The Incoherence Problem in the Many-Worlds Interpretation of Quantum Mechanics

Authors

DOI:

https://doi.org/10.37467/revhuman.v16.4782

Keywords:

Philosophy of physics, Quantum mechanics, Many Worlds Interpretation, Probability, Incoherence problem, Quantitative problem

Abstract

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 DOI: 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 DOI: 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 DOI: https://doi.org/10.4064/fm-17-1-298-329

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 DOI: 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 DOI: 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. DOI: https://doi.org/10.1063/1.3022331

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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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. DOI: https://doi.org/10.1093/bjps/47.2.159

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 DOI: 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 DOI: https://doi.org/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. DOI: https://doi.org/10.3989/arbor.2000.i659-660.1177

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. DOI: https://doi.org/10.1093/bjps/axq006

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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: 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 DOI: https://doi.org/10.1093/oxfordhb/9780195392043.013.0014

Downloads

Published

2023-02-28

How to Cite

Rubio Juan, M. (2023). The Incoherence Problem in the Many-Worlds Interpretation of Quantum Mechanics. HUMAN REVIEW. International Humanities Review / Revista Internacional De Humanidades, 16(1), 59–79. https://doi.org/10.37467/revhuman.v16.4782

Issue

Vol. 16 No. 1 (2023)

Section

Research articles

License

Those authors who publish in this journal accept the following terms:

  1. Authors will keep the moral right of the work and they will transfer the commercial rights.
  2. After 1 year from publication, the work shall thereafter be open access online on our website, but will retain copyright.
  3. In the event that the authors wish to assign an Creative Commons (CC) license, they may request it by writing to publishing@eagora.org