four-acceleration

In the theory of relativity, four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see three-acceleration in special relativity). Four-acceleration has applications in areas such as the annihilation of antiprotons, resonance of strange particles and radiation of an accelerated charge. Four-acceleration in inertial coordinates In inertial coordinates in special relativity, four-acceleration is defined as the rate of change in four-velocity with respect to the particle's proper time along its worldline. We can say: where , with the three-acceleration and the three-velocity, and and is the Lorentz factor for the speed (with ). A dot above a variable indicates a derivative with respect to the coordinate time in a given reference frame, not the proper time (in other terms, ).