Lorentz transformation. Time separation between two events in system S and system S' is given by Lorentz transformations(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\Delta t'=\frac{\Delta t-\frac{u \Delta x}{c^2}}{\sqrt{1-\frac{u^2}{c^2}}}[/tex]

If event 2 is caused by event 1 in system S then ##\Delta t=t_2-t_1##. But it is possible to choose ##\Delta x## in such way that ##\Delta t'## is negative. Which is very hard to understand. ##\Delta t'<0## only when ##\frac{u \Delta x}{c^2}>\Delta t## or

[tex]\frac{u}{c}>\frac{c\Delta t}{\Delta x} [/tex]

Now I am confused. ## \Delta x## is space separation between event 1 and event 2 and ##\Delta t## is time separation between events. Is it possible to choose some reference system S' in such way that event 2 occurs before event 1, even in case when event 2 is consequence of event 1?

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# Inequalities. Special relativity.

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