updates

Author: davidmeyer

_my_stuff/papers/physics/special_relativity/special_relativity 2.synctex.gz

@@ -1,4 +1,4 @@
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+This is LuaHBTeX, Version 1.13.0 (TeX Live 2021)  (format=lualatex 2022.3.20)  7 MAY 2025 12:58
  restricted system commands enabled.
  file:line:error style messages enabled.
 **special_relativity.tex
@@ -1629,7 +1629,7 @@ Here is how much of LuaTeX's memory you used:
  651 words of node memory still in use:
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-   avail lists: 1:1,2:2973,3:1664,4:54,5:272,6:37,7:5025,8:90,9:778,10:14,11:293
+   avail lists: 1:1,2:2969,3:1666,4:54,5:272,6:37,7:5023,8:90,9:778,10:14,11:293
 
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-Output written on special_relativity.pdf (4 pages, 118304 bytes).
+Output written on special_relativity.pdf (4 pages, 118308 bytes).
 
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_my_stuff/papers/physics/special_relativity/special_relativity.log

@@ -382,7 +382,7 @@ \section{Time Dilation}
 
 \bigskip
 \noindent
-To compute $t^{\prime}$, consider the $h$, $x^{\prime}$, $c t^{\prime}$ 
+To compute $t^{\prime}$, consider the $h-x^{\prime}-c t^{\prime}$ 
 triangle shown in Figure \ref{figure:observer_motion}, which is abstracted 
 in Figure \ref{figure:triangle}. 
 
@@ -391,7 +391,7 @@ \section{Time Dilation}
   \resizebox{0.35 \textwidth}{!} {                                                                      % resize the figure if you want
      \begin{tikzpicture} 
         \draw[->, line width=1pt] (-1.22,0) -- (4.22,0) node[right] {$x$}; 
-        \draw[->, line width=1pt] (0,-1.22) -- (0,5.22) node[above] {$y$}; 
+        \draw[->, line width=1pt] (0,-1.22) -- (0,5.22) node[above] {$t$}; 
         \draw [line width=1pt,red] (1,1) -- (3,1) -- (1,4) -- cycle; 
         \draw[draw=none] (1,1) -- (1,4) node [midway,left] {$h$};
         \draw[draw=none] (1,1) -- (3,1) node [midway,below] {$x^{\prime}$};
@@ -413,10 +413,10 @@ \section{Time Dilation}
      (c t^{\prime})^2
      &=& h^2 + {x^{\prime}}^2 					
      		&\hspace{5.00em} \mathrel{\#} \text{by the Pythagorean theorem} \\
-[15pt]
+[10pt]
      &\Rightarrow& (c t^{\prime})^2 = {(ct)}^2 + {x^{\prime}}^2 					
      		&\hspace{5.00em} \mathrel{\#} h = c t \\
-[10pt]
+[15pt]
 	&\Rightarrow& (c t^{\prime})^2 = (ct)^2 + (v t^{\prime})^2
 			&\hspace{5.00em} \mathrel{\#} x^{\prime} = v t^{\prime} \\
 [15pt]