III.2.7 Note IV (the effective mass):
Therefore, even when the object is moving at any velocity that could be very close to , its instantaneous velocity is always zero: , at the actual time of measurement, and its mass will still be the same rest mass: , because it is only detected as a particle, while its kinetic energy will be given by its relativistic mass: , and then its total energy equivalence, with relation to an observer moving at a constant (apparent) velocity , will be given by:
(3.11)
Thus, with the help of Lorentz factor , we could get rid of the confusion between rest mass and relativistic mass and just call it mass since the above equation 3.11 describes energy and not mass:
(3.12)
Which means that the mass of any particle is always the rest mass, it is not relativistic, but its energy is relativistic, primarily because energy is related to time and motion or velocity. However, since we have been using all over this article, we will keep using it as the rest mass, and as the effective mass, unless stated otherwise.