% miko:type: complete
% miko:title: Complete Special Relativity
% miko:summary: A structured path through Lorentz symmetry, intervals, and proper time.
% miko:tags: relativity
% miko:difficulty: undergrad
% miko:related: lorentz-transformation, minkowski-interval, proper-time
% miko:keywords: Lorentz, spacetime, invariant

\documentclass{article}
\usepackage{amsmath}
\title{Complete Special Relativity}
\begin{document}
\maketitle

\section{Postulates}

The laws of physics are the same in inertial frames, and the speed of light is
invariant.

\section{Lorentz Transformations}

For motion along $x$,

$$
t'=\gamma\left(t-\frac{vx}{c^2}\right),
\qquad
x'=\gamma(x-vt).
$$

\section{Spacetime}

The invariant interval is

$$
ds^2=-c^2dt^2+dx^2+dy^2+dz^2.
$$

\end{document}
