Mass in special relativity detail by Oliver Heaviside (1889) and George Frederick Charles Searle (1897). So the electrostatic energy behaves as having some sort of electromagnetic mass formula_25, which can increase the normal mechanical mass of the bodies. Then, it was pointed out by Thomson and Searle that this electromagnetic mass also increases with velocity. This was further elaborated by Hendrik Lorentz (1899, 1904) in the framework of Lorentz ether theory. He defined mass as the ratio of force to acceleration, not as the ratio of momentum to velocity, so he needed to distinguish between the mass formula_26 parallel to the direction of motion
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