All the elementary entities of quantum mechanics spin but matter only half spins. Spinning an object once in our space returns its original state but doing the same to an electron only half-turns it. It is said to half spin because it takes two turns to return it to its original state, and quarks are the same.
Yet an electron is a dimensionless point that shouldn’t spin at all, so particle physics gave up trying to understand quantum spin in physical terms:
“We simply have to give up the idea that we can model an electron’s structure at all. How can something with no size have mass? How can something with no structure have spin?” (Oerter, 2006), p95.
In contrast, we model an electron as a point particle with a photon structure that can spin. Physically, a photon is a one-dimensional ray but quantum theory says it vibrates into a complex dimension outside our space. This gives it a two-dimensional structure, like a piece of paper, so it can spin on its movement axis (Note 1). However the photons in an electron extend in two dimensions not one, so it can spin in two ways at right angles to each other. That quantum space lets photons vibrate in orthogonal directions (Note 2) is why a filter that blocks horizontally polarized light doesn’t block vertically polarized light (3.7.2).
Why then do electrons half spin? If an electron’s photons vibrate in two directions at right angles, only half of them will be visible for any line of view as the rest, like thin paper sheets, can’t be seen edge-on. If one photon is 100% visible, another at right angles will be 0%, for one that projects 99%, another will project only 1%, and so on, hence two spins are needed to turn all the photons of an electron.
In our space, one spin returns any object to its original state because spin needs one axis and two dimensions to rotate, which is three dimensions. But for electrons in four-dimensional quantum space, one rotation only turns half its photons, and another is needed to turn the other half. It takes two of our spins to return an electron to its original state, so they only half spin in our terms, and all matter entities are the same.
Note 1. For a photon moving in direction X, its quantum amplitude Q vibrates in plane QX, so the structure QX can spin.
Note 2. The orthogonal directions X, Y, Z of space give three orthogonal planes XY, YZ and XZ. A fourth dimension Q adds three more orthogonal planes Q1X, Q2Y, Q2Z, where Q1, Q2 and Q3 are at right angles.