Digital Quantum Reality

One of the classical textbook example that is used to illustrate quantum effects is certainly the particle in a box scenario. In this idealized case, a particle confined between two infinite potential barriers may only occupy certain energy levels . People say that the energy is quantized in this case. This scenario is very naturally represented in the local-realistic model of QM we are supporting throughout this blog. In an earlier post , we have anticipated that the key role to model the particle in a box is played by the External Reset condition, discussed here . An ER is activated whenever a particle (in an ensemble of similarly-prepared particles) captures an external "boson", i.e., experiences an external force. In our scenario, this means each time the particle hits one of the barriers. At an ER, the particle span (a memory of the distance traveled) changes sign. The effect is the same as if the particle had been emitted from a virtual source located at the other s...

This blog is aimed at discussing how quantum mechanics can be modeled in a local and realistic way. In a recent post , we have introduced the external force fields in the (one-dimensional, so far) model. The key roles in this respect are played by the external bosons and the External reset . The latter rule is activated each time an external boson is captured (i.e., each time an external force is experienced) and resets the particle's span (a counter carried on by each particle representing the space it has traveled since the source) to its inverse. With quadratic or other continuous potentials , where we have assumed that an external boson is captured at each iteration (a continuous effective momentum transfer conveniently incorporates the probability of actually finding an external boson), the ER rule plays no role. Also, as discussed in this post , quantum forces cannot be induced by continuous potentials only, since no span differences between successive particles of the ...

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...

In a recent post , we have discussed how the local-realistic model of quantum mechanics includes external forces. Probability densities of position, momentum, etc., can be derived from those rules of motion, which will be shown in this post. We limit our attention to force fields that standard physics describes as derived from quadratic potentials . In our terminology, the effective momentum transfer ('force' in the standard terminology) generally depends on the lattice node and has the form For what discussed in the aforementioned post, we treat this force as occurring at each node. We start considering ensemble of particles emitted by a single source. The general rules of motion prescribe that the span changes its sign at each external reset, that is, by virtue of the "equivalence" assumption above, at each iteration according to the expression Therefore, there are no possible differences between the span and the trace found. Consequently...