Relativistic Bohmian Mechanics Without a Preferred Foliation
Abstract
In nonrelativistic Bohmian mechanics the universe is represented by a probability space whose sample space is composed of the Bohmian trajectories. In relativistic Bohmian mechanics an entire class of empirically equivalent probability spaces can be defined, one for every foliation of spacetime. In the literature the hypothesis has been advanced that a single preferred foliation is allowed, and that this foliation derives from the universal wave function by means of a covariant law. In the present paper the opposite hypothesis is advanced, i.e., no law exists for the foliations and therefore all the foliations are allowed. The resulting model of the universe is basically the "union" of all the probability spaces associated with the foliations. This hypothesis is mainly motivated by the fact that any law defining a preferred foliation is empirically irrelevant. It is also argued that the absence of a preferred foliation may reduce the well known conflict between Bohmian mechanics and relativity.
 Publication:

Journal of Statistical Physics
 Pub Date:
 December 2015
 DOI:
 10.1007/s1095501513698
 arXiv:
 arXiv:1509.03463
 Bibcode:
 2015JSP...161.1268G
 Keywords:

 Bohmian mechanics;
 de BroglieBohm theory;
 Relativistic Bohmian mechanics;
 Hypersurface BohmDirac models;
 Typicality;
 Nonprobabilistic typicality;
 Quantum Physics;
 High Energy Physics  Theory
 EPrint:
 10 pages, minor changes in J. Stat. Phys (2015)