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
Four-velocity the 3d position vector, written as a column vector The components of the velocity formula_2 (tangent to the curve) at any point on the world line are Each component is simply written In Einstein's theory of relativity, the path of an object moving relative to a particular frame of reference is defined by four coordinate functions "x"("τ"), where μ is a spacetime index which takes the value 0 for the timelike component, and 1, 2, 3 for the spacelike coordinates. The zeroth component is defined as the time coordinate multiplied by "c", Each function depends on one parameter "τ" called