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The formulation of quantum mechanics on 3N-dimensional configuration space has been considered unfavourably since the early advent of the theory and is the main source of computational difficulties due to the exponential growth of data when the particle number $N$ augments. De Broglie expressed at the 1927 Solvay conference that

“if one wants to physically represent the evolution of a system of corpuscles, one must consider the propagation of N waves in space.” ^[1]

And Schrödinger hoped that

“in the end everything will indeed become intelligible in three dimensions again.” ^[1]

This hints towards a concept of one-particle wave functions or the wave function of a subsystem respectively, a concept that quantum mechanics usually prohibits through the effects of entanglement. But by fixing certain coordinates of the many-particle wave function to Bohmian trajectories the resulting one-particle conditional wave function will be determined by a non-unitary and non-linear (already including wave function collapse), non-autonomous (depending on the full wave function) conditional evolution equation. This equation incorporates an effective potential origination from the so-called potential network summing up all effects originating from entanglement to the missing particles. By choosing suitable approximations an efficient calculation of trajectories is possible.

Originally such a scheme was seemingly first proposed by ^[2] while in ^[3] a very similar idea is employed, where quantum and classical (Bohmian) position lead to a mixed dynamics. In ^[4] the concept is extended to QED and even to quantum gravity.