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Sin-itiro Tomonaga [ What is spin? The term spin has two meanings in physics. The first meaning is the ordinary one, namely rotation about a local axis. For example, a spinning top has angular momentum equal to the moment of inertia multiplied by the angular frequency. This rotational angular momentum can be (but usually isn't) called spin angular momentum. The top can also have angular momentum due to translational motion. For example, if the top is tied to a string and spun around in a circular orbit, the angular momentum would be the linear momentum (mass times velocity) multiplied by the length of the string. This type of angular momentum can be called orbital angular momentum. In this example the spin angular momentum may also be considered as a type of orbital angular momentum since the rotational motion can be interpreted as each piece of the top orbiting around the axis. In quantum mechanics, the spin angular momentum has not (yet) been explicitly related to rotational motion. For a classical wave, the spin angular momentum is associated with motion of the medium whereas orbital angular momentum is associated with propagation of the wave. The second meaning of spin relates
to the transformation of variable components under rotations. In
this context the spin is Waves always have two independent
states The four components of a
one-dimensional bispinor represent the forward positive, forward
negative, backward positive, and backward negative components of
the wave. Extension to three dimensional vector waves requires
eight free parameters which can be regarded as forward and
backward wave amplitudes (2 parameters) , rotation of polarization
axes (3), rotation of velocity axes (3) . (Although only two
rotation angles are required to specify a direction, a third
rotation angle is necessary to also specify the plane of Elementary particles with half-integer spin are called 'Fermions'. Elementary particles with integer spin are called 'Bosons'. Bispinors were first proposed in 1928 by Paul Dirac in order to model the electron. This author has not found any other physics literature mentioning that bispinors have a simple classical interpretation as solutions of ordinary classical wave equations. For more detail go to Chapter 3 of The Classical Theory of Matter Waves. |

Created: 27 February 2006; Last updated: 24 January 2008 Copyright © 2006-2007 Robert A. Close |