The bipolar coordinates of a point may be loosely defined as the distances of the point from each of two reference points. Consistent definitions are developed for the bipolar coordinates of a point on a sphere with the reference points at opposite ends of a diameter, and it is shown that the bipolar coordinates so defined transform like Pauli spin functions under rotations. The electron is visualized as a point mass with charge $e$ moving on the sphere with its motion expressed in terms of its bipolar coordinates. It is assumed observable only at two diametrically opposite points of its orbit. This picture allows an exact physical interpretation of the spin variable and the Pauli spin operators. The magnetic moment associated with the motion is $\frac{e\hslash }{2mc}$; the radius of the electron is taken as the radius of the sphere which is $\frac{\hslash }{2mc}$; the wave-length associated with the spinning motion is $\frac{h}{\mathrm{mc}}$. Two related functions must be introduced to take care of reflections and these together with the two original functions transform like Dirac spin functions under rotations, reflections, and Lorentz transformations.

Close

PrevNext

View figure in article