This short article explains how relativistic transformations can be replaced by the Doppler
effect when it affects mass.
The simplest formulation of relativistic mass and the Einstein invariance is
m0 = m sqrt(1 – v2/c2)
, where m0 is the rest-mass. The remainder of the Doppler effect for light affecting mass is
mS = m0 sqrt[(1 – v/c)/(1 + v/c)]
, where mS is the source-mass. These two equations together are the same as the full Doppler
effect for light affecting mass (causing mass change), namely
mS = m(1 – v/c)
, where the source-mass takes on the traditional place of the rest-mass. The resulting kinetic
KE = mc2 – mSc2 = pc
, where p is the impulse p = mv.
1 May 2012, Oegstgeest