Digital Quantum Reality

In a previous post , we have discovered that quantum mechanics can described equivalently to standard approaches, and in particular Bell's inequalities  can be violated in a Bell test with momentum-entangled pairs of particles, despite making use of local realist assumptions. However, it is a fact that Bell's theorem and its descendants are regularly used to dismiss any possibility that a local-realist quantum mechanical model could even exist. John Stewart Bell (1928-1990) How happens that our local-realist model captures BI violations and correctly reproduces QM statistics? How to solve this apparent paradox? Despite its mathematical simplicity, interpretation of Bell's theorem has given rise to a vast literature, in particular concerning its assumptions and the conclusions that can be drawn. The usual assumptions used in deriving Bell inequalities are realism (properties of physical systems are elements of reality, outcomes of tests are determined by some hidde...

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...

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 ...

Quantum Mechanics theory describes systems with wave functions  and their evolution with the Schrödinger equation . Probabilities of the outcomes of measurements on a quantum system are given by the Born rule . In particular, the probability of a single particle to be in a certain position is obtained by squaring the modulus of the wave function (which is a function of position). In our local-realistic model of quantum mechanics, there is no Hilbert space, no complex numbers, no wave functions. As we have illustrated in previous posts, probability density functions (themselves, large-time approximations of probability mass functions) are obtained directly  from the stochastic rules of motion assumed. For example, we have seen in this post that, for a free particle, the pdf of position is obtained as where the indexes l and λ represent any two of the possible source, x 0 their locations, P 0 their probability, δ their relative distance (reflected by the differenc...

In this post , I have introduced how a genuine quantum phenomenon, the two-slit experiment, is represented in the proposed local-realistic model for quantum mechanics. Illustration by user Sakurambo, Wikimedia Commons, https://commons.wikimedia.org/wiki/File:Young_diffraction.svg The QM mathematical machinery finds the good result by adding together ("superimposing") two different quantum states , corresponding to particles passing through either of the two slits. This is an application of the fundamental principle known as  quantum superposition . Each of the two states is described by a complex wavefunction, say, ψ 1 for the state where the particle passes through the first slit and ψ 2 for the state where the particle passes through the second slit. if the two slits are equally probable, the wavefunctions read (in lattice units, where m → 1, ℏ → 1/π): where k stands for 1, resp., 2, and x k is the k-th source position. According to the superposition prin...

In an earlier post , we have seen that the spacetime lattice that forms the backbone of the proposed local-realistic QM model , has dimensions that correspond to the Compton length and time. These quantities are claerly variable with the mass and thus particle-dependent. How can different particle ensembles coexist and evolve on the same lattice, then? That is possible if all particles have a mass that is an integer fraction of a common multiple m 0 . If, say, the electron mass is m e =m 0 /k e , that of the top quark mass is m t =m 0 /k t , that of the tau particle is m τ =m 0 /k τ , etc., with all the k 's integers. Now, what is this common multiple  m 0 ? Particles with different mass have different lattice steps that are nevertheless integer multiples of the same minimal length Scientists have worked on the hypothesis of a discrete spacetime since long time. Most often, people prefer the concept of minimal length scale , that is the fundamental limit to the resolution ...

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...