Spacetime

• in relativistic physics, space and time are intertwined through Lorentz Transformation
• almost analogous to space and time being bases for events
• different reference frame $\leftrightarrow$ rotation of $(x,y)$

$$\begin{array}{rl}{x}^{\prime }& =(\cos \theta )x+(\sin \theta )x\\ y^{\prime }& =-(\sin \theta )x+(\cos \theta )y\end{array}$$

• Lorentz Transformation is similar, almost like rotation of $xt$ frame

$$\begin{array}{rl}{x}^{\prime }& =(\gamma )x-(\gamma V)t\\ t^{\prime }& =-(\gamma V/c^2)+(\gamma )t\end{array}$$

• not perfect analogy tho, since
  • $\gamma ,\gamma V,\gamma V/c$ can exceed unity (can’t be sin/cos)
  • sign is different in $x^{\prime }$ equation