Digital Quantum Reality

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...

In my 2018 ArXiv paper, several one-dimensional scenarios are simulated to corroborate the model proposed to reproduce Quantum Mechanics in a localistic and realist fashion. Besides free particle , free faller , harmonic oscillator , and the particle-in-a-box scenarios, the last scenario of that paper is the Delta potential . In this scenario , the potential acting on particles has the shape of a Dirac delta function, that is, it is zero everywhere except for a single point, where it has an infinite value. To represent such circumstance, we have set the force function as a finite rectangular barrier, where λ is the amplitude of the Delta potential and ℓ is an arbitrary scale. Classically, particles coming from negative x are transmitted, if λ is smaller than their kinetic energy, or reflected, if λ is larger. Conversely, quantum mechanics, as well as our proposed model, predict that some particles are transmitted even in the latter case. This behavior is often called ...

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 ...