This experiment is often cited as demonstrating that angular momentum is quantised. In fact it does nothing of the sort, and indeed it clearly demonstrates that it is not, at least not in the way that physicists would have you believe.
The Stern Gerlach experiment was first carried out by German physicists Otto Stern(1888-1969) and Walther Gerlach(1889-1979) in 1922. It involved firing silver atoms through an inhomogeneous magnetic field at a target. The atoms are electrically neutral (not ionized) which avoids large deflections due to the orbit of charged particles moving through a magnetic field and allows spin effects to dominate.
The spinning electron can be regarded as a dipole and the non-uniform nature of the magnetic field means that the forces acting on one end of this dipole differ slightly from the forces acting on the other end. As a result the atoms are deflected by an amount which varies according to the angular momentum associated with the spinning electron. If the spin of the electron was to be a continuous variable then the extent of the deflection would vary continuously, but it does not. The electrons are seen to cluster into one of two regions, indicating that the spin on the electron is not continuous. Physicists argue that this is because angular momentum is quantised and can only take on certain discrete values and that these two regions of deflection correspond in some way to that quantisation.
Indeed it does show that the spin on the electron can only take on one of two discrete values, but this does not mean that angular momentum is quantised, far from it. What it does indicated is that the spin on the electron is always at some maximum value, but that it can take on one of two types, we can think of these as being clockwise or anticlockwise with respect to some datum within the atom. It means that the electron is never not spinning, it must always spin, but when it does so, it is always at some maximum value in one of only two possible orientations. The electron has very little mass and correspondingly low moment of inertia and so it comes as no surprise that almost any stimulus could cause it to spin. The fact that there is a limit to the rate of spin should also come as no surprise; if we think of the electron as a solid sphere, the limit to its spin must occur when the equatorial speed equals that of light.
So why does this not indicate that angular momentum is quantised everywhere?
The answer is simple and has to do with the size of the quantum of angular momentum postulated by physicists in the so called Standard Model. The Standard model holds that angular momentum is quantised and that the size of a quantum of angular momentum is equal to Planck’s constant. The trouble is that the Stern Gerlach experiment shows that the angular momentum of the spinning electron is some 106 times smaller than this. If angular momentum were quantised in units of Planck’s constant then the spin on the electron could only take on values which are equal to an integer multiple of Planck’s constant, the smallest such being unity. The fact that the spin on the electron is 10-6 times this blows this idea out of the water. If on the other hand the fundamental unit of angular momentum is associated with that of the spin on the electron, it makes a nonsense of the idea that angular momentum can only take on values which are an integer multiple of Planck’s constant necessary for the Bohr model and its descendants. On the scale of the atom angular momentum would, to all intents and purposes be continuously variable.