We establish a geometric connection of mechanical concepts such as center of mass and moment of inertia with optical coherence wave properties in terms of polarization and entanglement.
While optics and mechanics are two distinct branches of physics, they are connected. It is well known that the geometrical/ray treatment of light has direct analogies to mechanical descriptions of particle motion. However, connections between coherence wave optics and classical mechanics are rarely reported. Here we report links of the two through a systematic quantitative analysis of polarization and entanglement, two optical coherence properties under the wave description of light pioneered by Huygens and Fresnel. A generic complementary identity relation is obtained for arbitrary light fields. More surprisingly, through the barycentric coordinate system, optical polarization, entanglement, and their identity relation are shown to be quantitatively associated with the mechanical concepts of center of mass and moment of inertia via the Huygens-Steiner theorem for rigid body rotation. The obtained result bridges coherence wave optics and classical mechanics through the two theories of Huygens.
Nonrelativistic formalism is developed, which allows describing systems with internal degrees of freedom in the scalar potential field U, which is a function both on relative coordinates and time, and on relative speed and accelerations. The equation for energy, which is an integral of motion when U satisfies to certain differential condition, is derived for the general case. For a free mass point all solutions of the equations of motion in the center-of-inertia reference frame, moving with constant velocity, are obtained. As a result, the center of mass follows along a complicated trajectory round a direction of motion of the center of inertia. This motion can be interpreted as Zitterbewegung. It is shown that equation of moments is a consequence of the equation of motion. The general equation of motion for a spin which can be interpreted from positions of a classical mechanics is written down. Application of the obtained results to the electron leads to new conception of electrical charge, sign of which corresponds to a sign of spin polarization.