Variable-mass system events. The following derivation is for a body that is gaining mass (accretion). A body of time-varying mass "m" moves at a velocity v at an initial time "t". In the same instant, a particle of mass dm moves with velocity u. The initial momentum can be written as Now at a time "t" + d"t", let both the main body and the particle accrete into a body of velocity v + dv. Thus the new momentum of the system can be written as Since d"m"dv is the product of two small values, it can be ignored, meaning during d"t"
Mass–energy equivalence the velocity is small, the relativistic mass and the rest mass are almost exactly the same. Also Einstein (following Hendrik Lorentz and Max Abraham) used velocity- and direction-dependent mass concepts () in his 1905 electrodynamics paper and in another paper in 1906. However, in his first paper on (1905), he treated as what would now be called the "rest mass". Some claim that (in later years) he did not like the idea of "relativistic mass". When modern physicists say "mass", they are usually talking about rest mass, since if they meant "relativistic mass", they would just say "energy". Considerable debate