Entropic Dynamics: The Schroedinger equation and its Bohmian limit

Abstract: In the Entropic Dynamics (ED) derivation of the Schroedinger equation the physical input is introduced through constraints that are implemented using Lagrange multipliers. There is one constraint involving a "drift" potential that correlates the motions of different particles and is ultimately responsible for entanglement. The purpose of this work is to deepen our understanding of the corresponding multiplier. Its main effect is to control the strength of the drift relative to the fluctuations. We show that ED exhibits a symmetry: models with different values of the multiplier can lead to the same Schroedinger equation; different "microscopic" or sub-quantum models lead to the same "macroscopic" or quantum behavior. As the multiplier tends to infinity the drift prevails over the fluctuations and the particles tend to move along the smooth probability flow lines. Thus ED includes the causal or Bohmian form of quantum mechanics as a special limiting case.