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 extension a carbon-12 atom has a mass of exactly 12 u. This definition, however, might be changed by the proposed redefinition of SI base units, which will leave the Dalton very close to one, but no longer exactly equal to it. In some frameworks of special relativity, physicists have used differing definitions of the term "mass". However, such usage is controversial and has fallen out of favor. In these frameworks, two kinds of mass are defined: rest mass (invariant mass), and relativistic mass (which increases with velocity). Rest mass is the Newtonian mass as measured by an observer moving along