Foundations of Physics

, Volume 48, Issue 12, pp 1731–1752 | Cite as

Individual Particle Localization per Relativistic de Broglie–Bohm

  • David L. BartleyEmail author


The significance of the de Broglie/Bohm hidden-particle position in the relativistic regime is addressed, seeking connection to the (orthodox) single-particle Newton–Wigner position. The effect of non-positive excursions of the ensemble density for extreme cases of positive-energy waves is easily computed using an integral of the equations of motion developed here for free spin-0 particles in 1 + 1 dimensions and is interpreted in terms of virtual-like pair creation and annihilation beneath the Compton wavelength. A Bohm-theoretic description of the acausal explosion of a specific Newton–Wigner-localized state is presented in detail. The presence of virtual pairs found is interpreted as the Bohm picture of the spatial extension beyond single point particles proposed in the 1960s as to why space-like hyperplane dependence of the Newton–Wigner wavefunctions may be needed to achieve Lorentz covariance. For spin-1/2 particles the convective current is speculatively utilized for achieving parity with the spin-0 theory. The spin-0 improper quantum potential is generalized to an improper stress tensor for spin-1/2 particles.


Dirac de Broglie Bohm Relativistic Newton–Wigner Acausal Spin tensor Stress Pair creation Particle 



The author thanks Gordon Fleming for many discussions about Newton–Wigner localization.


  1. 1.
    Bohm, D.: A suggested interpretation of the quantum theory in terms of “hidden” variables. Phys. Rev. 85, 166 (1952)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Bohm, D.: Comments on an article of takabayasi conserning the formulation of quantum mechanics with classical pictures. Prog. Theor. Phys. 9, 273–287 (1953)ADSCrossRefGoogle Scholar
  3. 3.
    Bohm, D., Schiller, R., Tiomno, J.: A causal interpretation of the Pauli equation (A). Suppl. Nuovo Cimento 1, 48 (1955)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Bohm, D., Hiley, B.J.: Non-locality and locality in the stochastic interpretation of quantum mechanics. Phys. Rep. 172, 93–122 (1989)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    de Broglie, L.: Tentative d’Interpretation Causale et Nonlineaire de la Mechanique Ondulatoire. Gauthier-Villars, Paris (1956)zbMATHGoogle Scholar
  6. 6.
    Newton, T.D., Wigner, E.P.: Localized states for elementary systems. Rev. Mod. Phys. 21, 400 (1949)ADSCrossRefGoogle Scholar
  7. 7.
    Fleming, G.N.: Nonlocal properties of stable particles. Phys. Rev. 139, B963 (1965)ADSCrossRefGoogle Scholar
  8. 8.
    Feynman, R.P.: Space–time approach to quantum electrodynamics. Phys. Rev. 76(749), 769 (1949)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Feynman, R.P.: Quantum Electrodynamics. Benjamin, New York (1961)Google Scholar
  10. 10.
    Stückelberg, E.C.G.: Remarks on the creation of pairs of particles in the theory of relativity. Helv. Phys. Acta 14(32L), 588 (1941)Google Scholar
  11. 11.
    Holland, P.R.: The Quantum Theory of Motion. Cambridge University Press, Cambridge (1993)CrossRefGoogle Scholar
  12. 12.
    Dürr, D., Teufel, S.: Bohmian Mechanics. Springer, Heidelberg (2009)zbMATHGoogle Scholar
  13. 13.
    Tumulka, R.: On Bohmian Mechanics, Particle Creation, and Relativistic Space–Time: Happy 100th Birthday, David Bohm! arXiv:1804.08853v3 [quant-ph] (2018)
  14. 14.
    Tumulka, R.: Bohmian Mechanics, arXiv:1704.08017v1 [quant-ph] (2017)
  15. 15.
    Dürr, D., Goldstein, S., Norsen, T., Struyve, W., Zanghì, N.: Can Bohmian mechanics be made relativistic? Proc. R. Soc. A470, 20130699 (2014)ADSMathSciNetzbMATHGoogle Scholar
  16. 16.
    Hegerfeldt, G.C.: Remark on causality and particle localization. Phys. Rev. D 10, 3320 (1974)ADSCrossRefGoogle Scholar
  17. 17.
    Malament, D.B.: In defense of Dogma: why there cannot be a relativistic quantum mechanics of localizable particles. In: Clifton, R. (ed.) Perspectives on Quantum Reality, pp. 1–10. Kluwer Academic, Dordrecht (1996)Google Scholar
  18. 18.
    Fleming, G.N.: Observations on Hyperplanes: I. State Reduction and Unitary Evolution. (2003)
  19. 19.
    Wigner, E.P.: Relativistic equations in quantum mechanics. In: Nature, Mehra J. (ed.) The Physicist’s Conception of, pp. 320–330. Reidel, Dordrecht (1973)CrossRefGoogle Scholar
  20. 20.
    Fleming, G.N., Butterfield, J.: Strange positions. In: Butterfield, J., Pagonis, C. (eds.) From Physics to Philosophy, pp. 108–165. Cambridge University Press, Cambridge (1999)CrossRefGoogle Scholar
  21. 21.
    Fleming, G.N.: Observations on Hyperplanes: II. Dynamical Variables and Localization Observables. (2004)
  22. 22.
    Pryce, M.H.L.: The mass-centre in the restricted theory of relativity and its connexion with the quantum theory of elementary particles. Proc. R. Soc. Lond. A 195(1040), 62–81 (1948)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Fokker, A.D.: Relativiteitstheorie. P. Nordhoff, Gronigen (1929)zbMATHGoogle Scholar
  24. 24.
    Møller, C.: The Theory of Relativity. Oxford University Press, Oxford (1957)zbMATHGoogle Scholar
  25. 25.
    Ghose, P., Majumdar, A.S., Guha, S., Sau, J.: Bohmian trajectories for photons. Phys. Lett. A 290(5–6), 205 (2001)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    Nikolić, H.: QFT as Pilot-Wave Theory of Particle Creation and Destruction. arXiv:0904.2287v5 (2009)
  27. 27.
    Nikolić, H.: Time and Probability: From Classical Mechanics to Relativistic Bohmian Mechanics. arXiv:1309.0400 [quant-ph] (2013)
  28. 28.
    Tausk, D.V., Tumulka, R.: Can We Make a Bohmian Electron Reach the Speed of Light, at Least for One Instant? arXiv:0806.4476v4 [quant-ph] (2011)

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CincinnatiUSA

Personalised recommendations