Proper velocity addition formula: where formula_3 is the beta factor given by formula_4. or in terms of logarithms: Proper velocity is useful for comparing the speed of objects with momentum per unit rest mass ("w") greater than lightspeed "c". The coordinate speed of such objects is generally near lightspeed, whereas proper velocity tells us how rapidly they are covering ground on "traveling-object clocks". This is important for example if, like some cosmic ray particles, the traveling objects have a finite lifetime. Proper velocity also clues us in to the object's momentum, which has no upper bound. For example, a 45 GeV electron
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