  The standard Bloch sphere representation was recently generalized to the
'extended Bloch representation' describing not only systems of arbitrary
dimension, but also their measurements. This model solves the measurement
problem and is based on the 'hidden-measurement interpretation', according to
which the Born rule results from our lack of knowledge about the interaction
between measuring apparatus and the measured entity. We present here the
extended Bloch model and use it to investigate the nature of quantum spin and
its relation to our Euclidean space. We show that spin eigenstates cannot
generally be associated with directions in the Euclidean space, but only with
generalized directions in the Blochean space, which generally is a space of
higher dimension. Hence, spin entities have to be considered as genuine
non-spatial entities. We also show, however, that specific vectors can be
identified in the Blochean theater that are isomorphic to the Euclidean space
directions, and therefore representative of them, and that spin eigenstates
always have a predetermined orientation with respect to them. We use the
details of our results to put forward a new view of realism, that we call
'multiplex realism', providing a specific framework with which to interpret the
human observations and understanding of the component parts of the world.
Elements of reality can be represented in different theaters, one being our
customary Euclidean space, and another one the quantum realm, revealed to us
through our sophisticated experiments, whose elements of reality, in the
quantum jargon, are the eigenvalues and eigenstates. Our understanding of the
component parts of the world can then be guided by looking for the possible
connections, in the form of partial morphisms, between the different
representations, which is precisely what we do in this article with regard to
spin entities.
