Bohm's deterministic theory was designed to be equivalent to standard QM, but what I'm not sure about is whether that includes Von Neumann's rules. Von Neumann's rules for the evolution of the wave function are roughly described by: Between measurements, the wave function evolves according to Schrodinger's equation. If the wave function is [itex]\psi[/itex] immediately before a measurement, then after measuring an observable [itex]O[/itex] to have eigenvalue [itex]\lambda[/itex], the wave function will be equal to [itex]\psi'[/itex], which is the result of projecting [itex]\psi[/itex] onto the subspace of the Hilbert space where [itex]O[/itex] has eigenvalue [itex]\lambda[/itex] I don't want to argue about whether the second process, called "wave function collapse", is physical, or just epistemological, or just a rule of thumb with no particular meaning. But what I do want to know is whether Von Neumann's rules are consistent with Bohmian mechanics. In Bohmian mechanics, there is no collapse, because the particle is assumed to always have a definite position (and the assumption is made that any kind of measurement can be understood in terms of one or more position measurements). The wave function [itex]\psi[/itex] has a double role: (1) [itex]|psi(x}|^2[/itex] gives the distribution of possible values for the position variable [itex]x[/itex], and (2) the wave function acts as a "pilot wave", affecting the trajectory of the particle. The reason that I'm not certain about the equivalence of Bohmian mechanics and Von Neumann's QM is because after a measurement of position, according to Von Neumann, the wave function is now a delta-function (or at least is described by a highly localized function). But in Bohmian mechanics, there is no collapse, so the wave function continues to be whatever it was before the position measurement. So the two approaches--Von Neumann and Bohm--will be using different wave functions after the measurement. Those two situations don't sound equivalent to me. Now, maybe it is that in Bohmian mechanics, the act of measuring position causes the wave function to collapse in the same way as Von Neumann, if we take into account the interaction of the particle with whatever device measured position. Is that the resolution?