What is the significance of Planck's constant in De Broglie–Bohm theory or Pilot-wave theory? In standard QM, Planck's constant seems to be a constant that describes the smallest quanta of energy in some way. Does De Broglie–Bohm theory have an alternate interpretation of that constant and what it means about space-time or particles (or both)?
 A: Bohm's interpretation of the QM says that a particle moves along a trajectory, as in the classical mechanics, however, the potential in which this particle moves is supplemented by a "quantum potential". In all the equation of movement relevant for this question is
(1) $\frac {∂S}{∂t} + \frac {(\nabla S)^2}{2m} + \left[V(x) - \frac {\hbar ^2}{8m} \left(2\frac {\Delta P}{P} - \frac {(\nabla P)^2}{P^2} \right) \right] = 0$,
where $S$ and $P$ are defined by expressing the wave-function as
(2) $\psi = P \ e^{iS/ \hbar}$.
Here is what Bohm says about the constant $\hbar$ :
" ... in the classical limit $\hbar \to 0$ the above equations
are subject to a very simple interpretation. The function
$S(x)$ is a solution of the Hamilton-Jacobi equation."
However, as long as the limit $\hbar \to 0$ doesn't hold, the trajectory of a particle is influenced, besides $V(x)$, by a "quantum potential" generated by the wave-function,
$V^{quantum} = -\frac {\hbar ^2}{8m} \left(2\frac {\Delta P}{P} - \frac {(\nabla P)^2}{P^2} \right)$.
Thus, the magnitude of $\hbar$ relative to the considered problem separates between the classical and quantum behavior. 
