The Incoherence Problem in the Many-Worlds Interpretation of Quantum Mechanics
Keywords:
Philosophy of physics, Quantum mechanics, Many Worlds Interpretation, Probability, Incoherence problem, Quantitative problemAbstract
The Many Worlds Interpretation of Quantum Mechanics has been faced since its conception with the problem of how to reconcile the probabilistic nature of quantum theory with a deterministic description of the Universe in which all possibilities are actualised. This paper seeks to present the status of the problem through the solutions proposed by Lev Vaidman and David Deutsch and to relate them, as well as to present probability as an epistemological postulate, in accordance with the subjectivistic interpretation.
References
Albert, D. (2010). Probability in the Everett Picture. En S. Saunders et al. (Eds), Many Worlds? Everett, Quantum Theory, and Reality (pp. 355-368). Oxford Academic. https://doi.org/10.1093/acprof:oso/9780199560561.003.0013
Arana, J. (2002). El panteísmo de Erwin Schrödinger. Diálogos, 37(79), 11-34. https://revistas.upr.edu/index.php/dialogos/article/view/19643
Arana, J. (2012). El problema de la causalidad en la mecánica cuántica. Eikasia: revista de filosofía, 43, 17-34.
Barrett, J. (2018). “Everett’s Relative-State Formulation of Quantum Mechanics, The Stanford Encyclopedia of Philosophy (Winter 2018 Edition), Edward N. Zalta (Ed.). https://plato.stanford.edu/archives/win2018/entries/qm-everett/
Bernoulli, J. (1713). Ars conjectandi. En Die Werke von Jakob Bernoulli, Basel Naturforschende Gesellschaft, 1975. Traducción al inglés: Sung, B. (1996). Translations from James Bernoulli. Harvard University, Tecnical Report nº 2. Traducción al castellano: Rivadulla, A. (1993). Teoría de probabilidades. Universidad Complutense de Madrid. https://eprints.ucm.es/id/eprint/57575/1/ARS%20CONJECTANDI.pdf
Bohr, N. (1988). La teoría atómica y la descripción de la Naturaleza (M. Ferrero, Trad.). Alianza Editorial.
Cassinello, A. (1994). La interpretación de los muchos universos de la mecánica cuántica. Apuntes históricos. Arbor CXLVIII, 584, 47-68.
Cassinello, A., Sánchez Gómez, J. L. (2012). La realidad cuántica. Crítica.
Davies, P., Brown, J. (1989). El espíritu en el átomo. Alianza Editorial.
Dawid, R., & Thébault, K. P. Y. (2014). Against the Empirical Viability of the Deutsch-Wallace-Everett Approach to Quantum Mechanics. Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics, 47(1), 55-61. https://doi.org/10.1016/j.shpsb.2014.05.005
De Finetti, B. (1931). Sul significato soggetivo della probabilità. Fundamenta Mathematicae, 17, 298-329. En la traducción de B. Torretti (2020), Sobre el significado subjetivo de la probabilidad. Revista de Filosofía, 58, 171-198. https://revistafilosofia.uchile.cl/index.php/RDF/article/view/44080/46095
Deutsch, D. (1985). Quantum Theory as a Universal Physical Theory. International Journal of Theoretical Physics, 24(1), 1-41. https://doi.org/10.1007/BF00670071
Deutsch, D. (1997). The Fabric of Reality. Penguin Books.
Deutsch, D. (1999). Quantum Theory of Probability and Decisions. Proceedings of the Royal Society. Mathematical, Physical & Engineering Sciences, 455(1988), 3129-3137. https://doi.org/10.1098/rspa.1999.0443
DeWitt, B. S. (1970). Quantum mechanics and reality. Could the solution to the dilemma of indeterminism be a universe in which all possible outcomes of an experiment actually occur? Physics Today, 23(9), 155-165.
DeWitt, B. S. y Graham, N. (Eds.). (1973). The Many-Worlds Interpretation of Quantum Mechanics. Princeton University Press.
Elitzur, A. C. y Vaidman, L. (1993). Quantum Mechanical Interaction-Free Measurements. Found Phys 23, 987–997. https://doi.org/10.1007/BF00736012
Everet, III, H. (1957). “Relative State” Formulation of Quantum Mechanics. Reviews of Modern Physics, 29(3), 454-462. https://doi.org/10.1103/RevModPhys.29.454
Gherab Martín, K. J. (2020). Biología y filosofía de la complementariedad en Niels Bohr. Bajo Palabra, (24), 449–474. https://doi.org/10.15366/bp.2020.24.023
Gómez Pin, V. (2019). Tras la física. Arranque jónico y renacer cuántico de la filosofía. Abada Editores.
Greaves, H. (2004). 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. https://doi.org/10.1016/j.shpsb.2004.04.006
Groisman, B., Hallakoun, N. y Vaidman, L. (2013). The measure of existence of a quantum world and the Sleeping Beauty Problem. Analysis, 73(4), 695-706. https://doi.org/10.1093/analys/ant072
Lewis, P. J. (2007). Uncertainty and Probability for Branching Selves. Studies in History and Philosophy of Science Part B, 38(1), 1-14. https://doi.org/10.1016/j.shpsb.2006.02.001
Lockwood, M. (1996). “Many Minds” Interpretations of Quantum Mechanics. The British Journal for the Philosophy of Science, 47(2), 159-188.
McQueen, K. J. y Vaidman, L. (2019). In defence of the self-location uncertainty account of probability in the many-worlds interpretation. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 66, 14-23. https://doi.org/10.1016/j.shpsb.2018.10.003
McQueen, K. J. y Vaidman, L. (2020). How the Many Worlds Interpretation Brings Common Sense to Paradoxical Quantum Experiments. En R. Peels, J. de Ridder & R. van Woudenberg (Eds.), Scientific Challenges to Common Sense Philosophy (Chapter 3). Routledge. DOI:10.4324/9781351064224-3
Penrose, R. (1991). La nueva mente del emperador (J. García, Trad.). Penguin Random House.
Pérez Marcos, M. (2020). El universo inquieto de Max Born. En J. Arana. (Dir.), La cosmovisión de los grandes científicos del siglo XX (pp. 136-148). Tecnos.
Poundstone, W. (2015). El dilema del prisionero (D. Manzanares, Trad.). Alianza Editorial.
Ramsey, F. (1926). “Truth and Probability”. En The Foundations of Mathematics and Other Logical Essays, R.B. Braithwaite (Ed.). Kegan Paul, Trench, Trubner, & Co., 1931.
Rovelli, C. (2022). Helgoland (P. González, Trad.). Anagrama.
Sánchez Cañizares, J. (2020). Werner Heisenberg: entre incertidumbre e indeterminación. En J. Arana (Dir.), La cosmovisión de los grandes científicos del siglo XX (pp. 149-159). Tecnos.
Sánchez Gómez, J. L. (2000). Interpretación actual de la teoría cuántica: de los muchos universos a las historias consistentes. Arbor CLXVII, 659-660, 475-488.
Schrödinger, E. (2001). La nueva mecánica ondulatoria y otros escritos (J. Arana, Ed.). Editorial Biblioteca Nueva.
Selleri, F. (1986). El debate de la teoría cuántica (M. Ferrero, Trad.). Alianza Editorial.
Tappendent, P. (2011). Evidence and Uncertainty in Everett’s Multiverse. British Journal for the Philosophy of Science, 62(1), 99-123.
Vaidman, L. (2000). Discussion: Byrne and Hall on Everett and Chalmers. arXiv: Quantum Physics. https://doi.org/10.48550/arXiv.quant-ph/0001057
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), 245-261. https://doi.org/10.1080/02698599808573600
Vaidman, L. (2001). Probability and the Many-Worlds Interpretation of Quantum Theory. ArXiv: Quantum Physics. https://doi.org/10.48550/arXiv.quant-ph/0111072
Vaidman L. (2009) Interaction-Free Measurements (Elitzur—Vaidman, EV IFM). In D. Greenberger, K. Hentschel y F. Weinert (Eds.), Compendium of Quantum Physics (pp. 317-322). Springer. https://doi.org/10.1007/978-3-540-70626-7_98
Vaidman, L. (2012) Probability in the Many-Worlds Interpretation of Quantum Mechanics. In Y. Ben-Menahem y M. Hemmo (Eds.), Probability in Physics. The Frontiers Collection (pp. 299-311). Springer. https://doi.org/10.1007/978-3-642-21329-8_18
Vaidman, L. (2019). Ontology of the wave function and the many-worlds interpretation. En O. Lombardi, S. Fortin, C. López, & F. Holik (Eds.), Quantum Worlds: Perspectives on the Ontology of Quantum Mechanics (pp. 93-106). Cambridge: Cambridge University Press. https://doi.org/10.1017/9781108562218.007
Vaidman, L. (2021). "Many-Worlds Interpretation of Quantum Mechanics". The Stanford Encyclopedia of Philosophy (Fall 2021 Edition), Edward N. Zalta (Ed.). https://plato.stanford.edu/archives/fall2021/entries/qm-manyworlds
Wallace, D. (2003). 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. https://doi.org/10.1016/S1355-2198(03)00036-4
Wallace, D. (2007). 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. https://doi.org/10.1016/j.shpsb.2006.04.008
Wallace, D. (2011). The Everett Interpretation. [Preprint]. PhilSci Archive, 1-25. http://philsci-archive.pitt.edu/id/eprint/8888
Wallace, D. (2013). The Evertt Interpretation. En R. Batterman (Ed.), The Oxford Handbook of Philosophy of Physics. (pp. 460-488). Oxford Handbooks. https://doi.org/10.1093/oxfordhb/9780195392043.013.0014