Digital Quantum Reality

(Cover image from: A.G. Manning, R.I. Khakimov, R.G. Dall, and A.G. Truscott, "Wheeler’s delayed-choice gedanken experiment with a single atom", Nature Physics, vol. 11, July 2015, DOI: 10.1038/NPHYS3343) In previous posts, we have discussed several quantum mechanics scenarios (for example here , here , here , etc.) and seen how they are perfectly reproduced by our local-realistic model , both theoretically and numerically. In this post we shall describe a further test for our model, that is reproducing the non-classical behavior of interferometers. We shall consider in particular  atom interferometers , and leave those operating with photons to when we shall treat quantum electrodynamics. A rather general interferometer scheme, shown in the figure below, consists of: (i) a source S where a beam in a particular state is prepared, (b) a first splitting of the beam into two paths, BS1, with different momentum states and phases (iii) a recombination M of the two paths (...

The main results of this post about the stochastic motion of single particles can be obtained by considering such motion - for large times - as a Brownian motion with drift , where W(t) is a Wiener process  with zero mean and unit variance. The momentum propensity V here plays the role of the drift, while the variance is given by the diffusivity coefficient D  = 1- e , where e is the energy propensity (1+ V 2 )/2. For instance, we can derive the probability density from the Fokker-Planck equation of the Brownian motion, whose solution is clearly the Gaussian distribution shown in the aforementioned post, with the initial condition w = δ( x - x 0 ). Or, we can use the properties of stochastic processes to find the probability density of the  first return time to the source, i.e., the time at which the particle comes back for the first time at x =  x 0 . For some reason, I could not find a formula for that in the case of a Wiener proce...