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