Newtonian mechanics geometric optics

The geometric description of the light propagation and the kinetics description of motion were closely correlated in the history of science. Among the main evidence of classical Newtonian mechanics is Euclidean geometry based on optical effects. In Newtonian physics, space has an affine structure but time is absolute. The basic idea is the inertial system, and the relations are the linear force laws. The affine structure allows linear transformations in space between the inertial coordinate systems, but not in time. This is the Galilean transformation ... 

The fine distinction between traveling times and the shift in interference fringes may not be clear from the point of view of Newtonian mechanics, which predicts both to be changing. Finally, classical physics and the geometric optics are refuted or restricted by experience, notwithstanding the fact that these are self-consistent theories in their own right. 

In a strict sense, the classical Newtonian mechanics and the Maxwell s theory of electromagnetism are not compatible. The M-M-type experiments refuted the geometric optics completed by classical mechanics. In classical mechanics the inertial system was a basic concept, and the equation of motion must be invariant to the Galilean transformation Eq. (1). After the M-M experiments, Eq. (1) and so any equations of motion became invalid. Einstein realized that only the Maxwell equations are invariant for the Lorentz transformation. Therefore he believed that they are the authentic equations of motion, and so he created new concepts for the space, time, inertia, and so on. Within... 

Hamilton, Sir Wiiiiam Rowan (1805-65) Irish mathematician and physicist. Hamilton invented what is now known as the Hamiltonian formulation of Newtonian mechanics. In doing so, he discovered that there is a very close analogy between Newtonian mechanics and geometrical (ray) optics. He also invented quaternions in mathematics and found a number of applications of quaternions in physics. 

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