Rapiditet

Rapiditet, commonly called rapidity in English, is a parameter used in special relativity and high-energy physics to describe the velocity of a particle along a chosen direction. It is defined by the relation v = c tanh(y), where v is the particle’s speed along the chosen axis, c is the speed of light, and y is the rapidity. Equivalently, y = artanh(v/c) = 0.5 ln((1 + v/c)/(1 − v/c)). The Lorentz factor gamma equals cosh(y) and the velocity fraction beta equals tanh(y). A key property is that rapidities add for successive boosts along the same axis: y_total = y1 + y2. This makes rapidity a convenient variable for relativistic kinematics, especially in particle collisions.

In high-energy physics, rapidity is used because differences in rapidity are additive under boosts along the beam axis, and distributions in rapidity transform simply under such boosts. A related concept is pseudorapidity η, defined from the polar angle θ by η = −ln[tan(θ/2)], which approximates rapidity for massless particles and is widely used in detector analyses.

The term rapiditet derives from the French rapide/rapidité and reflects its interpretation as a hyperbolic angle parameterizing Lorentz boosts. Rapidité emphasizes the hyperbolic geometry underlying special relativity, where boosts correspond to Lorentz transformations in Minkowski space. Distinctions exist between rapidité and velocity: rapidité is a convenient, additive parameter linked to velocity through hyperbolic functions, not a direct measure of speed.