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 an electron is photons filling the channels of an axis, they have two different directions at right angles to vibrate into, so only half of them will be visible for any line of view, as the others, like ideal paper sheets, will be invisible edge on. If one photon is 100% visible, another at right angles will be 0%, for one that projects 99% there is another that projects only 1%, and so on. This is because photons can vibrate in two orthogonal directions not one.
This is why it takes two 360º degree turns to return an electron to its original state. In three dimensions, one turn returns any object to its original state, but for an electron, 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.