The Lorentz factor γ (gamma) appears throughout Special Relativity as the scaling factor that relates measurements in one inertial frame to measurements in another moving relative to it.
Its definition is:
γ = 1 / √(1 − v²/c²)
At v = 0, γ = 1 — no scaling. At v = 0.5c, γ ≈ 1.155. At v = 0.99c, γ ≈ 7.09. As v approaches c, γ approaches infinity.
In Special Relativity:
— Time dilation: Δt′ = γΔt
— Length contraction: L′ = L/γ
— Relativistic momentum: p = γmv
— Total energy: E = γmc²
In the revised framework of this theory, a modified factor γ′ is derived in Part II. At low velocities, γ′ ≈ γ to within experimental precision. The frameworks diverge at ultra-relativistic velocities.
The Lorentz factor is named after Hendrik Lorentz (1853–1928), who derived the transformation equations that bear his name before Einstein provided their physical interpretation.