualism. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy, fall 2017 edition. Metaphysics Research Lab, Stanford University.
Rohrlich, D., and Popescu, S. (1995). Nonlocality as an axiom for quantum theory. Presented at 60 Years of E.P.R. conference, Israel.
Samuel Reich, E. (2011). Quantum theorem shakes foundations. Nature. www.nature.com/news/quantum-theorem-shakes-foundations-1.9392.
Sartori, L. (1996). Understanding Relativity: A Simplified Approach to Einstein’s Theories. University of California Press.
Schreiber, O., and Spekkens, R. (2008). The power of epistemic restrictions in axiomatizing quantum theory: From trits to qutrits. Unpublished work. Videos of talks discussing this material are available: Spekkens R. W., Talk, July 17, 2008, University of Oxford, Spekkens R. W., Talk, August 10, 2008, Perimeter Institute, PIRSA:09080009.
Sebens, C. T., and Carroll, S. M. (2016). Self-locating uncertainty and the origin of probability in Everettian quantum mechanics. British Journal for the Philosophy of Science, 69(1):2574.
Seevinck, M. P. (2010). Can quantum theory and special relativity peacefully coexist? In Quantum Physics and the Nature of Reality. Oxford University Press.
Seevinck, M. P. (2010). Monogamy of correlations versus monogamy of entanglement. Quantum Information Processing, 9(2):273294.
Shahandeh, F. (2019). The Resource Theory of Entanglement, Springer International.
Shimony, A. (1990). Desiderata for a modified quantum dynamics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1990:4959.
Shimony, A. (2013). Bell’s theorem. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy, winter 2013 edition. Metaphysics Research Lab, Stanford University.
Sklar, L. (1993). Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics. Cambridge University Press.
Sklar, L. (2012). Philosophy and the Foundations of Dynamics. Cambridge University Press.
Spekkens, R. W. (n.d.). Private communication.
Spekkens, R. W. (2005). Contextuality for preparations, transformations, and unsharp measurements. Physical Review A, 71(5):052108.
Spekkens, R. W. (2007). Evidence for the epistemic view of quantum states: A toy theory. Physical Review A, 75(3):032110.
Stone, J. (2013). Bayes’ Rule: A Tutorial Introduction to Bayesian Analysis. Sebtel Press.
Strang, G. (2016). Introduction to Linear Algebra. Cambridge University Press.
Thomas, J., and Cover, T. (2006). Elements of Information Theory. Wiley.
Timpson, C. G. (2008). Philosophical aspects of quantum information theory. In Rickles, D., editor, The Ashgate Companion to Contemporary Philosophy of Physics. Ashgate.
Titelbaum, M. G. (2008). The relevance of self-locating beliefs. The Philosophical Review, 117(4):555605.
Toner, B. (2009). Monogamy of non-local quantum correlations. Proceedings of the Royal Society of London Series A, 465:5969.
Toner, B., and Verstraete, F. (2006). Monogamy of Bell correlations and Tsirelson’s bound. eprint arXiv:quant-ph/0611001.
Toroš, M., and Bassi, A. (2018). Bounds on quantum collapse models from matter-wave interferometry: Calculational details. Journal of Physics A: Mathematical and Theoretical, 51(11):115302.
Tsirelson, B. S. (1980). Quantum generalizations of Bell’s inequality. Letters in Mathematical Physics. 4:93100.
Tumulka, R. (2006). A relativistic version of the Ghirardi–Rimini–Weber model. Journal of Statistical Physics, 125(4):821840.
Tumulka, R. (2020). A relativistic GRW flash process with interaction. n.p.
Vaidman, L. (1998). On schizophrenic experiences of the neutron or why we should believe in the many-worlds interpretation of quantum theory. International Studies in the Philosophy of Science, 12(3):245261.
Valentini, A. (2010). Inflationary cosmology as a probe of primordial quantum mechanics. Physical Review D, 82(6): 063513.
Valentini, A., and Westman, H. (2005). Dynamical origin of quantum probabilities. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461(2053):253272.
Veitch, V., Ferrie, C., Gross, D., and Emerson, J. (2012). Negative quasi-probability as a resource for quantum computation. New Journal of Physics, 14(11):113011.
Veitch, V., Hamed Mousavian, S. A., Gottesman, D., and Emerson, J. (2014). The resource theory of stabilizer quantum computation. New Journal of Physics, 16(1):013009.
Wallace, D. (2007). The quantum measurement problem: State of play. In The Ashgate Companion to the New Philosophy of Physics. Ashgate.
Wallace, D. (2012). The Emergent Multiverse: Quantum Theory according to the Everett Interpretation. Oxford University Press.
Walleczek, J., and Grössing, G. (2014). The non-signalling theorem in generalizations of Bell’s theorem. In Journal of Physics: Conference Series, volume 504, page 012001. IOP Publishing.
Weinberg, S. (2014). Quantum mechanics without state vectors. Physical Review A, 90(4):042102.
Wharton, K. (2015). The universe is not a computer. In Aguirre, A., F. B., and Merali, G., editors, Questioning the Foundations of Physics. Springer.
Wigner, E. P. (1961). Remarks on the mind-body question. In Good, I. J., editor, The Scientist Speculates. Heineman.
Wiseman, H. M. (2006). From Einstein’s theorem to Bell’s theorem: A history of quantum non-locality. Contemporary Physics, 47:7988.
Żukowski, M., Zeilinger, A., Horne, M. A., and Ekert, A. K. (1993). ‘Event-ready-detectors’ Bell experiment via entanglement swapping. Physical Review Letters, 71:42874290.

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