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
Electron rest mass This quantity formula_5 is frame invariant and velocity independent. However, some texts group the Lorentz factor with the mass factor to define a new quantity called the "relativistic mass", formula_7. This quantity is evidently velocity dependent, and from it arises the notion that "mass increases with speed". This construction is optional, however, and adds little insight into the dynamics of Special Relativity. Since the electron mass determines a number of observed effects in atomic physics, there are potentially many ways to determine its mass from an experiment, if the values of other physical constants are already considered known. Historically, the