The Lorentz Factor

The Lorentz Factor

Special relativity rests on two postulates: the laws of physics are the same in all inertial frames, and the speed of light $c = 299{,}792{,}458$ m/s is the same for all observers. These innocent-sounding rules force us to abandon absolute time and space.

The quantity that appears in every relativistic formula is the Lorentz factor $\gamma$. It is built from the beta parameter $\beta$, the fraction of the speed of light:

$\beta = \frac{v}{c}$

$\gamma = \frac{1}{\sqrt{1 - \beta^2}}$

Behaviour

At everyday speeds $\gamma \approx 1$ and all relativistic effects are negligible. As $v \to c$, $\gamma$ diverges, meaning it takes infinite energy to reach light speed. The factor $\gamma$ will reappear in time dilation, length contraction, and relativistic momentum and energy.

Your Task

Implement lorentz_factor(v) that returns $\gamma$ for a velocity $v$ in m/s, and beta(v) that returns $\beta = v/c$. Use $c = 299792458.0$ m/s. Both constants must be defined inside each function.