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arXiv · 1505.02844

Bohmian Mechanics for a Degenerate Time Foliation

Ward Struyve·Roderich Tumulka
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Abstract

The version of Bohmian mechanics in relativistic space-time that works best, the hypersurface Bohm--Dirac model, assumes a preferred foliation of space-time into spacelike hypersurfaces (called the time foliation) as given. We consider here a degenerate case in which, contrary to the usual definition of a foliation, several leaves of the time foliation have a region in common. That is, if we think of the time foliation as a 1-parameter family of hypersurfaces, with the hypersurfaces moving towards the future as we increase the parameter, a degenerate time foliation is one for which a part of the hypersurface does not move as we increase the parameter. We show that the hypersurface Bohm--Dirac model still works in this situation; that is, we show that a Bohm-type law of motion can still be defined, and that the appropriate $|\psi|^2$ distribution is still equivariant with respect to this law.

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Ward Struyve, Roderich Tumulka. 2015-05-12. Bohmian Mechanics for a Degenerate Time Foliation. https://doi.org/10.1007/s40509-015-0048-4

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