A Local-Realistic Model of Quantum Mechanics Based on a Discrete Spacetime

Abstract

This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. 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 assess the model comprise of free particle, constant external force, harmonic oscillator, particle in a box, the Delta potential, particle on a ring, particle on a sphere and include quantization of energy levels and angular momentum.An event-based class of models have been recently proposed [25,26] that embody quantum behaviour into the constitutive models of the detectors and other devices, mostly using deterministic learning machines that generate events according to QM. This approach captures all of the features (R), (S), and (L). Interference, among other quantum phenomena, is not obtained as an intrinsic characteristic of the particles' trajectories but as a result of their interaction with the experimental apparatus.Other suggestions to make QM behaviour emerge from discrete time evolution [27] or vacuum fluctuations [2] were not pursued to the end, to our best knowledge.

Recovery of Global Symmetries in a 't Hooftian Universe

“…Bubbles also have a sinusoidal phase φ coupled to f , achieved by a recurrent algorithm. Together with the related variable ϕ, they implement interference and self-interference (see Sciarretta [11]). Each occupied register has ϕ = φ, which decays as…”

“…An alternative representation of the universe is developed in this work using the cellular automaton paradigm. The theme has been explored for a long time (see [2,3,4,5,6,7,8,9,10,11,12] for example). However, these studies generally remain in the abstract realm or present very limited models.…”

Recovery of Global Symmetries in a 't Hooftian Universe

“…This contributes to the appearance of self-interference, as in the case of the double slit experiment. This scheme was originally conceived by Sciarretta in [11]. The main idea is to leave a copy of the visitor's momentum on the lattice, which decays following the rule…”

“…An alternative representation of the universe is developed in this work using the cellular automaton paradigm. The theme has been explored for a long time (see [2,3,4,5,6,7,8,9,10,11,12] for example). However, these studies generally remain in the abstract realm or present very limited models.…”

Understanding quantum mechanics: a review and synthesis in precise language

“…One potential explanation is that interference may result from spacetime being discrete rather than continuous (see Sect. 1.6 above) [185, Part 1] [318], or otherwise differing from that assumed by classical mechanics [319, § 3]. Explanations are also possible in some theories based on system positions (see Sect.…”