The present paper reveals (non-relativistic) quantum mechanics as an emergent property of otherwise classical ergodic systems embedded in a stochastic vacuum or zero-point radiation field (zpf). This result provides a theoretical basis for understanding recent numerical experiments in which a statistical analysis of an atomic electron interacting with the zpf furnishes the quantum distribution for the ground state of the H atom. The action of the zpf on matter is essential within the present approach, but it is the ergodic demand (...) what ultimately leads to the matrix formulation of quantum mechanics. The paper thus represents a step forward in the quest for an elucidation of the fundamentals of quantum mechanics. (shrink)