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 the latest post , we have discussed how quantum mechanical behavior in a three dimensional space can be reproduced by a local-realistic model, which has been partly published here , here , and here . In 3D, we have introduced " polarization " as a collection of three rational numbers attributed to particles at their source. The role of such polarization will be clearer in this post, where we shall discuss how QM probability densities are retrieved. The procedure is quite similar to that already discussed here  (without external forces) and here (with external forces) for 1D motion. Following the same reasoning, after lattice training, the particle boson momenta (PBM) for span-trace pairs (ℓ, λ) tend to where all quantities have been introduced in previous posts (P 0 is the source probability dunction, ω is the lattice boson momentum (LBM) δ is the path difference, ρ is polarization, and the subscript d denotes the three dimensions. After lattice training, the ...

In all previous posts we have considered a local-realistic model for quantum mechanics working in a one-dimensional scenario, where motion is only along dimension x. However, ordinary space is made of three dimensions, thus the lattice geometry should reflect this fact. The extension of the model to the 3D case is not completely trivial and will be described here. A first element has been already introduced in this post , where the source preparation and the attribution of a source momentum to particles have been described. The key notion is the limiting condition that we recall here as Simple equations of motion are trivially extended to three dimensions. Basically, in the absence of quantum forces, each dimension is independent from the others, except for the limiting condition above. Similarly, no special treatment is required for external forces, which are intended to work separately on each dimension. Motion rules in the presence of quantum forces introduce a few new q...