Lorentz factor

Remarks

Example: for $v = 0.6 c$, one has $\beta^2 = 0.36$, $\sqrt{1 - 0.36} = 0.8$ and $\gamma = 1.25$. Non-example: for $v = c$ the denominator is $0$, so the Lorentz factor is not defined; it tends to $+\infty$ as $\abs{v} \to c$. Always $\gamma \ge 1$, with equality only at $v = 0$, and $\gamma = 1 + \tfrac{1}{2} \beta^2 + O(\beta^4)$ for small $\beta$. The useful identity $\gamma^2 (1 - \beta^2) = 1$ is equivalent to $\gamma^2 - (\gamma \beta)^2 = 1$.