Proper velocity Proper velocity In relativity, proper velocity, also known as celerity, is an alternative to velocity for measuring motion. Whereas velocity relative to an observer is distance per unit time where both distance and time are measured by the observer, proper velocity relative to an observer divides observer-measured distance by the time elapsed on the clocks of the traveling object. Proper velocity equals velocity at low speeds. Proper velocity at high speeds, moreover, retains many of the properties that velocity loses in relativity compared with Newtonian theory. For example, proper velocity equals momentum per unit mass at any speed, and therefore
Mass in special relativity derived form formula_44 is not valid because formula_45 in formula_46 is generally not a constant (see the section above on transverse and longitudinal mass). Even though Einstein initially used the expressions "longitudinal" and "transverse" mass in two papers (see previous section), in his first paper on formula_47 (1905) he treated "m" as what would now be called the "rest mass". Einstein never derived an equation for "relativistic mass", and in later years he expressed his dislike of the idea: Okun and followers reject the concept of relativistic mass. Also Arnold B. Arons has argued against teaching the concept of relativistic