Spin (physics)

Spin is an intrinsic angular momentum associated with quantum mechanical particles. Unlike classical "spinning" objects, which derive their angular momentum from the rotation of their constituent parts, spin angular momentum is not associated with any rotating internal masses. For example, elementary particles such as the electron possesses spin angular momentum, even though they are point particles.

When applied to spatial rotations, the principles of quantum mechanics state that the observed values of angular momentum (which are eigenvalues of the angular momentum operator) are restricted to integer or half-integer multiples of h/2π. This applies to spin angular momentum as well. Furthermore, the spin-statistics theorem states that particles with integer spin correspond to bosons, and particles with half-integer spin correspond to fermions.

A rotating charged body in an inhomogenous magnetic field will experience a force. Electrons in an inhomogenous magnetic field also experience a force, and this is why people have imagined the electron as "spinning around". The observed forces are different for different electrons, and are attributed to differences in spin. The spin of electrons is therefore typically measured by observing their deflection in an inhomogenous magnetic field. In accordance with the predictions of theory, only half-integer multipls of h/2π are ever observed for electrons.

History

Spin was first discovered in the context of the emission spectrum of alkali metals. In 1924, Wolfgang Pauli (who was possibly the most influential physicist in the theory of spin) introduced what he called a "two-valued quantum degree of freedom," associated with the electron in the outermost electron shell. The Pauli exclusion principle was formulated at this time.

Ralph de Laer Kronig, Pauli's assistant, suggested that this "degree of freedom" was produced by a spinning electron. Pauli ridiculed this idea, noting that, in order for the electron to rotate quickly enough to produce the necessary angular momentum, its (hypothetical) surface would have to be moving faster than light, violating the theory of relativity. As a result, Kronig never published his proposal.

Two young Dutch physicists, George Uhlenbeck and Samuel Goudsmit, independently developed the same idea as Kronig in 1925. Under the advice of Paul Ehrenfest, they published their results in a small paper. It met a favorable response, especially after L.H. Thomas managed to resolve a factor of two discrepancy between experimental results and Uhlenbeck and Goudsmit's calculations. This discrepancy was due to a relativistic effect, known as the Thomas precession.

Despite his initial objections to the idea, Pauli formalized the theory of spin in 1927, using the modern theory of quantum mechanics discovered by Schrodinger and Heisenberg. He pioneered the use of Pauli matrices as a representations of the spin operators, and introduced a two-component spinor wave-function.

In 1928, Paul Dirac developed the Dirac equation, which described the relativistic electron. In the Dirac equation, a four-component spinor (known as a "Dirac spinor") 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 integer spin.