Abstract
In this paper we shall argue that conformal transformations give some new aspects to a metric and changes the physics that arises from the classical metric. It is equivalent to adding a new potential to relativistic Hamilton–Jacobi equation. We start by using conformal transformations on a metric and obtain modified geodesics. Then, we try to show that extra terms in the modified geodesics are indications of a background force. We obtain this potential by using variational method. Then, we see that this background potential is the same as the Bohmian non-local quantum potential. This approach gives a method stronger than Bohm’s original method in deriving Bohmian quantum potential. We do not use any quantum mechanical postulates in this approach.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D Bohm, Phys. Rev. 85(2), 166 (1952)
P R Holland, The quantum theory of motion (Cambridge University Press, Cambridge, 1993)
D Bohm, Wholeness and the implicate order (Routledge & Kegan Paul, 1980)
D Bohm and B J Hiley, The undivided universe: An ontological interpretation of quantum theory (Routledge, 1993)
J Dunningham and V Vedral, Phys. Rev. Lett. 99, 180404 (2007)
D Dürr, S Goldstein and N Zanghi, Quantum physics without quantum philosophy (Springer, 2013)
J Bell, Rev. Mod. Phys. 38, 3 (1966)
J Bell, Beables for quantum field theory, CERN-TH, 4035/84 (1984)
H Nikolic, Found. Phys. Lett. 17(4), 363 (2004)
H Nikolic, Found. Phys. Lett. 18(6), 549 (2005)
L De Broglie, Ann. de la Fondation Louis de Broglie 12(4) (1987)
R D Carrol, Fluctuations, information, gravity and the quantum potential (Springer, 2006)
D Bohm and B J Hiley, Found. Phys. 12(10), 1001 (1982)
D Bohm, Wholeness and the implicate order (Routledge, 1980)
R M Wald, General relativity (The University of Chicago Press, 1984)
R Penrose, The road to reality: A complete guide to the laws of the universe (Jonathan Cape, London, 2004)
M Atiq, M Karamian, and M Golshani, Found. Phys. 39, 33 (2009)
M Atiq, M Karamian, and M Golshani, Ann. de la Fond. Louis de Broglie 34, 67 (2009)
Here by classical quantities we mean quantities that can be defined without considering background field ψ(x). The quantity Q is defined by using the background field ψ(x); But m and p are definable as in the classical world.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
RAHMANI, F., GOLSHANI, M. & SARBISHEI, M. Deriving relativistic Bohmian quantum potential using variational method and conformal transformations. Pramana - J Phys 86, 747–761 (2016). https://doi.org/10.1007/s12043-015-1076-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12043-015-1076-7