Digital Quantum Reality

In an earlier post , we have seen that two of the building blocks of a local and realistic model of Quantum Mechanics are the assumption of a discrete spacetime (the size of Compton wavelenght) and a three-valued momentum as a random variable, whose probability distribution is completely determined by its expected value, or momentum propensity . At a given iteration, quantum propensity V is the sum of two contributions, where v Q is the momentum contribution of quantum forces, and v F that of standard, "external" forces. Quantum momentum The quantum momentum is a quantity carried by the particle, which is first assigned at a certain value during the particle's preparation and may subsequently vary as a function of quantum forces. When a particle is prepared at a source,  v Q  is initialized to a value that we denote as  v 0  , the  source momentum . This quantity is itself a random variable: it can take rational values and is uniformly distribu...

In an earlier post , we have seen that in the proposed digital QM model, evolution happens on nodes of a spatiotemporal lattice. At each iteration, position can increase of one lattice node in either directions or remain at the same it hold at the previous iteration. The corresponding possible values of momentum v are thus 1 (positive or "up" direction), 0 (rest), or -1 (negative or "down" direction). In this post we will learn more on this random variable. Since v can only take three values, its probability distribution is completely defined by two parameters. These two parameters are, e.g., the expected value and the variance. The expected value of momentum plays a special role in the model and is called momentum propensity , here denoted as V (bold v in the papers). Instead of the momentum variance, we take the expected value of the momentum squared (a quantity that can take only the values 0 and 1), which we call energy propensity and denote as e . T...

Evolution of particles on a lattice The proposed model assumes a discrete spacetime . Let us limit the discussion to one dimension for simplicity. The values of position are thus restricted to the integer multiples of a fundamental quantity X . Similarly, the values of time are restricted to the integer multiples of the fundamental quantity T . The spacetime may be therefore thought as if it is constituted by a grid, or lattice , whose nodes can be visitued by particles during their evolution. Illustration of the lattice The evolution of a particle is the particular succession of nodes x[n] , t[n] , where n is the integer counter that describe advance in history, called number of iterations . Advance in time is unidirectional and unitary, that is Advance in space is still unitary, but a particle can either advance in one of the two directions, or stay at rest, where v is a random variable called momentum . The whole motion is regulated by this variable, whic...

This post is about the blog's title. So, why: Digital Quantum Reality? In fact, the words "Digital" and "Reality" refer to two of the main distinguishing features of the quantum mechanical  model I have proposed . This model contrasts with existing models (or, interpretations) of Quantum Mechanics by virtue of several features. Considering, for example, the entries of the comparison table in the Wikipedia's article on the Interpretations of Quantum Mechanics , here is how the proposed model can be described: DETERMINISTIC?: NO (It is Stochastic) WAVE FUNCTION REAL?: NO (No wavefunctions at all) UNIQUE HISTORY?: YES (part of Realism) HIDDEN VARIABLES?: YES (Actually, several) COLLAPSING WAVEFUNCTIONS?: NO (No wavefunctions at all) OBSERVER ROLE?: NO (part of Realism) LOCAL DYNAMICS?: YES COUNTERFACTURAL DEFINITESS?: YES (part of Realism) UNIVERSAL WAVEFUNCTION EXISTS?: NO Image from Flickr user Politropix under Creative Commons licence S...

In the paper  A Local-Realistic Model of Quantum Mechanics Based   on a Discrete Spacetime  (Foundations of Physics,  January 2018 , Volume 48, Issue 1, pp 60–91), I have proposed  a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. From the paper abstract: "The proposed model only uses integer-valued quantities and operations on probabilities, in particular assuming a discrete spacetime under the form of a Euclidean lattice. Individual (spinless) particle trajectories are described as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice nodes they visit during the walk. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. The scenarios considered to asses...