Digital Quantum Reality

In a recent post , we have discussed how the local-realistic model of quantum mechanics includes external forces. Probability densities of position, momentum, etc., can be derived from those rules of motion, which will be shown in this post. We limit our attention to force fields that standard physics describes as derived from quadratic potentials . In our terminology, the effective momentum transfer ('force' in the standard terminology) generally depends on the lattice node and has the form For what discussed in the aforementioned post, we treat this force as occurring at each node. We start considering ensemble of particles emitted by a single source. The general rules of motion prescribe that the span changes its sign at each external reset, that is, by virtue of the "equivalence" assumption above, at each iteration according to the expression Therefore, there are no possible differences between the span and the trace found. Consequently...

Although we have denoted as " quantum forces " the interactions between a particle and the previous instances in an ensemble (interactions mediated by the lattice ) that are ultimately rensponsible of quantum behavior, in the previous posts we have considered free particles that do not interact with the external world and are not subject to external "true" forces. However, the local-realistic model of quantum mechanics that we promote in this blog describes external forces as well. The principle is similar to that governing quantum forces: during their walk on the fundamental lattice, particles m ay capture external bosons , which mediate external forces, and incorporate their momentum. The event of encountering and capturing an external boson is denoted as " External Reset (ER)", in analogy to the Quantum Reset (QR) discussed in this post . Figure by Borb, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=3816716 A force field is t...

In Quantum Mechanics, position and momentum are conjugate variables . The probability density function in momentum space, φ(p;t), is the Fourier transform  of the wave function in position space, ψ(x;t). A consequence of that is the Kennard inequality that describes the Uncertainty principle . A related consequence is that position and momentum operators are noncommuting, thus these observables are said to be incompatible and cannot in general be measured simultaneously. In our  local-realistic model , there is no need of the abstract mathematical formulation of standard quantum mechanics. In the latest post we have seen that the Schrödinger equation and the Born rule can be retrieved without appealing to complex wave functions. Indeed, we have already evaluated the position probability density function (in the case of a free particle with any type of source preparation) from the model's  elementary rules of motion . The key role in this evaluation is played by ex...