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This text begins with a series of critical considerations on the initial interpretation of quantum phenomena observed in atomic systems. The bewildering explanations advanced during the construction of quantum mechanics are shown to have distanced the new theory from the rest of scientific knowledge, by introducing indeterminism, acausality, nonlocality, and even subjectivism as part of its interpretative framework. The conclusion drawn from this unsatisfactory interpretative landscape is that quantum mechanics lacks a key ontological ingredient. Arguments are given in favour of the random zero-point radiation field (ZPF) as the element needed to complete the quantum ontology. The (wave-mediated) quantum stochastic process is shown to be essentially different from Brownian motion, and more amenable to an analogy with the hydrodynamic case. The new perspective provided by the introduction of the ZPF is used to explain some salient features of quantum systems, such as the stationary atomic states and the transitions between them, and the apparent nonlocality expressed in the entangled states. Notably, the permanent presence of the field drastically affects the dynamics of the (otherwise classical) particle, which eventually falls under the control of the field. This qualitative change is reflected in the transition from the initial classical description in space-time, to the final quantum one in the Hilbert space. The clarification of the mechanism of quantization leads us to consider the possibility that a similar phenomenon occurs in other physical systems of corpuscles subjected to an oscillating background, of which the walking-droplet system is a paradigmatic example.