Effective wave function in Bohmian mechanics

If $\Psi (q,y)=\psi (q)\Phi (y)+{\Psi }^{\perp }(q,y)$ and the actual environmental configuration $Y$ lies in the support of $\Phi$ disjoint from the environmental support of ${\Psi }^{\perp }$, then evaluating the guidance equation at $(Q,Y)$ gives the velocity generated by $\psi$. This is effective collapse without deleting a universal empty wave.