Special Relativity
Special Relativity Symmetry $$ t' = \gamma(t - \frac{v}{c^2}x) \\ x' = \gamma(x - vt) $$or: $$ ct' = \gamma(ct - \beta x) \\ x' = \gamma(x - \beta ct) $$Which is same for interval as a vector. What does it say? It means we describe the 4-vector component in another frame $\Sigma’$ by $\Sigma$. That’s means basis will changes reversely($t’ \hat{t’} + r’ \hat{r’}$). It’s symmetric that $x’^\mu = \Lambda^\mu_\nu x^\nu \lrarr x^\mu = \Lambda^{-1 \mu }_\nu x^\nu$. ...