Digital Quantum Reality

In this blog we are presenting and supporting a local and realist model for quantum mechanics , based on simple rules of (stochastic) motion on a discrete spatiotemporal lattice. The model is realist in the sense that at each instant particles have definite properties such as position, momentum, energy, etc. and these are independent of any possible measurement. Locality means that particles interact only with other beables that are resident in the lattice nodes actually visited. In particular, quantum behavior is reproduced for an ensemble of similarly-prepared particles and thanks to a footprint mechanism where particles leave some information in the node they visit which influece the behavior of subsequent particles. One of the most common objections to the fact that one even tries to build a local and realist model, is that these models are simply impossible, as they are supposedly ruled out by Bell 's theorem . In this post and in future ones we shall demonstrate that the op...

(Cover image from: A.G. Manning, R.I. Khakimov, R.G. Dall, and A.G. Truscott, "Wheeler’s delayed-choice gedanken experiment with a single atom", Nature Physics, vol. 11, July 2015, DOI: 10.1038/NPHYS3343) In previous posts, we have discussed several quantum mechanics scenarios (for example here , here , here , etc.) and seen how they are perfectly reproduced by our local-realistic model , both theoretically and numerically. In this post we shall describe a further test for our model, that is reproducing the non-classical behavior of interferometers. We shall consider in particular  atom interferometers , and leave those operating with photons to when we shall treat quantum electrodynamics. A rather general interferometer scheme, shown in the figure below, consists of: (i) a source S where a beam in a particular state is prepared, (b) a first splitting of the beam into two paths, BS1, with different momentum states and phases (iii) a recombination M of the two paths (...

In a previous post we have described the rules that apply at each " External Reset ", that is, when a particle encounters an external force-carrier, an external "boson". In particular, the span is reversed according to the 1D rule (1) which is generalized to the 3D rule described in this post  (2), where the resulting spans are intended to be rounder at the nearest integer. However, these rules alone are not sufficient to represent the emergence of quantum behavior such as self-interference and superposition. Thus, it is now time for some more details. Let us come back to the double slit experiment. Consider such an apparatus as illustrated in the figure below, where O is the source of particles, S1 and S2 are the two slits, and P is the recording screen. In standard QM the wave function at the screen is obtained as the superposition of two wave functions emitted at slits S1 and S2 and propagated to the screen. This is possible because of th...

In this blog, we are supporting the view that a localist and realist interpretation ("model") of quantum mechanics is indeed possible. This view has many benefits, as we have discussed in several previous posts . For instance, no need for such controversial concepts as wafunction collapse (no need for wavefunctions at all). The proposed model has been published here and here . The key feature of the model is motion on a discrete spatio-temporal lattice . In recent posts , we have presented the local-realistic rules that govern motion and interactions of particles in a three-dimensional spatial lattice. Moreover, we have disucssed how geometric constraints (such as motion on a line or surface) can be embodied while still keeping the universal structure of the lattice. In this post we want to discuss one particular application of constrained motion, that is, the scenario commonly known as "particle on a ring". In this scenario, a particle is confined on a set of ...

The local-realistic model for quantum mechanics that we are presenting in this blog is based on a set of rules for particles' motion and interactions in a discrete spatiotemporal lattice. In a previous post , we have introduced the 3D lattice and how the model rules (earlier described in a 1D space) are generalized to it. It is time to present a Matlab code that implements the multi-dimensional model as a program. We start from the fully trained expected-motion program , where both the lattice and the particles are " trained " and in addition we simulate the expected values of momentum and position, not their actual values (this in order to limit the computing times; for a "realistic" simulation see this code  instead). For the sake of clarity we limit the number of dimensions to two; adding the third is straightforward. The main addition to the code concern the inclusion of polarization (below noted as px, py), as we have seen in the corresponding post. %...

A possible objection to the assumption of a fixed three-dimensionl lattice (with dimensions of the order of the Planck length ) where quantum-mechanical objects evolve, is that this assumption could be in contrast with motion on an arbitrary subset of the lattice, e.g., a line or a surface. However, these scenarios can be easily represented in the proposed model. Consider a line, that is, a succession of lattice nodes that are described by a set of numbers {a} whose sum of squares is equal to one. We have discussed in the previous post that these numbers are the direction cosines of the normal vector to the line. In that post, we have also presented the generalized rules of motion when these node represent a potential barrier . Particle hitting such nodes experience an external force (i.e., they capture an external "boson" residing in the node) with a consequent momentum propensity change, as well as a span reset. Now, imagine that all nodes outside the prescribed line...

Keeping on our quest for a local-realistic model for quantum mechanics (QM), we have recently discussed a set of rules for motion in three dimensions that yields the correct probability density functions as those predicted by QM. These rules include both quantum and external forces. We shall now discuss how potential barriers  (that have been introduced  here  for 1D motion) are described in the proposed model. Potential barriers are represented as sets of nodes where external bosons reside (when they are captured, they immediately reform) whose momentum is a function of the particle's momentum propensity V. Each of these nodes is characterized by a parameter a = {a d }, such that Each time a particle hits the barrier, it gains an external-boson momentum The meaning of the a's is now clear: they act like direction cosines of the normal vector to the barrier. For instance, for a 1D potential barrier, like those discussed in a previous post , we...