In special relativity, rapidity is a mathematical quantity that replaces velocity to simplify the description of motion and transformations between reference frames. Unlike velocity, which becomes complicated to add at relativistic speeds due to the speed-of-light limit, rapidity has a simple additive property under Lorentz transformations.
Rapidity is defined using hyperbolic functions and grows without bound, even as velocity approaches the speed of light. This makes it particularly useful in high-energy physics and special relativity calculations. For two observers moving at relativistic speeds, the difference in their rapidities directly gives the Lorentz boost needed to transform from one frame to another.
One key advantage of rapidity is that, while velocities add nonlinearly, rapidities add linearly, much like angles in Euclidean rotations. This makes it easier to handle multiple successive boosts (relativistic “velocity changes”) in a consistent mathematical framework.
Though not as intuitive as velocity in everyday terms, rapidity provides a powerful tool for analyzing relativistic motion, especially in particle physics and theoretical formulations of spacetime symmetries.