Rapiditatea

Rapiditatea is a Romanian term for speed or rate of motion. In physics, rapiditatea (rapidity) is a kinematic quantity used in special relativity and high-energy physics to describe the state of motion of a particle in a way that simplifies calculations involving boosts.

For a particle moving with velocity v along a chosen axis, the rapiditatea y is defined by tanh(y) = v/c, where c is the speed of light. Equivalently, y = artanh(v/c) = (1/2) ln[(1 + v/c) / (1 − v/c)]. This leads to the relations γ = cosh(y), β = v/c = tanh(y), and βγ = sinh(y), where γ is the Lorentz factor and β is the velocity as a fraction of c.

A key property is that rapidities add for successive boosts along the same direction: y_total = y1 + y2. This linearity makes rapidity a convenient parameter in relativistic kinematics, even though rapidity itself is not a Lorentz scalar. In collider physics, rapidity distributions are often preferred because boosts along the beam axis translate into simple shifts in rapidity.

Pseudorapidity, η, is a related concept defined from the polar angle θ by η = −ln tan(θ/2). For massless particles, rapidity y and pseudorapidity η coincide; for massive particles they differ, though the two quantities are closely related in many experimental contexts.

See also Lorentz transformation, hyperbolic angle, and pseudorapidity.