Lorentzfactor

The Lorentzfactor, denoted by gamma (γ), is a dimensionless factor that arises in special relativity and mediates the transformation between inertial frames moving at relative speed v with respect to the invariant speed of light c. It is defined as γ = 1 / sqrt(1 − v^2/c^2). When v is much less than c, γ ≈ 1 + v^2/(2c^2). As v approaches c, γ increases without bound.

Its consequences include time dilation, length contraction, and the relativistic increase of momentum and energy. For an interval measured in a moving frame, the relation to proper time is Δt = γ Δτ. A rod moving relative to an observer is measured to be L = L0/γ. A particle of rest mass m has momentum p = γ m v and total energy E = γ m c^2, with kinetic energy K = (γ − 1) m c^2.

The Lorentzfactor is central in particle physics, accelerator design, and astrophysics, where particles reach relativistic speeds. It also underpins precision timing and navigation technologies that must account for relativistic time dilation, such as satellite-based clocks. In the broader framework of relativity, γ reduces to 1 in the nonrelativistic limit, illustrating how relativistic effects fade at low speeds.