Mass in special relativity what causes these particles to be termed "massless." However, even massless particles have a relativistic mass, which varies with their observed energy in various frames of reference, The invariant mass is the ratio of four-momentum (the four-dimensional generalization of classical momentum) to four-velocity: and is also the ratio of four-acceleration to four-force when the rest mass is constant. The four-dimensional form of Newton's second law is: The relativistic expressions for "E" and "p" obey the relativistic energy–momentum relation: where the m is the rest mass, or the invariant mass for systems, and "E" is the total energy. The equation is
Group velocity amplitudes diminish as they approach the leading edge. The longer waves travel more slowly, and their amplitudes diminish as they emerge from the trailing boundary of the group. The group velocity is defined by the equation: where is the wave's angular frequency (usually expressed in radians per second), and is the angular wavenumber (usually expressed in radians per meter). The phase velocity is: . The function , which gives as a function of , is known as the dispersion relation. One derivation of the formula for group velocity is as follows. Consider a wave packet as a function of position