Atreyu:
What is the position of modern science concerning the idea of spin?
In classical mechanics, the equations of angular momentum are to some extent analogous to the equations that describe linear momentum - i.e. movement in a straight line. The linear momentum of an object is simply its mass times its velocity. So increasing either mass or velocity increases momentum. In the equations for circular motion, the equivalent of the velocity is the angular velocity (number of rotations per unit time) and the equivalent of mass is a quantity called "moment of inertia" (sometimes, for that reason, called "angular mass"). Greater the moment of inertia or angular velocity, greater the angular momentum.
Rotational motion in "classical objects" is observed to have various properties that are described by the equations of classical mechanics, and when you start looking at very small objects, in which the laws of quantum mechanics dominate, you start to find analogous behaviour. So, just as with the classical concept of linear momentum, some of the maths of classical angular momentum can be carried over. So, for example, in quantum mechanics orbital angular momentum (an object going around another object) and intrinsic angular momentum (an object spinning on its axis) are measured in exactly the same units as with classical mechanics (in standard base units: kg m
2 s
-1). But with elementary particles, the spin comes in discrete values that, for simplicity and brevity, are not normally expressed in these standard units of angular momentum but are expressed as multiples of a fixed quantity called the "reduced Planck's constant". It's been observed that they always spin with these discrete values. Electrons, for example, always spin on their own axis with an angular momentum that is exactly half of this reduced Planck's constant. This has profound consequences for things like the structure of the periodic table, in Chemistry.
Analogies to much of the behaviour of large-scale spinning objects can be seen in elementary particles. For example, when an electrically charged particle like an electron orbits something or spins on its axis, you can observe something similar to the kinds of electromagnetic behaviours which the classical laws of electromagnetism predict. The classical laws of electromagnetism, among other things, say that moving electric charges create a magnetic field. That's how a solenoid or electromagnet works - electric charge moving round and round in circles in a wire and result in a magnetic field. An iron permanent magnet works in the same way, but in that case the electric charge moving in a circle is a result of the electrons associated with the iron atoms spinning on their own axes.
There are all kinds of other ways that the laws of classical electromagnetism and mechanics inform our understanding of the quantum mechanical concept of angular momentum. For example, if you've seen a gyroscope spinning you'll have seem that it "precesses" i.e. its axis of rotation is at an angle to the vertical and it slowly rotates. (The same happens with the spinning of the Earth on its axis). There is an analogous behaviour in charged particles like electrons and protons which is actually made use of in medical imaging technology. Things like MRI scanners - "Magnetic Resonance Imaging" - use it.
So spin in elementary particles is pretty well described and predicted by quantum mechanics and those descriptions and predictions are used for lots of practical purposes as well as being essential to the properties of all the chemical elements in the periodic table. As to the question of whether quantum mechanics
explains subatomic spin, or what subatomic spin actually "is", that, I guess, is where the philosophy starts.