This paper provides elements in support of the random zero-point radiation field (zpf) as an essential ontological ingredient needed to explain distinctive properties of quantum-mechanical systems. We show that when an otherwise classical particle is connected to the zpf, a drastic, qualitative change in the dynamics takes place, leading eventually to the quantum dynamics. In particular, we demonstrate that in parallel with the evolution of the canonical variables of the particle into quantum operators satisfying the basic commutator $\left[\widehat{x},\widehat{p}\right]=i\mathsf{\hslash }$, also the field canonical variables are transformed, giving rise to the corresponding creation and annihilation operators ${\widehat{a}}^{†},\widehat{a}$, satisfying $\left[\widehat{a},{\widehat{a}}^{†}\right]=1$. This allows for an explanation of quantum features such as quantum fluctuations, stationary states and transitions, and establishes a natural contact with (nonrelativistic) quantum electrodynamics.

The electron spin correlation is shown to be expressible in terms of a bona fide probability distribution function with an associated geometric representation. With this aim, an analysis is presented of the probabilistic features of the spin correlation within the quantum formalism, which helps clarify the concepts of contextuality and measurement dependence. The dependence of the spin correlation on conditional probabilities allows for a clear separation between system state and measurement context; the latter determines how the probability space should be partitioned in calculating the correlation. A probability distribution function $\rho \left(\varphi \right)$ is then proposed, which reproduces the quantum correlation for a pair of single-particle spin projections and is amenable to a simple geometric representation that gives meaning to the variable $\varphi$. The same procedure is shown to be applicable to the bipartite system in the singlet spin state. This endows the spin correlation with a clear probabilistic meaning and leaves the door open for a possible physical picture of the electron spin, as discussed at the end of the paper.