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). |
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
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.
► BibTeX data
► 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
Cited by
[1] Cyril Elouard, Philippe Lewalle, Sreenath K. Manikandan, Spencer Rogers, Adam Frank, and Andrew N. Jordan, "Quantum erasing the memory of Wigner's friend", Quantum 5, 498 (2021).
[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] Brian Drummond, "Quantum Mechanics: Statistical Balance Prompts Caution in Assessing Conceptual Implications", Entropy 24 11, 1537 (2022).
[5] R. E. Kastner, "Unitary Interactions Do Not Yield Outcomes: Attempting to Model “Wigner’s Friend”", Foundations of Physics 51 4, 89 (2021).
[6] Veronika Baumann and Časlav Brukner, Jerusalem Studies in Philosophy and History of Science 91 (2020) ISBN:978-3-030-34315-6.
[7] 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).
[8] Kok-Wei Bong, Aníbal Utreras-Alarcón, Farzad Ghafari, Yeong-Cherng Liang, Nora Tischler, Eric G. Cavalcanti, Geoff J. Pryde, and Howard M. Wiseman, "A strong no-go theorem on the Wigner’s friend paradox", Nature Physics 16 12, 1199 (2020).
[9] Nuriya Nurgalieva and Renato Renner, "Testing quantum theory with thought experiments", Contemporary Physics 61 3, 193 (2020).
[10] Armando Relaño, "Decoherence framework for Wigner's-friend experiments", Physical Review A 101 3, 032107 (2020).
[11] Jacques Pienaar, "A Quintet of Quandaries: Five No-Go Theorems for Relational Quantum Mechanics", Foundations of Physics 51 5, 97 (2021).
[12] 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).
[13] 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).
[14] Flavio Del Santo and Nicolas Gisin, "Physics without determinism: Alternative interpretations of classical physics", Physical Review A 100 6, 062107 (2019).
[15] 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).
[16] Flavio Del Santo, The Frontiers Collection 63 (2021) ISBN:978-3-030-70353-0.
[17] Jeffrey Bub, Jerusalem Studies in Philosophy and History of Science 199 (2020) ISBN:978-3-030-34315-6.
[18] Jacques Pienaar, "QBism and Relational Quantum Mechanics compared", Foundations of Physics 51 5, 96 (2021).
[19] Igor Salom, "To the rescue of Copenhagen interpretation", arXiv:1809.01746, (2018).
[20] Nuriya Nurgalieva and Lídia del Rio, "Inadequacy of Modal Logic in Quantum Settings", arXiv:1804.01106, (2018).
The above citations are from Crossref's cited-by service (last updated successfully 2023-06-05 19:25:38) and SAO/NASA ADS (last updated successfully 2023-06-05 19:25:39). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
Pingback: Weekly Papers on Quantum Foundations (42)