Two-observer diagram of causality violation in special relativity.

Causality.tex

\documentclass[crop=true, border=10pt]{standalone}
\usepackage{comment}
\begin{comment}
:Title: Causality Violation
:Author: J A Miller (millerja@uah.edu), 2020/02/04, 2018/03/29

Two-observer diagram showing causality violation in some frame for two spacelike events.

Plot style from McNees
https://gist.github.com/mcnees/45b9f53ad371c38ba6f3759df5880fb1
\end{comment}


\usepackage{xcolor}

\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{angles}
\usetikzlibrary{quotes}

% McNees color scheme
% https://gist.github.com/mcnees
\definecolor{plum}{rgb}{0.36078, 0.20784, 0.4}
\definecolor{chameleon}{rgb}{0.30588, 0.60392, 0.023529}
\definecolor{cornflower}{rgb}{0.12549, 0.29020, 0.52941}
\definecolor{scarlet}{rgb}{0.8, 0, 0}
\definecolor{brick}{rgb}{0.64314, 0, 0}
\definecolor{sunrise}{rgb}{0.80784, 0.36078, 0}
\definecolor{lightblue}{rgb}{0.15,0.35,0.75}



\begin{document}

% Define the boost
\newcommand*\vrel{0.6}  			% velocity of primed frame
\newcommand*\gamrel{1.25}  		% gamma of primed frame
\newcommand*\etarel{0.75}		% their product


% Set some points to plot, if desired
\newcommand*\xpt{4}
\newcommand*\tpt{6}

\newcommand*\xpti{8}
\newcommand*\tpti{7}



\begin{tikzpicture}[scale=1,domain=-1:11]
	\tikzstyle{axisarrow} = [-{Latex[inset=0pt,length=8pt]}]
	\coordinate (origin) at (0,0);

	% Draw the grid.
	%\draw [cornflower!30,step=0.2,thin] (-1,-1) grid (11,11);  % minor grid lines
	\draw [cornflower!60,step=1.0,thin] (-1,-1) grid (11,11);  % major grid lines

	% Clip all lines that would fall outside the grid
	\clip(-1,-1) rectangle (11,11);
	
	% Draw unprimed axes
	\draw[thick,axisarrow,cornflower] (0,-1) -- (0,11) node (tup) {};
	\node[inner sep=0pt] at (0.25,10.75) {$t$};
	\draw[thick,axisarrow,cornflower] (-1,0) -- (11,0) node (xup) {};
	\node[inner sep=0pt] at (10.75,-0.25) {$x$};
	
	% Draw primed axes
	\draw[thick,axisarrow,scarlet] (0,0) -- (11*\vrel,11) node (tp) {};
	\node[inner sep=0pt] at (11*\vrel+0.25,10.75) {$t^\prime$};
	\draw[thick,axisarrow,scarlet] (0,0) -- (11,11*\vrel) node (xp) {};
	\node[inner sep=0pt] at (10.75,11*\vrel-0.35) {$x^\prime$};
	
	% Draw lines of constant xprime
	\foreach \xprime in {-11,-10,-9,...,12}
		{
			\draw[scarlet!60,thin] plot (\x,\x/\vrel - \xprime/\etarel);
		} 
		
	% Draw lines of constant tprime
	\foreach \tprime in {-11,-10,-9,...,12}
		{
			\draw[scarlet!60,thin] plot (\x,\x*\vrel + \tprime/\gamrel);
		} 
		
	% Add some points if needed
	\node[circle,draw=cornflower!70,fill=cornflower!20,inner sep=2pt,label={below:Shoot}](A) at (\xpt,\tpt)  {};
	\node[circle,draw=cornflower!70,fill=cornflower!20,inner sep=2pt,label={Impact}](B) at (\xpti,\tpti)  {};
	
	

\end{tikzpicture}
		
\end{document}