To Spin or not to Spin

Spin is an intrinsic property of elementary particles that was first observed in electrons. In the 1880's scientists studying the spectrum of light emitted by mercury vapor discovered that light emitted by atoms was not a continuous range of frequencies (frequency of light is directly proportional to its energy) but rather a discrete one. If you shine white light through a prism you get a continuos band of light that looks like this . On the other hand if you are Johann Balmer in 1887 studying the spectrum emitted from Hydrogen gas you get a series of lines . The light comes from charged electrons moving about the nucleus emitting energy in the form of light as they move from higher energy states to lower ones. For many years physicists were puzzled by the discrete nature of the light emitted and why the electrons didn't just lose all the energy they had and fall into the nucleus as a result.

This observation was satisfactorily explained in 1913 by the Bohr model of the atom. Niels Bohr postulated that the electrons can only rotate about the nucleus at certain set distances away from it specifically that the angular momentum of the electrons (mass X velocity X radius of the orbit) = n X h, where n is just an integer = 1,2,3,... ad infinitum and h is a constant called the Planck constant. The larger the radius of the electrons orbit the larger its rotational energy so the orbits are referred to as energy levels. By jumping from higher energy levels to lower ones electrons emit the energy they lose as light whose energy is the precise difference between the two levels. The Bohr model not only successfully explained the discreteness of the line spectra but was also able to predict the correct sequence of lines in the Balmer series of Hydrogen. Bohr had thus introduced the concept of "quantization" of angular momentum and the magic integers, n, are now referred to as "quantum numbers".

As instruments measuring the emission spectra of various elements acquired more and more resolving power it was discovered that the discrete lines in the emission spectra of alkali metals are themselves formed of a set of even finer lines. Just as the initial coarser splitting of the emission spectra was due to the properties of the orbital angular momentum of electrons around the nucleus, in 1925, two Dutch physicists Samuel Goudsmith and George Uhlenbeck, attributed this new fine structure splitting to an intrinsic angular momentum of the electron separate from its orbital angular momentum. At first, it was assumed that this intrinsic angular momentum was due to the electron spinning about an axis and so it was called the spin of an electron, however, when the magnetic properties of the electron were measured and compared to that of a macroscopic charged sphere rotating about its axis, it was discovered that it did not agree with the expected properties from a spinning charged sphere. This along with other evidence led physicists to abandon the idea that the intrinsic angular momentum of an electron is due to a spin but surmised however that it is a special property of the electron. Unfortunately the misnomer spin stuck. Like orbital angular momentum, spin too has a special set of quantum numbers associated with it. For an electron (and electron like particles) the spin quantum numbers go like 1/2,3/2,5/2 ...

Fermions and Bosons

Electrons belong to a different family of elementary particles other than quarks called leptons. Like electrons other elementary particles also have spin-like properties. For elementary particles there are 2 types of spin: quarks and leptons are fermions (named after Enrico Fermi) whose spin quantum numbers are integer multiples of 1/2 (spin = 1/2,3/2,5/2...) and the so called gauge bosons (named after Satyendra Nath Bose); photons, gluons, Ws, Zs; with integer spin (spin = 0 ,1, 2). In particle physics everything is a particle even forces! the gauge bosons are the particles responsible for the forces that govern the behavior of quarks and leptons. Photons are carriers of the electromagnetic force, W and Z bosons carry the weak force and gluons carry the strong force. Theorists are constantly attempting to integrate Einstein's theory of relativity into this picture by posutlating the existance of gravitons, bosons that carry the gravitational force.

Spin plays an integral part in our understanding of the interactions of particles. Spin adds an extra dimension to the symmetry described by parity. Fermions have odd parity under the inversion of co-ordinates in their wave functions (the mathematical description of the physical state of a system) while bosons are parity even.

The different spin quantum numbers of Fermions and bosons are therefore connected to their statistical behaviour, that is to say the mathematics that governs the behaviour of a system containing more than one of a given species. If you want to calculate the probability that a fermion is going to behave in a certain way you have to use Fermi-Dirac statistics and if want to make a prediction about the behaviour of a boson you use Bose-Einstein statistics. An example of the different statistical behaviour of fermions and bosons is that no two fermions like to occupy the same quantum mechanical state i.e. no two fermions can have the same orbital angular momentum quantum number AND spin quantum number AND occupy the same physical space; this is known as the Pauli exclusion princple. In laymans terms: fermions can't sit next to each other in the same place if they both have the same spin orientation. Call it the subatomic equivalence of sibling rivlary. Bosons on the other hand, make great buddies, they just love being together. The probability that a boson will appear in a state in which there are already N number of bosons is directly proportional to the square root of N ; the more the merrier. It is this property of Bose-Einstein statistics that makes lasers possible. Lasers being of course dependant on having lots of photons, which are bosons, occupying the same quantum mechanical state.

Incidentally, Bose-Einstein statistics were originally developed to predict the properties of a strange state of matter called a Bose-Einstein condensate of which liquid Helium and super conductors are an example. Bose-Einstein condensates were postulated more than 70 years ago, long before the discovery of the W and Z bosons at CERN in 1983.