Digital Quantum Reality

In recent posts, we have been discussing how external forces are represented in our proposal of local-realistic model for quantum mechanics. We have discussed some results with both constant and variable force fields, in particular the case of quantum harmonic oscillator. Such a scenario is instructive also because it introduces stationary states . In standard QM, stationary states are defined as quantum states with observable that are independent of time. For a single particle, this means that the probability distribution of position, momentum, etc., is constant. In the standard picture, these states are found as the eigenvectors of the system's Hamiltonian (eigenstates). The Hamiltonian of the quantum harmonic oscillator presents several eigenvectors, forming a family where n = 0,1,2,... and the functions H n are the Hermite polynomials . In order to check if the proposed model retrieves these stationary states, we prepare the particle ensemble to represent ...

The local-realistic model of quantum mechanics we are presenting in this blog can adequately describe external force fields . A first example (constant force) has been discussed in the latest post . Among the other possible force fields that particles can experience, a classical textbook example is the Quantum Harmonic Oscillator (QHO), which we shall discuss here. A QHO is defined by an effective "force" f that varies with the position in the lattice, according to the rule   where Ω is a parameter and x is counted from the center of the force field. The expected position under this force is obtained as This result is useful to calculate the probability densities a priori, using the procedure discussed in this post . We turn now our attention to simulation of a few scenarios, which are discussed in the 2017 ArXiV paper . We use a value Ω = 0.005. In the first scenario, particles of the ensemble are emitted from a single source, so that only the external force...

In a recent post , we have discussed how external forces are described alongside with quantum forces in the local-realistic model of quantum mechanics that we defend in this blog. In order to simulate force field scenarios, we use the accelerated code presented in this post  (the one simulating the expected motion) and we modify it as shown below. In this post we discuss a constant force scenario (suggestively denoted here as "the free faller"), characterized by a constant parameter f. %%% Simulate an ensemble of Np particles emitted at intervals Ti  %%% from either of Ns distinct sources xs(1,...,Ns) having %%% probability Ps(1,...,Ns), in the presence of a constant force %%% field f . Evaluate the frequency of arrivals  at a 'screen'  %%% after Nt iterations. %%% %%% Parameters: Np,Ns,Nt,xs,Ps, f . %%% %%% Evaluate the number of possible bosons for this scenario  B = Ns*(Ns-1)/2;  %%% Evaluate the probability of each Quantum Reset ...

We have discussed in previous posts the emergence of quantum forces in the proposed local-realistic model and how this process leads to probability densities . We have also introduced external forces  and explicitly evaluated the probability densities (in the case if quadratic potentials) when they act alone. In this post we are going to evaluate the probability densisites when both quantum forces and an external force are present. A typical situation is a quadratic potential field with particles emitted from many sources (e.g., a gaussian or plane wave preparation). Illustration by Lucas Taylor/CERN under Wikimedia Commons,  https://commons.wikimedia.org/wiki/File:CMS_Higgs-event.jpg In this situation, the role of the source momentum in dictating the average motion due to the external force is now played by the quantum momentum, that is, Following the 2018 arxiv paper the position pdf can be now computed. We start with evaluating the average quantum momentu...