On Formalisms and Interpretations
1Faculty of Informatics, Università della Svizzera italiana, Via G. Buffi 13, CH-6900 Lugano, Switzerland
2Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| Published: | 2018-10-15, volume 2, page 99 |
| Eprint: | arXiv:1710.07212v6 |
| Doi: | https://doi.org/10.22331/q-2018-10-15-99 |
| Citation: | Quantum 2, 99 (2018). |
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Abstract
One of the reasons for the heated debates around the interpretations of quantum theory is a simple confusion between the notions of formalism $\textit{versus}$ interpretation. In this note, we make a clear distinction between them and show that there are actually two $\textit{inequivalent}$ quantum formalisms, namely the relative-state formalism and the standard formalism with the Born and measurement-update rules. We further propose a different probability rule for the relative-state formalism and discuss how Wigner's-friend-type experiments could show the inequivalence with the standard formalism. The feasibility in principle of such experiments, however, remains an open question.
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► References
[1] Yakir Aharonov, Sandu Popescu, Daniel Rohrlich, and Paul Skrzypczyk. Quantum cheshire cats. New Journal of Physics, 15 (11): 113015, 2013. 10.1088/1367-2630/15/11/113015.
https://doi.org/10.1088/1367-2630/15/11/113015
[2] Veronika Baumann, Arne Hansen, and Stefan Wolf. The measurement problem is the measurement problem is the measurement problem. arXiv:1611.01111, 2016. URL https://arxiv.org/abs/1611.01111.
arXiv:1611.01111
[3] John S Bell. On the Einstein Podolsky Rosen paradox. Physics, 1 (3): 195–200, 1964. 10.1103/PhysicsPhysiqueFizika.1.195.
https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195
[4] John Stewart Bell. Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy. Cambridge university press, 2004. 10.1017/CBO9780511815676.
https://doi.org/10.1017/CBO9780511815676
[5] Max Born. The statistical interpretation of quantum mechanics. Nobel Lecture, 11: 1942–1962, 1954. 10.1126/science.122.3172.675.
https://doi.org/10.1126/science.122.3172.675
[6] Caslav Brukner. On the quantum measurement problem. arXiv:1507.05255, 2015. URL https://arxiv.org/abs/1507.05255.
arXiv:1507.05255
[7] Giulio Chiribella, G Mauro D'Ariano, and Paolo Perinotti. Quantum circuit architecture. Physical Review Letters, 101 (6): 060401, 2008. 10.1103/PhysRevLett.101.060401.
https://doi.org/10.1103/PhysRevLett.101.060401
[8] Giulio Chiribella, Giacomo Mauro D'Ariano, and Paolo Perinotti. Probabilistic theories with purification. Physical Review A, 81 (6): 062348, 2010. 10.1103/PhysRevA.81.062348.
https://doi.org/10.1103/PhysRevA.81.062348
[9] David Deutsch. Quantum theory as a universal physical theory. International Journal of Theoretical Physics, 24 (1): 1–41, 1985. 10.1.1.205.5427.
[10] 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. 10.1098/rspa.1999.0443.
https://doi.org/10.1098/rspa.1999.0443
[11] Detlef Dürr, Sheldon Goldstein, and Nino Zanghi. Bohmian mechanics as the foundation of quantum mechanics. In Bohmian mechanics and quantum theory: an appraisal, pages 21–44. Springer, 1996. 10.1007/978-94-015-8715-0_2.
https://doi.org/10.1007/978-94-015-8715-0_2
[12] Hugh Everett III. "Relative State" formulation of quantum mechanics. Reviews of Modern Physics, 29 (3): 454, 1957. 10.1103/RevModPhys.29.454.
https://doi.org/10.1103/RevModPhys.29.454
[13] Daniela Frauchiger and Renato Renner. Quantum theory cannot consistently describe the use of itself. Nature communications, 9 (1): 3711, 2018. 10.1038/s41467-018-05739-8.
https://doi.org/10.1038/s41467-018-05739-8
[14] Christopher A Fuchs. Qbism, the perimeter of quantum bayesianism. arXiv:1003.5209, 2010. URL https://arxiv.org/abs/1003.5209.
arXiv:1003.5209
[15] Gian Carlo Ghirardi, Alberto Rimini, and Tullio Weber. Unified dynamics for microscopic and macroscopic systems. Physical Review D, 34 (2): 470, 1986. 10.1103/PhysRevD.34.470.
https://doi.org/10.1103/PhysRevD.34.470
[16] Lucien Hardy. Quantum theory from five reasonable axioms. arXiv:quant-ph/0101012, 2001. arXiv:quant-ph/0101012.
arXiv:quant-ph/0101012
[17] Grete Hermann. Die naturphilosophischen Grundlagen der Quantenmechanik. Naturwissenschaften, 23 (42): 718–721, 1935. 10.1007/BF01491142.
https://doi.org/10.1007/BF01491142
[18] Grete Hermann and Dirk Lumma. The foundations of quantum mechanics in the philosophy of nature. The Harvard Review of Philosophy, 7 (1): 35–44, 1999. 10.5840/harvardreview1999715.
https://doi.org/10.5840/harvardreview1999715
[19] Simon Kochen and Ernst P Specker. The problem of hidden variables in quantum mechanics. In The logico-algebraic approach to quantum mechanics, pages 293–328. Springer, 1975. 10.1007/978-94-010-1795-4_17.
https://doi.org/10.1007/978-94-010-1795-4_17
[20] Johannes Kofler and Časlav Brukner. Classical world arising out of quantum physics under the restriction of coarse-grained measurements. Physical Review Letters, 99 (18): 180403, 2007. 10.1103/PhysRevLett.99.180403.
https://doi.org/10.1103/PhysRevLett.99.180403
[21] Lluís Masanes and Markus P Müller. A derivation of quantum theory from physical requirements. New Journal of Physics, 13 (6): 063001, 2011. 10.1088/1367-2630/13/6/063001.
https://doi.org/10.1088/1367-2630/13/6/063001
[22] Ognyan Oreshkov, Fabio Costa, and Časlav Brukner. Quantum correlations with no causal order. Nature communications, 3: 1092, 2012. 10.1038/ncomms2076.
https://doi.org/10.1038/ncomms2076
[23] Karl Popper. Logik der Forschung. Springer, 1935. 10.1524/9783050050188.
https://doi.org/10.1524/9783050050188
[24] Carlo Rovelli. Relational quantum mechanics. International Journal of Theoretical Physics, 35 (8): 1637–1678, 1996. 10.1007/BF02302261.
https://doi.org/10.1007/BF02302261
[25] Simon Saunders. Derivation of the Born rule from operational assumptions. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, volume 460, pages 1771–1788. The Royal Society, 2004. 10.1098/rspa.2003.1230.
https://doi.org/10.1098/rspa.2003.1230
[26] Sally Shrapnel, Fabio Costa, and Gerard Milburn. Updating the born rule. New Journal of Physics, 20 (5): 053010, 2018. 10.1088/1367-2630/aabe12.
https://doi.org/10.1088/1367-2630/aabe12
[27] Anthony Sudbery. Quantum mechanics and the particles of nature. Cambridge University Press, 1986.
[28] Anthony Sudbery. Single-world theory of the extended Wigner's friend experiment. Foundations of Physics, 47 (5): 658–669, 2017. 10.1007/s10701-017-0082-7.
https://doi.org/10.1007/s10701-017-0082-7
[29] John Archibald Wheeler, Wojciech Hubert Zurek, and Leslie E Ballentine. Quantum theory and measurement. American Journal of Physics, 52 (10): 955–955, 1984. 10.1119/1.13804.
https://doi.org/10.1119/1.13804
[30] Eugene P Wigner. The problem of measurement. American Journal of Physics, 31 (1): 6–15, 1963. 10.1119/1.1969254.
https://doi.org/10.1119/1.1969254
[31] Wojciech Hubert Zurek. Decoherence, einselection, and the quantum origins of the classical. Reviews of Modern Physics, 75 (3): 715, 2003. 10.1103/RevModPhys.75.715.
https://doi.org/10.1103/RevModPhys.75.715
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[2] Reinhold A. Bertlmann, "Real or not real that is the question...", The European Physical Journal H 45 2-3, 205 (2020).
[3] Kyrylo Simonov, "Particle mixing and the emergence of classicality: A spontaneous-collapse-model view", Physical Review A 102 2, 022226 (2020).
[4] R. E. Kastner, "Unitary Interactions Do Not Yield Outcomes: Attempting to Model “Wigner’s Friend”", Foundations of Physics 51 4, 89 (2021).
[5] Veronika Baumann and Časlav Brukner, Jerusalem Studies in Philosophy and History of Science 91 (2020) ISBN:978-3-030-34315-6.
[6] Veronika Baumann, Flavio Del Santo, Alexander R. H. Smith, Flaminia Giacomini, Esteban Castro-Ruiz, and Caslav Brukner, "Generalized probability rules from a timeless formulation of Wigner's friend scenarios", Quantum 5, 524 (2021).
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[8] Nuriya Nurgalieva and Renato Renner, "Testing quantum theory with thought experiments", Contemporary Physics 61 3, 193 (2020).
[9] Armando Relaño, "Decoherence framework for Wigner's-friend experiments", Physical Review A 101 3, 032107 (2020).
[10] Jacques Pienaar, "A Quintet of Quandaries: Five No-Go Theorems for Relational Quantum Mechanics", Foundations of Physics 51 5, 97 (2021).
[11] Michael Dascal, "What's left for the neo-Copenhagen theorist", Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 72, 310 (2020).
[12] Philippe Allard Guérin, Veronika Baumann, Flavio Del Santo, and Časlav Brukner, "A no-go theorem for the persistent reality of Wigner’s friend’s perception", Communications Physics 4 1, 93 (2021).
[13] Flavio Del Santo and Nicolas Gisin, "Physics without determinism: Alternative interpretations of classical physics", Physical Review A 100 6, 062107 (2019).
[14] Marek Żukowski and Marcin Markiewicz, "Physics and Metaphysics of Wigner’s Friends: Even Performed Premeasurements Have No Results", Physical Review Letters 126 13, 130402 (2021).
[15] Flavio Del Santo, The Frontiers Collection 63 (2021) ISBN:978-3-030-70353-0.
[16] Jeffrey Bub, Jerusalem Studies in Philosophy and History of Science 199 (2020) ISBN:978-3-030-34315-6.
[17] Jacques Pienaar, "QBism and Relational Quantum Mechanics compared", Foundations of Physics 51 5, 96 (2021).
[18] Nuriya Nurgalieva and Lídia del Rio, "Inadequacy of Modal Logic in Quantum Settings", arXiv:1804.01106.
[19] Igor Salom, "To the rescue of Copenhagen interpretation", arXiv:1809.01746.
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