Consider some particle P characterized by its wavevector and the total number of quarks it contains . Report on any changes relative to a frame of reference F which is characterized using the average wavevector of the quarks in F. The momentum of P in the F-frame is defined as

Let the frame of reference be formed from a large component and a smaller part that surrounds P so that

and

Let the large part of F be responsible for any gravitons that interact with P so that when gravitational effects are completely negligible

Then P’s momentum is given by

From de Broglie’s postulate we have , so

To simplify, set in the expression above to define as the wavelength of P in a non-dispersive surrounding medium

Many different combinations of photons and media are usefully characterized by defining the ratio

This number is called the index of refraction. Then in environments where there is no dispersion, and motion is described by