From 02329aaf48538030a4c075dd5d8b316e95e9b488 Mon Sep 17 00:00:00 2001 From: Jack Date: Sun, 11 Aug 2024 17:05:14 +0800 Subject: [PATCH] Update study notes --- parts/special-relativity.tex | 17 +++++++---------- study-notes.pdf | Bin 20781917 -> 20782157 bytes 2 files changed, 7 insertions(+), 10 deletions(-) diff --git a/parts/special-relativity.tex b/parts/special-relativity.tex index 62efe12..0cfd6ba 100644 --- a/parts/special-relativity.tex +++ b/parts/special-relativity.tex @@ -531,18 +531,15 @@ \subsubsection{\hfil \S3. Lorentz Transformation - Quantifying Non-Simultaneity Eq.~\ref{eq:transformation},~\ref{eq:x-transformation},~\ref{eq:y-transformation},~\ref{eq:z-transformation}: \begin{align} -\tau &= \varphi(v)\left[ t - \frac{v}{V^2 - v^2} (x - vt) \right] \\ - &= \varphi(v)\left( \frac{V^2t - v^2t - vx + v^2t}{V^2 - v^2} \right) \\ - &= \varphi(v)\left( \frac{V^2t - vx}{V^2 - v^2} \right) \\ - &= \varphi(v)\frac{V^2}{V^2 - v^2}\left( t - \frac{v}{V^2}x \right) +&\tau &= \varphi(v)\left[ t - \frac{v}{V^2 - v^2} (x - vt) \right] \\ + &= \varphi(v)\left( \frac{V^2t - v^2t - vx + v^2t}{V^2 - v^2} \right) \\ + &= \varphi(v)\left( \frac{V^2t - vx}{V^2 - v^2} \right) \\ + &= \varphi(v)\frac{V^2}{V^2 - v^2}\left( t - \frac{v}{V^2}x \right) \\ +\xi &= \varphi(v)\left( \frac{V^2}{V^2 - v^2} \right) (x - vt) \\ +\eta &= \varphi(v)\frac{V}{\sqrt{V^2 - v^2}}y \\ +\zeta &= \varphi(v)\frac{V}{\sqrt{V^2 - v^2}}z \\ \end{align} -\begin{equation} - \xi = \varphi(v)\left( \frac{V^2}{V^2 - v^2} \right) (x - vt) -\end{equation} - - - It does not lose generality to say if $k$ is moving relative to $K$ at speed $v$ then $K$ is moving relative to $k$ at speed $-v$. 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