Special Relativity

The Two Postulates

1. The laws of physics are the same in all inertial reference frames.
2. The speed of light in vacuum is $c \approx 3\times 10^8\,\text{m/s}$ for all observers.

Lorentz Factor

$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$

Time Dilation and Length Contraction

$$\Delta t' = \gamma\,\Delta t \qquad L' = L/\gamma$$

Mass-Energy Equivalence

$$E = mc^2 \qquad E^2 = (pc)^2 + (mc^2)^2$$

See also article-general-relativity for the curved-spacetime extension.

The pendulum animation above demonstrates classical mechanics intuition before we break it with relativity.