How much is the amount of uncertainty in initial positions in Bohmian Mechanics?

In Bohmian mechanics, it is believed that the randomness (uncertainty, lack of knowledge) which is seen in the outcome of experiments is due to the uncertainty in the initial particle positions at the beginning of the universe. I want to know "how much" uncertainty we have about the initial positions at the beginning of the universe.

For example, if we have a Gaussian distribution in our experiment, according to Schrodinger's equation, is the distribution for the initial position a narrower Gaussian, meaning that we have less uncertainty for the initial positions? I think the minimum uncertainty has to be larger that the quanta of length (plank length, 10^-33 m).

• The initial positions of what at the beginning of the universe ? You might also consider this in relation to the answer to Did the Big Bang happen at a point ? – StephenG Oct 6 '18 at 6:05
• I mean the initial positions of "particles" trajectories of which is concerned in Bohmian mechanics. I think they don't talk about big bang. In Bohmian mechanics, they say that the appearance of randomness in the outcome of experiments is due to randomness in this initial positions. Their uncertainty (randomness) is proportional to psi^2 (born's rule). Now I want to know how psi^2 evolves with time. Is a Gaussian diatribution, for example, broaden as time passes? – Ali Lavasani Oct 7 '18 at 7:16

It is a theorem in Bohmian mechanics that if you know the initial wave-function, you cannot gain more knowledge on the initial positions of particles than the $$|\psi|^2$$-distribution. This is the decisive difference to classical mechanics and leads to the term absolute uncertainty used in this important paper: https://arxiv.org/abs/quant-ph/0308039