Counterfactuality and the physical reality: lessons from quantum mechanics

Auteurs

DOI :

https://doi.org/10.51359/2357-9986.2022.248685

Mots-clés :

counterfactual definiteness, interaction-free measurements, counterfactuality, metaphysics, quantum mechanics

Résumé

In this essay, I'll present an example of counterfactual physical phenomena. More precisely, counterfactual definiteness and interaction-free measurements in quantum mechanics. The example used will be the Elitzur-Vaidman bomb testing experiment, which shows how we can probe the properties of objects, even when they have not been measured, i. e., counterfactual measurements. This type of physical phenomenon seems to operate by the same laws of causality as counterfactual reasoning in decision-making. After all, how can something that doesn't happen affect the real world? I suggest that some mathematical tools used in quantum mechanics may be of interest to those who wish to better model counterfactual possibilities in the decision process or philosophers interested in better understanding the metaphysical implications of quantum mechanics.

Biographie de l'auteur

Nicholas Kluge Corrêa, Pontifícia Universidade Católica do Rio Grande do Sul (PUC-RS), Programa de Pós-graduação em Filosofia

Corrêa, N. K. é doutorando em Filosofia pela PPGF-PUCRS, 2020 - Mestre em Engenharia Elétrica pela Pontifícia Universidade Católica do Rio Grande do Sul - PUCRS. Minha pesquisa gira em torno da ética da IA e do problema do alinhamento de valores. Atualmente filiado ao Programa de Pós-graduação em Filosofia da PUCRS.

Références

AERTS, D.; SOZZO, S. From ambiguity aversion to a generalized expected utility. Modeling preferences in a quantum probabilistic framework. J. Math. Psychol, 74, 2016, 117-127.

AERTS, D.; HAVEN, E.; SOZZO, S. A proposal to extend expected utility in a quantum probabilistic framework. Econ. Theory, 2017. doi 10.1007/s00199-017-1051-2

AERTS, D.; GERIENTE, S.; MOREIRA; C.; SOZZO, S. Testing ambiguity and Machina preferences within a quantum-theoretic framework for decision-making. Journal of Mathematical Economics, 78, 2018, 176-185.

AHARONOV, Y.; VAIDMAN, L. Properties of a quantum system during the time interval between two measurements. Phys. Rev. A, 41, 11, 1990. doi:https://doi.org/10.1103/PhysRevA.41.11

Carsten, R.; Wolfgang, A.; Emary, C.; Meschede, D.; Alberti, A. Atomic bomb testing: the Elitzur–Vaidman experiment violates the Leggett–Garg inequality. Applied Physics B, 123 (1), 12, 2016. doi:10.1007/s00340-016-6581-y

DIMITROVA, T.; WEIS, A. The wave–particle duality of light: a demonstration experiment. Am. J. Phys, 76, 2008 137–142.

DIRAC, P. Principles of Quantum Mechanics. Oxford, UK, The Clarendon Press, 1930.

ELITZUR, A.; VAIDMA, L. Quantum mechanical interaction-free measurements. Foundations of Physics, 23 (7), 1993, 987–997. doi:10.1007/BF00736012

EVERETT, H. Relative State Formulation of Quantum Mechanics. Reviews of Modern Physics, 29, 1957, 454–462.

GRIFFIN, M. Leibniz, God and Necessity. Cambridge, UK, Cambridge University Press, 2012. doi:10.1017/CBO9781139022286

GRIFFITHS, R. Quantum Counterfactuals and Locality. Foundations of Physics, Springer Nature, 42 (5), 2012, 674–684. doi:10.1007/s10701-012-9637-9. ISSN 0015-9018

HERNANDEZ, H. Probability Density Functions of Imaginary and Complex Random Variables. Report number: FRR 2019-09, 2019. doi.10.13140/RG.2.2.20867.66083.

HUME, D. An Enquiry Concerning Human Understanding. Beauchamp, T. L. (Ed), Oxford, UK, Oxford University Press, 1999.

KONG, F.; JU, C.; HUANG, P.; et al. Experimental Realization of High-Efficiency Counterfactual Computation. Physical Review Letters, 115 (8), 2015, 080501. doi:10.1103/PhysRevLett.115.080501.

KWIAT, P. G.; WEINFURTER, H.; HERZOG, T.; ZEILINGER, A.; KASEVICH, M. A. Interaction-free Measurement. Phys. Rev. Lett, 74 (24), 1995, 4763–4766. doi:10.1103/PhysRevLett.74.4763

LIU, Y., JU, L., LIANG, X., et al. Experimental Demonstration of Counterfactual Quantum Communication. Physical review letters, 109, 2012, 030501. doi:10.1103/PhysRevLett.109.030501.

MITCHISON, G.; JOZSA, R. Counterfactual computation. Proceedings of the Royal Society of London A, 457, 2001, 1175–1193. doi:10.1098/rspa.2000.0714

PEREIRA, A.; OSTERMANN, F.; CAVALCANTI, C. On the use of a virtual Mach–Zehnder interferometer in the teaching of quantum mechanics. Physics Education, 44 (3), 2009, 281–291. doi:10.1088/0031-9120/44/3/008

PUTNAM, W. P. Noninvasive electron microscopy with interaction-free quantum measurements. Physical Review A, 80 (4), 2009. doi:10.1103/PhysRevA.80.040902

SCHLOSSHAUER, M. Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev. Mod. Phys, 76(4), 2005, 1267–1305. doi:10.1103/RevModPhys.76.1267

SCHRÖDINGER, E. An Undulatory Theory of the Mechanics of Atoms and Molecules. Physical Review, 28 (6), 1926, 1049–1070. doi:10.1103/PhysRev.28.1049

SUDARSHAN, E. C. G.; MISRA, B. The Zeno's paradox in quantum theory. Journal of Mathematical Physics, 18 (4), 1977, 756–763. doi:10.1063/1.523304

VAIDMAN, L. The Meaning of the Interaction-Free Measurements. Foundations of Physics, 33(3), 2003. doi: 10.1023/A:1023767716236

VAIDMAN, L. Counterfactuals in Quantum Mechanics. In Compendium of Quantum Physics, D. Greenberger, K. Hentschel, F. Weinert (Eds). Springer, Berlin, Heidelberg, 2009, 132 – 136.

WHITE, A. G. Interaction-free imaging. Physical Review A, 58 (1), 1998, 605–613. doi:10.1103/PhysRevA.58.605.

YUKALOV, V. I.; SORNETTE, D. Quantitative Predictions in Quantum Decision Theory. In IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48(3), 2018, 366-381. doi: 10.1109/TSMC.2016.2596578.

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Publiée

2022-05-03

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Dossiê temático sobre Epistemologia, Filosofia da Ciência e Naturalismo