Foundations of Physics

, Volume 49, Issue 12, pp 1365–1371 | Cite as

Simple Explanation of the Classical Limit

  • Alejandro A. HniloEmail author


The classical limit is fundamental in quantum mechanics. It means that quantum predictions must converge to classical ones as the macroscopic scale is approached. Yet, how and why quantum phenomena vanish at the macroscopic scale is difficult to explain. In this paper, quantum predictions for Greenberger–Horne–Zeilinger states with an arbitrary number q of qubits are shown to become indistinguishable from the ones of a classical model as q increases, even in the absence of loopholes. Provided that two reasonable assumptions are accepted, this result leads to a simple way to explain the classical limit and the vanishing of observable quantum phenomena at the macroscopic scale.


Foundations of quantum mechanics Classical limit GHZ states 



Many thanks to Prof. Federico Holik for a critical reading of the first version of this manuscript, his observations and advices. This contribution received support from the Grants N62909-18-1-2021 Office of Naval Research Global (USA), and PIP 2017-027C CONICET (Argentina).


  1. 1.
    Bagarello, F., Passante, R., Trapani, C. (Ed.) Non Hermitian Hamiltonians in quantum physics. In: Selected Contributions from the 15th Conference on Non-Hermitian Hamiltonians in Quantum Physics, Palermo, Italy, Springer Proceedings in Physics, Vol. 184, 18–23 May 2015 (2016)Google Scholar
  2. 2.
    Ghirardi, G.C., Rimini, A., Weber, T.: Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D 34, 470 (1986)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Everett, H.: Relative state formulation of quantum mechanics. Rev. Mod. Phys. 29, 454 (1957)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Bassi, A., Lochan, K., Satin, S., et al.: Models of wave-function collapse, underlying theories and experimental tests. Rev. Mod. Phys. 85, 471 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    Belot, G., Earman, J.: Chaos out of order: quantum mechanics, the correspondence principle and chaos. Stud. Hist. Philos. Mod. Phys. 28, 147 (1997)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Castagnino, M., Lombardi, O.: Non-integrability and mixing in quantum systems. Stud. Hist. Philos. Mod. Phys. 38, 482 (2007)CrossRefGoogle Scholar
  7. 7.
    David Mermin, N.: Extreme quantum entanglement in a superposition of macroscopically distinct states. Phys. Rev. Lett. 65, 1838 (1990)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Hnilo, A.: On testing objective local theories by using GHZ states. Found. Phys. 24, 139 (1994)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Margalit, Y., et al.: Analysis of a high-stability Stern-Gerlach spatial fringe interferometer. New J. Phys. 21, 073040 (2019)ADSCrossRefGoogle Scholar
  10. 10.
    Gisin, N., Gisin, B.: A local variable model for entanglement swapping exploiting the detection loophole. Phys. Lett. A 297, 279 (2002)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Hepp, K.: Quantum theory of measurement and macroscopic observables. Helv. Phys. Acta 45, 237 (1972)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.CEILAP, Centro de Investigaciones en Láseres y Aplicaciones, UNIDEF (MINDEF-CONICET), CITEDEFVilla MartelliArgentina

Personalised recommendations