LorentzFaktor

LorentzFaktor, commonly referred to as the Lorentz factor or gamma, is a dimensionless quantity in special relativity that describes how measurements transform for observers in relative motion. It is defined by gamma = 1 / sqrt(1 - v^2/c^2), where v is the object's speed and c is the speed of light in vacuum. Gamma equals 1 at rest and grows without bound as v approaches c, reflecting increasingly strong relativistic effects.

The Lorentz factor governs several key relativistic phenomena. Time dilation is expressed as t = gamma t0, meaning moving clocks run slower relative to a stationary observer. Length contraction occurs along the direction of motion: L = L0 / gamma. In modern formulations, the concept of relativistic mass is discouraged; instead, relationships among energy, momentum, and invariant mass are used.

Energy and momentum are linked by E^2 = (pc)^2 + (mc^2)^2, where E is total energy, p is momentum, m is invariant (rest) mass, and c is the speed of light. The kinetic energy is K = (gamma - 1) mc^2, and the total energy is E = gamma mc^2. The Lorentz factor also appears in momentum p = gamma mv and in various relativistic corrections relevant to high-velocity particles.

Historically, the factor is named after Hendrik Lorentz and is central to Einstein's theory of special relativity. It is widely used in physics, including particle physics, astrophysics, and navigation systems such as GPS, where relativistic time corrections are essential for accuracy.