Intro to modern physics
Space, time, and relativity
Equations
\begin{equation}
\textbf{u} = \textbf{u}' + \textbf{v} \tag{1.1}
\end{equation}
\begin{equation}
\textbf{a}' = \frac{d \textbf{u}'}{dt'} \tag{1.2}
\end{equation}
\begin{equation}
\textbf{a}' = \textbf{a} - \frac{d \textbf{v}}{dt} \tag{1.3}
\end{equation}
- Newton's laws hold in any inertial reference frame.
- The speed of light is the same in any inertial reference frame.
\begin{equation}
\Delta t = \frac{\Delta t'}{\sqrt{1 - \beta \, ^2}} \tag{1.4}
\end{equation}
\begin{equation}
\beta = \frac{v}{c}
\end{equation}
\begin{equation}
\gamma = \frac{ 1 }{\sqrt{1 - \beta \, ^2}} = \frac{ 1 }{\sqrt{1 - (v/c)^2}} \tag{1.5}
\end{equation}
\begin{equation}
\gamma \geq 1 \tag{1.6}
\end{equation}
\begin{equation}
\Delta t_0 = \frac{\Delta t}{\gamma} \tag{1.7}
\end{equation}
\begin{equation}
l = v \Delta t \tag{1.8}
\end{equation}