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March 18, 2021 21:08
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Two-observer diagram of causality violation in special relativity.
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\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} |
Author
jamesamiller
commented
Mar 18, 2021
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