Ehrenfest’s Theorem revisited
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Abstract
Historically, Ehrenfest’s theorem (1927) is the first one which shows that classical physics can emerge from quantum physics as a kind of approximation. We recall the theorem in its original form, and we highlight its generalizations to the relativistic Dirac particle and to a particle with spin and izospin. We argue that apparent classicality of the macroscopic world can probably be explained within the framework of standard quantum mechanics.
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References
Arodź, H., 1982. Colored, spinning classical particle in an external non-abelian gauge field. Physics Letters B, 116(4), pp.251–254. Available at: https://doi.org/10.1016/0370-2693(82)90336-7.
Arodź, H. and Ruijgrok, T., 1988. On a Classical Limit of the Dirac Equation with an External Electromagnetic Field. Part I. Proper-Time Evolution, Lorentz Covariant Expectation Values and Classical Equations of Motion. Acta Physica Polonica B [Online], 19(2), pp.99–140. Available at: <http://www.actaphys.uj.edu.pl/fulltext?series=Reg&vol=19&page=99> [Accessed 21 May 2019].
Białynicki-Birula, I., Cieplak, M. and Kamiński, J., 1991. Teoria kwantów: mechanika falowa [Quantum Theory: Wave Mechanics], Biblioteka Fizyki t. 13. Warszawa: Wydawnictwo Naukowe PWN.
Curtright, T., Fairlie, D. and Zachos, C., 2014. A Concise Treatise on Quantum Mechanics in Phase Space. New Jersey: World Scientific.
Ehrenfest, P., 1927. Bemerkung über die angenäherte Gültigkeit der klassischen Mechanik innerhalb der Quantenmechanik. Zeitschrift für Physik, 45(7), pp.455–457. Available at: https://doi.org/10.1007/BF01329203.
Ghirardi, G.C., Pearle, P. and Rimini, A., 1990. Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles. Physical Review A, 42(1), pp.78–89. Available at: https://doi.org/10.1103/PhysRevA.42.78.
Heller, M., 2018. What does it mean ‘to exist’ in physics? Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) [Online], (65), pp.9–22. Available at: <http://zfn.edu.pl/index.php/zfn/article/view/436> [Accessed 28 June 2019].
Hilgevoord, J. and Wouthuysen, S.A., 1963. On the spin angular momentum of the Dirac particle. Nuclear Physics, 40, pp.1–12. Available at: https://doi.org/10.1016/0029-5582(63)90246-3.
Landau, L.D. and Lifshitz, E.M., 1971. The Classical Theory of Fields [Online] (M. Hamermesh. Trans.). Third Edition, Course of Theoretical Physics 2. Oxford ; New York et al.: Pergamon Press. Available at: <http://archive.org/details/TheClassicalTheoryOfFields>.
Rosen, G., 1969. Formulations of Classical and Quantum Dynamical Theory, Mathematics in science and engineering v. 60. New York: Academic Press.
Schiff, L.I., 1968. Quantum Mechanics. Third Edition [Online]. New York [etc.]: McGraw-Hill. Available at: <http://archive.org/details/QuantumMechanics_500> [Accessed 28 June 2019].
Siegel, W., 1976. On the classical limit of quantum mechanics. Acta Physica Polonica B [Online], 7(1), pp.29–38. Available at: <http://www.actaphys.uj.edu.pl/fulltext?series=Reg&vol=7&page=29> [Accessed 21 May 2019].
Wong, S.K., 1970. Field and particle equations for the classical Yang-Mills field and particles with isotopic spin. Il Nuovo Cimento A, 65(4), pp.689–694. Available at: https://doi.org/10.1007/BF02892134.
Zeh, H.D., 1970. On the interpretation of measurement in quantum theory. Foundations of Physics, 1(1), pp.69–76. Available at: https://doi.org/10.1007/BF00708656.
Zurek, W.H., 2003. Decoherence, einselection, and the quantum origins of the classical. Reviews of Modern Physics, 75(3). Available at: https://doi.org/10.1103/RevModPhys.75.715.
Zurek, W.H., 2009. Quantum Darwinism. Nature Physics, 5(3), pp.181–188. Available at: https://doi.org/10.1038/nphys1202.