What is the EPR paradox? A didactic reconstruction of the article by Einstein, Podolsky and Rosen
DOI:
https://doi.org/10.55767/2451.6007.v33.n3.36001Keywords:
EPR, Quantum theory, History and philosophy, Primary sources, EntanglementAbstract
The objective of this work is to provide a didactic reconstruction of the article by Einstein, Podolsky e Rosen, introducing the theoretical aspects necessary for the understanding of the work (which are usually presented in the initial phases of Quantum Mechanics courses), discussing the structure of the original argument and explaining the paradox from the very statements taken from the article. Based on the presentation we are proposing, the EPR paradox can be presented in introductory under-graduate courses in Quantum Mechanics (for bachelors and licentiate degrees) enabling the understanding of the discussion on the completeness of quantum theory proposed by Einstein, Podolsky and Rosen and by the genesis of the concept that would later become known as quantum entanglement.
References
Auletta, G., Fortunato, M., & Parisi, G. (2009). Quantum Mechanics. New York, USA: Cambridge University Press.
Bell, J. S. (1964). On the Einstein Podolsky Rosen Paradox*. Physics Physique Fizika, 1, 195–200. https://doi.org/https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195
Bender, C. ., Brody, D. C., & Jones, H. F. (2003). Must a Hamiltonian be Hermitian? American Journal of Physics, 71(11), 1095–1102. https://doi.org/https://doi.org/10.1119/1.1574043
Bohm, D. (1952a). A suggested interpretation of the Quantum Theory in terms of “ hidden” variables.I. Physical Review, 85(2), 166-179. https://doi.org/https://doi.org/10.1103/PhysRev.85.166
Bohm, D. (1952b). A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables. II. Physical Review, 85(2), 180–193. https://doi.org/https://doi.org/10.1103/PhysRev.85.180
Bohr, N. (1935). Can Quantum-Mechanical Description of Physical Reality be Considered Complete? Phys. Rev., 48(8), 696–702. https://doi.org/10.1103/PhysRev.48.696
Bohr, Niels. (1934). Teoria atómica e a descrição da Natureza. Cambridge, England: Cambridge University Press.
Bunge, M. (1973). Filosofia da Física. Lisboa, Portugal: edições 70.
Bunge, M. (2007). Física e Filosofia (1a ed). São Paulo, Brasil: Perspectiva.
Butkov, E. (1988). Física Matemática. Rio de Janeiro, Brasil: LTC.
Chevallard, Y. (1991). La Transposition didactique: du savoir savant au savoir enseigné. Grenoble, França: La Pensée Sauvage.
Cohen-Tannoudji, C., Diu, B., & Laloë, F. (1977). Quantum Mechanics. New York, USA: John Wiley and Sons.
Cushing, J. (1994). Quantum Mechanics - Historical contingency and the Copenhaguen hegemony. Chicago, USA: University of Chicago Press.
Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47(10), 777-780. https://doi.org/10.1103/PhysRev.47.777
Freire Jr., O., Pessoa Jr., O., & Bromberg, J. L. (2011). Teoria quântica: estudos históricos e implicações culturais. São Paulo, Brasil: EDUEPB.
Freire, O. (2015). The Quantum Dissidents: Rebuilding the Foundations of Quantum Mechanics (1950-1990). New York, USA: Springer.
Gomatam, R. (2007). Niels Bohr’s interpretation and the Copenhagen interpretation - Are the two incompatible? Philosophy of Science, 74(5), 736–748. https://doi.org/10.1086/525618
Gottfried, K., & Yan, T.-M. (2003). Quantum Mechanics: Fundamentals (2 ed). New York, USA: Springer.
Griffiths, D. J. (2011). Introduction to Quantum Mechanics (2 ed). São Paulo, Brasil: Pearson.
Griffiths, R. B. (1987). Correlations in separated quantum systems: A consistent history analysis of the EPR problem. American Journal of Physics, 55(1), 11–17. https://doi.org/10.1119/1.14965
Howard, D. (2004). Who invented the “Copenhagen interpretation”? A study in mythology. Philosophy of Science, 71(5), 669–682. https://doi.org/10.1086/425941
Jammer, M. (1974). The Philosophy of Quantum Mechanics. New York, USA: John Wiley and Sons.
Jammer, M. (1966). The conceptual develpment of Quantum Mechanics. New York, USA: McGraw-Hill Book Company.
Karam, R. (2020). Schrödinger’s original struggles with a complex wave function. American Journal of Physics, 88(6), 433–438. https://doi.org/10.1119/10.0000852
Karam, R. (2021). Considerações metodológicas sobre o uso de fontes primárias no ensino de Física. Revista Brasileira de Ensino de Ciências e Matemática, 4(ed. especial), 1067–1082. https://doi.org/https://doi.org/10.5335/rbecm.v4i3.12908
Laloë, F. (2001). Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems. American Journal of Physics, 69(6), 655–701. https://doi.org/https://doi.org/10.1119/1.1356698
Landau, L. D., & Lifshitz, E. M. (1977). Quantum Mechanics: Non-Relativistic Theory (3th ed). New York, USA: Pergamon Press.
Lima, N., Cavalcanti, C., & Ostermann, F. (2021). Concepções de Dualidade Onda-Partícula: Uma proposta didática construída a partir de trechos de fontes primárias da Teoria Quântica. Revista Brasileira de Ensino de Física, 43, e20200270. https://doi.org/10.1590/1806-9126-rbef-2020-0270
Lima, N., & Karam, R. (2021). Particle velocity = group velocity: A common assumption in the different theories of Louis de Broglie and Erwin Schrödinger. American Journal of Physics, 89(5), 521–528. https://doi.org/10.1119/10.0003165
Mermin, N. D. (1985). Is the moon there when nobody looks? Reality and the quantum theory. Physics Today, 38(4), 38–47. https://doi.org/https://doi.org/10.1063/1.880968
Mostafazadeh, A. (2001). Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian. Journal of Mathematical Physics, 43(1), 205–214. https://doi.org/https://doi.org/10.1063/1.1418246
Neumann, J. Von. (1932). Mathematical Foundations of Quantum Mechanics (1st ed.). Berlin, Germany: Julius Springer.
Ostermann, F., Pereira, A., Cavalcanti, C. J. de H., & Pessoa Jr., O. (2012). Uma abordagem conceitual e fenomenológica dos postulados da física quântica. Caderno Brasileiro de Ensino de Física, 29(2), 831–863. https://doi.org/10.5007/2175-7941.2012v29nesp2p831
Reisler, D. L. (1971). The Epistemological Basis of Einstein’s, Podolsky’s, and Rosen’s Objection to Quantum Theory. American Journal of Physics, 39, 821–831. https://doi.org/10.1119/1.1986291
Sakurai, J. J., & Napolitano, J. (2013). Mecânica Quântica Moderna (2 ed). Porto Alegre, Brasil: Bookman.
Schrödinger, E. (1935). Discussion of Probability Relations between Separated Systems. Mathematical Proceedings of the Cambridge Philosophical Society, 31(4), 555–563. https://doi.org/10.1017/S0305004100013554
Schrödinger, E. (1936). Probability relations between separated systems. Mathematical Proceedings of the Cambridge Philosophical Society, 32(3), 446–452. https://doi.org/10.1017/S0305004100019137
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