The elementary entities of quantum mechanics all spin, but matter only half spins. Spinning an object once in our space returns its original state, but spinning an electron 360 degrees only half-turns it. It takes two whole turns to return an electron to its original state. The same applies to all matter entities, so they are said to half spin because it takes two 360º turns to spin them once.
For this reason, and because an electron is a dimensionless point that shouldn’t spin at all, particle physics has simply given up trying to understand quantum spin:
“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.
However in this model, an electron has a structure despite being a point particle, as it is made of photons that also have a structure. A photon travelling in a direction seems one-dimensional, but it vibrates into an unseen quantum dimension outside space, based on its polarization, to give a two-dimensional structure, like a piece of paper, that can also spin (Note 1), as photons do. It is also expected, again like a thin piece of paper, that it can’t be seen when it is viewed edge-on.
In addition, the four dimensions of quantum space let photons vibrate in two different directions at right angles to each other (Note 2), which explains why horizontal filters stop horizontally polarized light but not vertically polarized light (see 3.7.2).
Now if the photons of an electron fill the channels of an axis, they vibrate in two different directions at right angles, so only half of them will be visible for a line of view as the others, like an ideal paper sheet, will be invisible 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, because these photons vibrate in two orthogonal directions, not one.
In our space, one turn returns any object to its original state because a rotation needs an axis line and two dimensions to rotate around. That adds up to three dimensions, but electrons exist in four-dimensional quantum space, so it takes two 360º turns to return them to their original state. One 360º turn only turns half its photons, and another 360º turn is needed to turn the other half. Hence, electrons only half spin in our terms, and other 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.