Physics Faces

William Rowan Hamilton  (1805-1865)

 “The celebrated equations that now bear his name were, for Hamilton, an adjunct of a more fundamental interest in optics. Like Jacobi, Hamilton knew the formal connection between point mechanics and geometrical optics for which Fermat’s principle corresponds to the action principle for particles and light-ray surfaces of constant phase (which Hamilton called his “characteristic function”) are analogous to level surfaces of action. He solved a variety of optical problems with the characteristic function including a prediction that a light-ray incident on a biaxial crystal should emerge as a hollow cone. Its demonstration two months later caused a sensation in the scientific community. Hamilton’s use of the eccentricity invariant of the Kepler problem occurred in relation to his application of the characteristic function to problems of celestial mechanics. Hamilton’s other beautiful discovery was that of quaternions, a four-dimensional generalization of the two-dimensional complex variable. The algebra of these quantities is the same as that of four-dimensional rotations, an amazing coincidence with the symmetry algebra of Kepler motion of which Hamilton was not aware.”

From: The Shaggy Steed of Physics by David Oliver, Springer-Verlag, 1994.