Georgina & all, if you will kindly forgive my intrusion:
" ... according to the chosen convention for describing it, where/when there is spin that is anticlockwise and clockwise."
That's a problem that Joy Christian's quantum measurement framework has solved, with an extra degree of freedom analogous to the 3-dimension phenomenon inherent in the Dirac belt trick, or the Filipino plate dance. At what point (where?) and at what time (when?) can the belt be said to have transformed from one state of motion to the other, or the plate in the dancer's hand? The motion is continuous; the pair of states is continuous. And yet because the states are a pair, a quantum bit, they have 2 discrete values. As fundamental quantum mechanics informs us, a pair of values can be correlated or anti-correlated; correlation is the coincidence of 2 spins, anti-correlation is the opposite of coincidence. Quantum theory allows that the values and their correlations are entirely random for each measure, while classical (i.e., continuous function) physics allows a continuum of correlated values measured from an initial condition, without random coincidences.
The problem with classical physics is that to solve the equations, which are ordinary differential or partial differential equations, one must define boundary conditions. The equations can be solved exactly, yet not satisfactorily, because there are too many solutions. On the other hand, the equations of quantum theory can be solved satisfactorily though not exactly. Indeterminism is built into the model.
"The motion is now starting to look something like an electromagnetic wave."
You got it, sister. :-) Classical theories are based in continuous wave phenomena, and continuous wave phenomena evolve deterministically; correlated and anticorrelated points of the wave are not discrete objects. It requires an extra degree of freedom imparted by an extradimensional framework, however, to show that mathematically -- and it takes a continuous measurement correlation function experimentally (catching measured values 'on the fly').
Joy Christian has met the challenge mathematically -- quantum correlations are points of the 3-sphere Hopf fibration that precisely correspond to locally real measures in 2-sphere classical space. Think of how sine wave amplitudes are smoothly correlated with their troughs; if this mathematically smooth and continuous function is shown to underly all basic physics, then there is no true randomness and cherished ideas of conventional quantum theory (probabilism, entanglement, nonlocality, wave function collapse) have to be discarded.
The big question is, where does the extra degree of freedom come from? It's beautifully built into the topology of the 3-sphere -- where every point of origin is a point at infinity. It takes a little study and training in topology to appreciate the implications, though to make a long story longer, the simple point at infinity is such that while dividing by zero is an arithmetic no-no, the 3-sphere structure defines n/0 = oo. Because this feature is also available to real analysis via the real projective line, the 3-sphere topological framework projects as well to the curved manifold of the 2-sphere.
So getting back to the where and the when of spin characteristics, if the qubit state is continuous, there is no where or when that one of the pair's state transforms into the other -- although the transformation (as with the Dirac trick or the Filipino dance) is completely described and determined by the initial condition of a measurement. And this goes for the initial condition of all measured quantum correlations, whether one is measuring spin (which in the quantum world does not at any rate actually correspond to classical angular direction and momentum) or any other quantum characteristic.