  The purpose of this article is threefold. Firstly, it aims to present, in an
educational and non-technical fashion, the main ideas at the basis of Aerts'
creation-discovery view and hidden measurement approach: a fundamental
explanatory framework whose importance, in this author's view, has been
seriously underappreciated by the physics community, despite its success in
clarifying many conceptual challenges of quantum physics. Secondly, it aims to
introduce a new quantum-machine - that we call the delta-quantum-machine -
which is able to reproduce the transmission and reflection probabilities of a
one-dimensional quantum scattering process by a Dirac delta-function potential.
The machine is used not only to demonstrate the pertinence of the above
mentioned explanatory framework, in the general description of physical
systems, but also to illustrate (in the spirit of Aerts' epsilon-model) the
origin of classical and quantum structures, by revealing the existence of
processes which are neither classical nor quantum, but irreducibly
intermediate. We do this by explicitly introducing what we call the k-model and
by proving that its processes cannot be modelized by a classical or quantum
scattering system. The third purpose of this work is to exploit the powerful
metaphor provided by our quantum-machine, to investigate the intimate relation
between the concept of potentiality and the notion of non-spatiality, that we
characterize in precise terms, introducing for this the new concept of
process-actuality.
