Lorentz transformation

\[\begin{equation}\label{lorentz} \begin{aligned} x' &= \frac{x-ut/c^2}{\sqrt{1-u^2/c^2}} \\ t' &= \frac{t-ux/c^2}{\sqrt{1-u^2/c^2}}\\ y' &= y \\ z' &= z \end{aligned} \end{equation}\]

Rotation

\[\begin{equation}\label{rotation} \begin{aligned} x' &= x\cos(\theta) + y\sin(\theta) \\ y' &= y\cos(\theta) - x\sin(\theta) \\ z' &= z \\ t' &= t \end{aligned} \end{equation}\]

Equation \eqref{lorentz} is beautiful. So is equation \eqref{rotation}.

References

• The Feynman Lectures on Physics First Year Photos (1961‑62) Lecture 17
• Lorentz transformation on Wikipedia