Proper velocity by Hermann Minkowski's flat-space metric equation . Here a reference map frame of yardsticks and synchronized clocks define map position x and map time "t" respectively, and the "d" preceding a coordinate means infinitesimal change. A bit of manipulation allows one to show that proper velocity where as usual coordinate velocity . Thus finite "w" ensures that "v" is less than lightspeed "c". By grouping "γ" with v in the expression for relativistic momentum p, proper velocity also extends the Newtonian form of momentum as mass times velocity to high speeds without a need for relativistic mass. The proper velocity
Front velocity any medium tends to one as the frequency tends to infinity, that the wave discontinuity, called the "front", propagates at a speed less than or equal to the speed of light "c" in any medium. In fact, the earliest appearance of the front of an electromagnetic disturbance (the precursor) travels at the "front velocity", which is "c", "no matter what the medium". However, the process always starts from zero amplitude and builds up. Front velocity In physics, front velocity is the speed at which the first rise of a pulse above zero moves forward. In mathematics, it is used to