Abstract
Tsang and Caves suggested the idea of a quantum-mechanics-free subsystem in 2012. We contend that Sudarshan’s viewpoint on Koopman-von Neumann mechanics is realized in the quantum-mechanics-free subsystem. Since quantum-mechanics-free subsystems are being experimentally realized, Koopman-von Neumann mechanics is essentially transformed into an engineering science.
Similar content being viewed by others
Notes
I am tempted to recall here the maxim quoted in [6] and attributed to Sidney Coleman: “The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction."
References
Tsang, M., Caves, C.M.: Evading quantum mechanics: engineering a classical subsystem within a quantum environment. Phys. Rev. X 2, 031016 (2012). https://doi.org/10.1103/PhysRevX.2.031016
Koopman, B.O.: Hamiltonian systems and transformation in Hilbert space. Proc. Natl. Acad. Sci. USA 17(5), 315–318 (1931). https://doi.org/10.1073/pnas.17.5.315
Neumann, J.: Zur operatorenmethode in der klassischen mechanik. Ann. Math. 33(3), 587–642 (1932). https://doi.org/10.2307/1968537
Sudarshan, E.C.G.: Interaction between classical and quantum systems and the measurement of quantum observables. Pramana 6(3), 117–126 (1976). https://doi.org/10.1007/BF02847120
Sherry, T.N., Sudarshan, E.C.G.: Interaction between classical and quantum systems: a new approach to quantum measurement II. Theoretical considerations. Phys. Rev. D 20, 857–868 (1979). https://doi.org/10.1103/PhysRevD.20.857
Zhang, P., Zhao, Q., Horvathy, P.A.: Gravitational waves and conformal time transformations. Ann. Phys. 440, 168833 (2022). https://doi.org/10.1016/j.aop.2022.168833
Kohler, J., Gerber, J.A., Dowd, E., Stamper-Kurn, D.M.: Negative-mass instability of the spin and motion of an atomic gas driven by optical cavity backaction. Phys. Rev. Lett. 120, 013601 (2018) https://doi.org/10.1103/PhysRevLett.120.013601
Gross, C., Strumia, A., Teresi, D., Zirilli, M.(2021) Is negative kinetic energy metastable? .Phys. Rev. D . 103(11): 115025. https://doi.org/10.1103/PhysRevD.103.115025
Møller, C.B., Thomas, R.A., Vasilakis, G., Zeuthen, E., Tsaturyan, Y., Balabas, M., Jensen, K., Schliesser, A., Hammerer, K., Polzik, E.S.: Quantum back-action-evading measurement of motion in a negative mass reference frame. Nature 547(7662), 191–195 (2017). https://doi.org/10.1038/nature22980
Lépinay, L.M., Ockeloen-Korppi, C.F., Woolley, M.J., Sillanpää, M.A.: Quantum mechanics–free subsystem with mechanical oscillators. Science 372(6542), 625–629 (2021). https://doi.org/10.1126/science.abf5389
Ockeloen-Korppi, C.F., Damskägg, E., Pirkkalainen, J.-M., Clerk, A.A., Woolley, M.J., Sillanpää, M.A.: Quantum backaction evading measurement of collective mechanical modes. Phys. Rev. Lett. 117, 140401 (2016). https://doi.org/10.1103/PhysRevLett.117.140401
Mauro, D.: Topics in Koopman-von Neumann Theory (2003). https://doi.org/10.48550/arXiv.quant-ph/0301172
Chashchina, O.I., Sen, A., Silagadze, Z.K.: On deformations of classical mechanics due to Planck-scale physics. Int. J. Mod. Phys. D 29(10), 2050070 (2020). https://doi.org/10.1142/S0218271820500704
Bondar, D.I., Cabrera, R., Lompay, R.R., Ivanov, M.Y., Rabitz, H.A.: Operational dynamic modeling transcending quantum and classical mechanics. Phys. Rev. Lett. 109, 190403 (2012). https://doi.org/10.1103/PhysRevLett.109.190403
Sen, A., Parida, B.K., Dhasmana, S., Silagadze, Z.K.: Eisenhart lift of Koopman-von Neumann mechanics. J. Geom. Phys. 185, 104732 (2023). https://doi.org/10.1016/j.geomphys.2022.104732
Zurek, W.H.: Environment induced superselection rules. Phys. Rev. D 26, 1862–1880 (1982). https://doi.org/10.1103/PhysRevD.26.1862
McCaul, G., Zhdanov, D.V., Bondar, D.I.: The wave operator representation of quantum and classical dynamics (2023). https://doi.org/10.48550/arXiv.2302.13208
Morgan, P.: An algebraic approach to Koopman classical mechanics. Ann. Phys. 414, 168090 (2020). https://doi.org/10.1016/j.aop.2020.168090
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Silagadze, Z.K. Evading Quantum Mechanics à la Sudarshan: Quantum-Mechanics-Free Subsystem as a Realization of Koopman-von Neumann Mechanics. Found Phys 53, 92 (2023). https://doi.org/10.1007/s10701-023-00734-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10701-023-00734-6