Faster than light? Twin paradox Causality paradox

1. SPECIAL RELATIVITY • PARADOXES • (NOT) • Faster than light? • Twin paradox • Causality paradox

2. Violation of ultimate speed (not) Laura @ ¾ c George @ ¾ c You What is speed of Laura relative to George? • ¾ c is Laura’s speed in Your IRF, but relative to George • Your clock runs slower (time dilation) • Your distances are longer (length contraction) • George concludes Laura’s speed (distance/time) relative to • You is less than You measure – less than ¼ c actually • George agrees his speed is ¾ c relative to you • Total less than c Note: Disagreements only for 3rd party speeds

3. Twin Paradox (not) Observers in uniform relative motion both say the others clock runs slow Ages less than X years FACT Ages X years Stay-at-Home twin IRF : Travelling twin time dilates, ages slower Travelling twin IRF : Distance travelled is contracted, takes less time

4. Violation of Causality (not) Two observers in relative motion disagree about the temporal order of events… There was a young lady named Bright, Whose speed was far faster than light She set out one day In a relative way, And returned home the previous night. - Arthur Henry Reginald Buller A long, long way away Two observers passing in the street disagree about whether the alien fleet has yet set out to invade Earth Note: causality is not violated YES NO