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
Mass–energy equivalence Mass–energy equivalence In physics, mass–energy equivalence states that anything having mass has an equivalent amount of energy and vice versa, with these fundamental quantities directly relating to one another by Albert Einstein's famous formula: formula_1 This formula states that the equivalent energy () can be calculated as the mass () multiplied by the speed of light ( = about m/s) squared. Similarly, anything having energy exhibits a corresponding mass given by its energy divided by the speed of light squared . Because the speed of light is a very large number in everyday units, the formula implies that even an