Special Relativity

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Einstein's postulate of special realtivity

1st The laws of physics are the same in all inertial reference frames.
*An inertial reference frame is in constant state of rectilinear motion in reference to another inertial reference frame (Not accelerating)
2nd Light propagates through space with velocity $c$ independent of the motion of the source.

Newtonian Physics --> Galilean Transformations
Special Relativity --> Lorentz Transformations

Equations: \begin{equation} \gamma = \frac{1}{\sqrt{1-v^2/c^2}} \end{equation} \begin{equation} m=\gamma m_0 \end{equation} \begin{equation} t=\gamma t_0 \end{equation} \begin{equation} l= l_0 / \gamma \end{equation} \begin{equation} v= c \sqrt{1-1/\gamma^2} \end{equation}

Lorentz Transformation Equations

\begin{equation} x=ut+x'\sqrt{1-u^2/c^2} \ \ \ , \ \ \ x'=\frac{x-ut}{\sqrt{1-u^2/c^2}} \end{equation} \begin{equation} t=t'\sqrt{1-u^2/c^2} + ux/c^2 \ \ \ , \ \ \ t'=\frac{t-ux/c^2}{\sqrt{1-u^2/c^2}} \end{equation} \begin{equation} v= \frac{v'+u}{1+ \frac{v' u}{c^2}} \ \ \ , \ \ \ v'=\frac{v-u}{1-vu/c^2} \end{equation} \begin{equation} u=\frac{v-v'}{1-vv'/c^2} \end{equation}

Relativistic Doppler effect

\begin{equation} f=\sqrt{\frac{c+u}{c-u}} f_0 \end{equation}

The relativistic triangle

\begin{equation} E = m c^2 = \gamma m_0 c^2 \end{equation} \begin{equation} E_0 = m_0 c^2 \end{equation} \begin{equation} E = E_0 + KE \end{equation} \begin{equation} E^2 = (m_0 c^2)^2 + (pc)^2 \end{equation} \begin{equation} KE = (\gamma -1) m_0 c^2 \end{equation} \begin{equation} p=m_0 c \sqrt{\gamma^2 -1} \end{equation} \begin{equation} \cos \theta = \frac{1}{\gamma} \end{equation} \begin{equation} \theta = \tan^{-1}(\frac{pc}{m_0 c^2}) \end{equation} Units:
E -> [MeV]
p-> [MeV/c]