Abstract
In 1952 Bohm presented a theory about non-relativistic point-particles that move deterministically along trajectories and showed how it reproduces the predictions of standard quantum theory. This theory was actually presented before by de Broglie in 1926, but Bohm’s particular formulation of the theory inspired Epstein to come up with a different trajectory model. The aim of this paper is to examine the empirical predictions of this model. It is found that the trajectories in this model are in general very different from those in the de Broglie-Bohm theory. In certain cases they even seem bizarre and rather unphysical. Nevertheless, it is argued that the model seems to reproduce the predictions of standard quantum theory (just as the de Broglie-Bohm theory).
Similar content being viewed by others
References
de Broglie, L.: La nouvelle dynamique des quanta. In: Électrons et Photons: Rapports et Discussions du Cinquième Conseil de Physique, Gauthier-Villars, Paris, 105 (1928). English translation: G. Bacciagaluppi and A. Valentini, Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference. Cambridge University Press, Cambridge (2009). arXiv:quant-ph/0609184
Bohm, D.: A suggested interpretation of the quantum theory in terms of “hidden” variables, I. Phys. Rev. 85, 166 (1952)
Bohm, D.: A suggested interpretation of the quantum theory in terms of “hidden” variables, II. Phys. Rev. 85, 180 (1952)
Dürr, D., Goldstein, S., Zanghì, N.: Quantum equilibrium and the origin of absolute uncertainty. J. Stat. Phys. 67, 843 (1992). arXiv:quant-ph/0308039
Goldstein, S., Struyve, W.: On the uniqueness of quantum equilibrium in Bohmian mechanics. J. Stat. Phys. 128, 1197 (2007). arXiv:0704.3070 [quant-ph]
Bohm, D.: Proof that probability density approaches |ψ|2 in causal interpretation of the quantum theory. Phys. Rev. 89, 458 (1953)
Valentini, A.: Signal-locality, uncertainty, and the subquantum H-theorem, I. Phys. Lett. A 156, 5 (1991)
Bohm, D., Hiley, B.J.: The Undivided Universe. Routledge, New York (1993)
Holland, P.R.: The Quantum Theory of Motion. Cambridge University Press, Cambridge (1993)
Dürr, D., Goldstein, S., Zanghì, N.: Quantum equilibrium and the role of operators as observables in quantum theory. J. Stat. Phys. 116, 959 (2004). arXiv:quant-ph/0308038
Dürr, D., Teufel, S.: Bohmian Mechanics. Springer, Berlin (2009)
Epstein, S.T.: The causal interpretation of quantum mechanics. Phys. Rev. 89, 319 (1952)
Epstein, S.T.: The causal interpretation of quantum mechanics. Phys. Rev. 91, 985 (1953)
Allori, V., Goldstein, S., Tumulka, R., Zanghì, N.: On the common structure of Bohmian mechanics and the Ghirardi Rimini Weber theory. Br. J. Philos. Sci. 59, 353 (2008). arXiv:quant-ph/0603027
Struyve, W., Valentini, A.: de Broglie-Bohm guidance equations for arbitrary Hamiltonians. J. Phys. A 42, 035301 (2009). arXiv:0808.0290 [quant-ph]
Bohm, D.: Comments on a letter concerning the causal interpretation of the quantum theory. Phys. Rev. 89, 319 (1953)
Deotto, E., Ghirardi, G.C.: Bohmian mechanics revisited. Found. Phys. 28, 1 (1998). arXiv:quant-ph/9704021
Holland, P.R.: New trajectory interpretation of quantum mechanics. Found. Phys. 28, 881 (1998)
Goldstein, S., Taylor, J., Tumulka, R., Zanghì, N.: Are all particles identical? J. Phys. A 38, 1567 (2005). arXiv:quant-ph/0405039
de Polavieja, G.G.: A causal quantum theory in phase space. Phys. Lett. A 220, 303 (1996)
de Polavieja, G.G.: Nonstatistical quantum-classical correspondence in phase space. Found. Phys. Lett. 9, 411 (1996)
Author information
Authors and Affiliations
Corresponding author
Additional information
Postdoctoral Fellow FWO.
Rights and permissions
About this article
Cite this article
Struyve, W. On Epstein’s Trajectory Model of Non-Relativistic Quantum Mechanics. Found Phys 40, 1700–1711 (2010). https://doi.org/10.1007/s10701-010-9475-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-010-9475-6