# E = mc^2: Identity or equality

by pmb_phy
Tags: equality, identity
 P: 328 Inertial mass is not relativistic mass as I have mathematically proven here in the past. Relativistic mass has no place in modern relativity as it is just a redundant name for relativistic energy which is defined as the time element of the momentum four-vector of the first kind. From the definition of the momentum four-vector of the second kind one has $$P^{0} = p^{0} + (q/c)\phi ^{0}$$ This yields $$E_{R} = E_{tot} - E_{pot}$$ $$E_{R}$$ is the relativistic energy and what is innapropriately called relativistic mass. You also missname energy parameter by total energy as well which is unfortunate, but even if by that mistake you have identified relativistic mass with the energy parameter instead of the total energy, you have still "identified" it with an energy. That should end your questioning whether it is an identity because even though you have identified it with the wrong energy, you have still "identified" it yourself. To see more about what I am refering to conserning the different kinds of momentum four-vectors see http://www.geocities.com/zcphysicsms/chap3.htm