Translations:The eikonal equation - book/13/en

The eikonal equation is a restatement of Fermat’s principle of least time. In other words, a raypath must be a flow line. A flow line is orthogonal to all the wavefronts. The eikonal equation is the fundamental equation that connects the ray (which corresponds to the fuselage of the airplane) to the wavefront (which corresponds to both wings of the airplane). The wings let the fuselage feel the effects of points removed from the path of the fuselage. The eikonal equation makes a traveling wave (as envisaged by Huygens) fundamentally different from a traveling particle (as envisaged by Newton). Hamilton perceived that there is a wave-particle duality, which provides the mathematical foundation of quantum mechanics. Hamilton’s work is based on the principle of least action, which is a more general formulation of the principle of least time (Robinson and Douze, 1985).