Rapidité

Rapidité is a French noun meaning speed or the quality of being rapid. In everyday language it describes how quickly something happens or moves. The term comes from Old French rapidité, from Latin rapiditas, itself from rapidus meaning swift.

In physics, rapidité has two related but distinct meanings. Speed is the scalar magnitude of the velocity vector; velocity is a vector with magnitude and direction. Rapidity, in the framework of special relativity, is a measure of relativistic velocity along a chosen axis that adds linearly under successive boosts. For motion along the z-axis, rapidity y is defined by tanh y = v/c, so y = arctanh(v/c). Equivalently, y can be written as y = 0.5 ln[(E+pz)/(E-pz)], where E is the energy and pz the longitudinal momentum (c restored as needed).

In collider physics, rapidity and pseudorapidity are used to describe particle angles. Pseudorapidity η is defined as η = -ln[tan(θ/2)], where θ is the polar angle relative to the beam axis. For massless particles, rapidity and pseudorapidity approximately coincide (y ≈ η). A key property is that differences in rapidity are invariant under Lorentz boosts along the beam axis, making rapidity a convenient variable for describing particle production and detector geometry.

See also: velocity, speed, pseudorapidity.