3.4.1 Spin Angular Momentum
In 1922, Otto Stern (1888-1969) and Walther Gerlach (1889-1979) shot silver atoms through an inhomogeneous magnetic field. They noticed that the atoms would always be deflected a constant distance either up or down, which implied that the property of the atom which corresponds to the magnet’s orientation must be quantized, because the atoms are not deflecting freely from any angle.
In 1925, Ralph Kronig (1904-1995) proposed that particles rotate, or “spin”, about an axis and this would account for the missing magnetic moment, because this rotation can be either left or right, which allows two electrons in the same orbital to occupy distinct quantum states if they spin in opposite directions, thus satisfying the exclusion principle, as described in section 4.2. The quantum number represented the sense of positive or negative spin.
Spin is one of two types of angular momentum, the other being orbital angular momentum, and it is an intrinsic property carried by elementary particles, composite particles, or hadrons, and also atomic nuclei. Spin is like a vector quantity, but its direction is quantized. All particles of a given kind have the same magnitude of spin angular momentum, which is indicated by assigning the particle a spin quantum number, but the direction could be different.
The mathematical theory and spin-statistics was developed by Pauli in 1927, and when Dirac derived his relativistic quantum mechanics in 1928, as will be discussed in section 5.2, electron spin was an essential part of it.
When the concept of spin was suggested, Pauli criticized it severely, noting that the electron’s hypothetical surface would have to be moving faster than the speed of light in order for it to rotate quickly enough to produce the necessary angular momentum. Despite his initial objections, Pauli formalized the theory of spin in 1927, using the new Quantum Mechanics invented by Schroedinger and Heisenberg. He pioneered the use of Pauli matrices as a representation of the spin operators, and introduced a two-component spinor wave-function.
Pauli’s theory of spin was non-relativistic, but when Dirac published his equation in 1928, it described the relativistic electron using a four-component spinor, known as a Dirac spinor, which was used for the electron wave-function. In 1940, Pauli proved the spin-statistics theorem, which states that fermions have half-integer spin and bosons have integer spin, as will be described further when we talk about the Standard Model of elementary particles, in section 5.18.