Skip to main content
Springer Nature Link
Log in

Emergence of classical trajectories in quantum systems: the cloud chamber problem in the analysis of Mott (1929)

  • Published:

Abstract

We analyze the paper "The wave mechanics of \(\alpha \)-ray tracks" Mott (Proc R Soc Lond A 126:79–84, 1929), published in 1929 by N. F. Mott. In particular, we discuss the theoretical context in which the paper appeared and give a detailed account of the approach used by the author and the main result attained. Moreover, we comment on the relevance of the work not only as far as foundations of Quantum Mechanics are concerned but also as the earliest pioneering contribution in decoherence theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+
from 17,985円 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Similar content being viewed by others

Discover the latest articles, books and news in related subjects, suggested using machine learning.

Notes

  1. Sir Nevill Francis Mott (30 September 1905 to 8 August 1996) was an English physicist. He won the Nobel Prize for Physics in 1977 for his work on the electronic structure of magnetic and disordered systems. The award was shared with P. W. Anderson and J. H. Van Vleck (for further details see e.g. B. Pippard, Biographical Memoirs of Fellows of the Royal Society, 44, 314–328, 1998).

References

  • Adami, R., R. Figari, D. Finco, and A. Teta. 2006. On the asymptotic dynamics of a quantum system composed by heavy and light particles. Communications in Mathematical Physics 268(3): 819–852.

    Article MathSciNet MATH Google Scholar

  • Bacciagaluppi, G., and A. Valentini. 2009. Quantum theory at the crossroads: reconsidering the 1927 Solvay conference. Cambridge: Cambridge University Press.

    MATH Google Scholar

  • Bohr, N. 1928. The quantum postulate and the recent development of atomic theory. Nature 121: 580–590.

    Article MATH Google Scholar

  • Born, M. 1926. Zur Quantenmechanik der Stossvorgänge. Physikalische Zeitschrift 37: 863–867. (English translation reprinted in: Wheeler J.A., W. Zurek. Quantum theory and measurement. Princeton University Press, 1983).

    Article MATH Google Scholar

  • Born, M., and P. Jordan. 1925. Zur Quantenmechanik. Physikalische Zeitschrift 34: 858. (English translation reprinted in: van der Waerden B.L. Source of quantum mechanics. Dover Publications Inc., 1967).

    Article MATH Google Scholar

  • Carazza, B., and H. Kragh. 2000. Classical behavior of macroscopic bodies from quantum principles: early discussions. Archive for History Exact Sciences 55: 43–56.

    Article MathSciNet MATH Google Scholar

  • Claverie, P., and G. Jona-Lasinio. 1986. Instability of tunnelling and the concept of molecular structure in quantum mechanics: the case of pyramidal molecules and the enantiomer problem. Physical Review A 33: 2245–2253.

    Article Google Scholar

  • Cushing, J.T. 1994. Quantum mechanics, historical contingency and the Copenhagen hegemony. Chicago: The University of Chicago Press.

    MATH Google Scholar

  • Darwin, C.G. 1929. A collision problem in the wave mechanics. Proceedings of the Royal Society London A 124: 375–394.

    Article MATH Google Scholar

  • Dell’Antonio, G., R. Figari, and A. Teta. 2008. Joint excitation probability for two harmonic oscillators in dimension one and the Mott problem. Journal of Mathematical Physics 49(4): 042105.

    Article MathSciNet Google Scholar

  • Dell’Antonio, G., R. Figari, and A. Teta. 2010. A time dependent perturbative analysis for a quantum particle in a cloud chamber. Annales Henri Poincare 11(3): 539–564.

    Article MathSciNet MATH Google Scholar

  • Falkenburg, B. 1996. The analysis of particle tracks: a case for trust in the unity of Physics. Studies in History and Philosophy of Modern Physics 27(3): 337–371.

    Article Google Scholar

  • Gamow, G. 1928. Zur quantentheorie des atomkernes. Physikalische Zeitschrift 51: 204.

    Article MATH Google Scholar

  • Giulini, D., E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and H.D. Zeh. 1996. Decoherence and the appearance of a classical world in quantum theory. Berlin: Springer.

    Book MATH Google Scholar

  • Grecchi, V., A. Martinez, and A. Sacchetti. 2002. Destruction of the beating effect for a non-linear Schrödinger equation. Communications in Mathematical Physics 227: 191–209.

    Article MathSciNet MATH Google Scholar

  • Heisenberg, W. 1925. Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Physikalische Zeitschrift 33: 879–893. (English translation reprinted in: van der Waerden B.L. Source of quantum mechanics. Dover Publications Inc., 1967).

    Article MATH Google Scholar

  • Heisenberg, W. 1927. Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Physikalische Zeitschrift 43: 172–198. (English translation reprinted in: Wheeler J.A. and W. Zurek. Quantum theory and measurement. Princeton University Press, 1983).

  • Heisenberg, W. 1930. The physical principles of the quantum theory. Chicago: The University of Chicago Press.

  • Hornberger, K., and J.E. Sipe. 2003. Collisional decoherence reexamined. Physical Review A 68(012105): 1–16.

    Google Scholar

  • Jammer, M. 1989. The conceptual development of quantum mechanics, 2nd edn. New York: American Institute of Physics.

  • Joos, E., and H.D. Zeh. 1985. The emergence of classical properties through interaction with the environment. Physikalische Zeitschrift B59: 223–243.

    Google Scholar

  • Leone, M., and N. Robotti. 2004. A note on the Wilson cloud chamber (1912). European Journal of Physics 25: 781–791.

    Article Google Scholar

  • Mott, N.F. 1929. The wave mechanics of \(\alpha \)-ray tracks. Proceedings of the Royal Soceity of London A 126: 79–84. (Reprinted in: Wheeler J.A., W. Zurek. Quantum theory and measurement, Princeton University Press, 1983).

  • Robert, D. 1998. Semi-classical approximation in quantum mechanics. A survey of old and recent mathematical results. Helvetica Physica Acta 71: 44–116.

    MathSciNet Google Scholar

  • Schrödinger, E. 1978. Collected papers on wave mechanics, 2nd edn. Vermont: Chelsea Publishing Co.

  • Stepansky, B.K. 1997. Ambiguity: aspects of the wave-particle duality. The British Journal for the History of Science 30: 375–385.

    Article MathSciNet Google Scholar

  • von Neumann, J. 1932. Mathematische Grundlagen der Quantenmechanik. Berlin: Springer. (English translation Mathematical foundations of quantum mechanics, Princeton University Press, 1955).

    MATH Google Scholar

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Scienze Fisiche, Università di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia, Edificio 6, 80126, Napoli, Italy

    Rodolfo Figari

  2. Istituto Nazionale di Fisica Nucleare, Complesso Universitario di Monte S. Angelo, Via Cintia, Edificio 6, 80126, Naples, Italy

    Rodolfo Figari

  3. Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università di L’Aquila, via Vetoio (Coppito 1), 67010, L’Aquila, Italy

    Alessandro Teta

Authors
  1. Rodolfo Figari
  2. Alessandro Teta

Corresponding author

Correspondence to Rodolfo Figari.

Additional information

Communicated by : T. Sauer.

About this article

Cite this article

Figari, R., Teta, A. Emergence of classical trajectories in quantum systems: the cloud chamber problem in the analysis of Mott (1929). Arch. Hist. Exact Sci. 67, 215–234 (2013). https://doi.org/10.1007/s00407-012-0111-z

Download citation

  • Received:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1007/s00407-012-0111-z

Keywords

AltStyle によって変換されたページ (->オリジナル) /