PX155 - I3 - causality

LTs can change the order of two events

consider: $t^{\prime }=\gamma (t-\frac{ux}{c^2})$

two events separated by $\mathrm{\Delta }t$ and $\mathrm{\Delta }x$:

if $\mathrm{\Delta }t>0$, $\mathrm{\Delta }{t}^{\prime }>0$ if $\frac{u\mathrm{\Delta }x}{c^2}<\mathrm{\Delta }t$

$LHS$ is maximized when $u\to c$

events occur in some order if $\mathrm{\Delta }x<c\mathrm{\Delta }t$

called cause limits because light could have travelled the distance between the events in the time between the events

causality is lorentz invariant