Skip to main content
Log in

The Stern–Gerlach Phenomenon According to Classical Electrodynamics

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

We present a description of the Stern–Gerlach type experiments using only the concepts of classical electrodynamics and the Newton’s equations of motion. The quantization of the projections of the spin (or the projections of the magnetic dipole) is not introduced in our calculations. The main characteristic of our approach is a quantitative analysis of the motion of the magnetic atoms at the entrance of the magnetic field region. This study reveals a mechanism which modifies continuously the orientation of the magnetic dipole of the atom in a very short time interval, at the entrance of the magnetic field region. The mechanism is based on the conservation of the total energy associated with a magnetic dipole which moves in a non uniform magnetic field generated by an electromagnet. A detailed quantitative comparison with the (1922) Stern–Gerlach experiment and the didactical (1967) experiment by J.R. Zacharias is presented. We conclude, contrary to the original Stern–Gerlach statement, that the classical explanations are not ruled out by the experimental data.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dechoum, K., França, H.M., Malta, C.P.: Classical aspects of Pauli–Schrödinger equation. Phys. Lett. A 93, 248 (1998)

    Google Scholar 

  2. Rabi, I.I., Ramsey, N.F., Schwinger, J.: Use of rotating coordinates in magnetic resonance problems. Rev. Mod. Phys. 26, 167 (1954)

    Article  MATH  ADS  Google Scholar 

  3. Bohm, D, Schiller, R., Tiomno, J.: A causal interpretation of the Pauli equation. Nuovo Cimento Suppl. 1, 48 (1955)

    Article  MathSciNet  Google Scholar 

  4. Schiller, R.: Quasi-classical theory of the spinning electron. Phys. Rev. 125, 1116 (1962)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. Dewdney, C., Holland, P.R., Kyprianidis, A., Vigier, J.P.: Spin and non-locality in quantum mechanics. Nature 336, 536 (1988)

    Article  ADS  Google Scholar 

  6. Dewdney, C., Holland, P.R., Kyprianidis, A.: What happens in a spin measurement? Phys. Lett. A 119, 259 (1986)

    Article  ADS  Google Scholar 

  7. Holland, P.R.: The Quantum Theory of Motion. Cambridge Univ., Cambridge (1993), chapter 9

    Google Scholar 

  8. Boyer, T.H.: Classical spinning magnetic dipole in classical electrodynamics with classical electromagnetic zero-point radiation. Phys. Rev. A 29, 2389 (1984)

    Article  ADS  Google Scholar 

  9. Barranco, A.V., Brunini, S.A., França, H.M.: Spin and paramagnetism in classical stochastic electrodynamics. Phys. Rev. A 39, 5492 (1989)

    Article  ADS  Google Scholar 

  10. de la Peña, L., Cetto, A.M.: In: van der Merwe, A. (ed.) The Quantum Dice. An Introduction to Stochastic Electrodynamics. Kluwer, Dordrecht (1996)

    Google Scholar 

  11. Marshall, T.W.: Random electrodynamics. Proc. R. Soc. Ser. A 276, 475 (1963)

    Article  MATH  ADS  Google Scholar 

  12. França, H.M., Santos, R.B.B.: Anomalous paramagnetic behaviour: the role of zero-point electromagnetic fluctuations. Phys. Lett. A 238, 227 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. França, H.M., Santos, R.B.B.: Resonant paramagnetic enhancement of the thermal and zero-point Nyquist noise. Phys. Lett. A 251, 100 (1999)

    Article  ADS  Google Scholar 

  14. Stern, O.: Z. Phys. 7, 249 (1921). See the English translation: A way towards the experimental examination of spatial quantisation in a magnetic field, Z. Phys. D 10, 114 (1988)

    Article  ADS  Google Scholar 

  15. Gerlach, W., Stern, O.: Der experimentelle Nachweis des magnetischen Moments des Silberatoms. Z. Phys. 8, 110 (1921)

    ADS  Google Scholar 

  16. Gerlach, W., Stern, O.: Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld. Z. Phys. 9, 349 (1922)

    Article  ADS  Google Scholar 

  17. Taylor, J.B.: Magnetic moments of the alkali metal atoms. Phys. Rev. 28, 576 (1926). See in particular the comments concerning the width of the slits on page 580

    Article  ADS  Google Scholar 

  18. Rabi, I.I.: Refraction of beams of molecules. Nature 123, 163 (1929)

    Article  MATH  ADS  Google Scholar 

  19. Fraser, R.G.J.: Molecular Rays. Cambridge Univ. Press, London (1931). See pages 117 and 150

    Google Scholar 

  20. Rabi, I.I.: Zur methode der ablenkung von molekularstrahlen. Z. Phys. 54, 190 (1929). See the Fig. 5 on page 196

    Article  ADS  Google Scholar 

  21. Jackson, J.D.: Classical Electrodynamics, 2nd edn. Wiley, New York (1975). Section 5.7

    MATH  Google Scholar 

  22. Smith, K.F.: Molecular Beams. Methuen & Co Ltd., London (1955). Chapters 2 and 4

    MATH  Google Scholar 

  23. French, A.P., Taylor, E.F.: An Introduction to Quantum Physics. Norton, New York (1978). Chapter 10

    Google Scholar 

  24. Estermann, I., Simpson, O.C., Stern, O.: The magnetic moment of the proton. Phys. Rev. 52, 535 (1937)

    Article  ADS  Google Scholar 

  25. Rañada, A.F., Rañada, M.F.: The Stern–Gerlach quantum-like behaviour of a classical charged particle. J. Phys. A 12, 1419 (1979)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Humberto M. França.

Rights and permissions

Reprints and permissions

About this article

Cite this article

França, H.M. The Stern–Gerlach Phenomenon According to Classical Electrodynamics. Found Phys 39, 1177–1190 (2009). https://doi.org/10.1007/s10701-009-9338-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-009-9338-1

Keywords

Navigation