% miko:type: atomic
% miko:title: Proper Time
% miko:summary: The time measured by a clock moving along a worldline.
% miko:tags: relativity
% miko:difficulty: undergrad
% miko:related: lorentz-transformation, minkowski-interval, complete-special-relativity
% miko:keywords: worldline, time dilation, spacetime

\documentclass{article}
\usepackage{amsmath}
\title{Proper Time}
\begin{document}
\maketitle

\section{Definition}

For timelike motion,

$$
d\tau = \frac{1}{c}\sqrt{-ds^2}.
$$

\section{Time Dilation}

For speed $v$ in an inertial frame,

$$
d\tau = dt\sqrt{1-\frac{v^2}{c^2}}.
$$

\end{document}
