I have found an article about Bohmian mechanics on a lattice with discrete space and time, the link of which is given below:


Here the motion of quantum particles is described by a $|\Psi|^2$ - distributed Markov chain. It is discussed that "the discreteness is by itself responsible for the randomness of the motion on the basic level", and

The transformation of a discrete distribution $|\Psi(t_0)|^2$, e.g. at the slits, into the discrete distribution $|\Psi(t)|^2$, e.g. far from the slits, cannot be made in a non-stochastic manner, as it would require transitions from every (initial or intermediate) state into a single subsequent state.

What do the quoted sentences exactly mean? Pilot-wave theory is deterministic in a continuous space-time. Can someone explain to me why a pilot-wave theory needs to be non-deterministic in a discrete space-time? Is this stochasticity necessary for it to be able to reproduce the predictions of Quantum mechanics?


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