Key formulae — Special relativity

Summary of special relativity formulae (ch. 20). Derivations and limits of validity are in the chapter.

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

Time dilation and length contraction $\Delta t = \gamma\,\Delta\tau \qquad L = \frac{L_0}{\gamma}$

Relativistic velocity addition $u = \frac{u' + v}{1 + u'v/c^2}$

Energy and momentum

$E = \gamma m c^2 \qquad p = \gamma m v \qquad E^2 - (pc)^2 = (mc^2)^2$

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Topics: Special relativity Concepts: Time dilation · Length contraction · Mass-energy equivalence