Nonlocality, Lorentz invariance, and Bohmian quantum theory

We discuss the problem of finding a Lorentz invariant extension of Bohmian mechanics. Due to the nonlocality of the theory there is (for systems of more than one particle) no obvious way to achieve such an extension. We present a model invariant under a certain limit of Lorentz transformations, a limit retaining the characteristic feature of relativity, the nonexistence of absolute time, i.e., of simultaneity. The analysis of this model exemplifies an important property of any Bohmian quantum theory: the quantum equilibrium distribution ρ=‖ψ${\mathrm{\Vert }}^2$ cannot simultaneously be realized in all Lorentz frames of reference. © 1996 The American Physical Society.