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Lecture05

Lecture05 - t x C B A Q BC =(v/c x/c CP = QP γ t x P O OA...

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2 Paradoxes Twin Temporal The Lorentz Transformation Velocity Transformation Summary
3 2013.6 8 light years 2010 2020 2030 Ann’s Now in 2020 Ann’s Now in 2010 Ann’s Now in 2030 2012 E-mail sent by Ann in 2012, Ann’s time, received by Betty in 2016, Betty’s time. 2028 E-mail sent by Betty in 2016, Betty’s time, received by Ann in 2028, Ann’s time. Puzzle : Why is Betty younger?

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4 Ann’s Worldline 2010 2013.6 Ann’s Now in 2010 2020 Ann’s Now in 2020 Ann and Betty’s Now in 2007.2 2007.2 2008
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6 Define t = BC + CP x = OA + AB What is the map between the two different frames of reference?

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Unformatted text preview: t' x' C B A Q BC = (v/c) x/c CP = QP/ γ t x P O OA = OQ/ γ AB = vt x' = OQ t' = QP 7 t' x' C B A Q BC = (v/c) x/c CP = QP/ γ t x P O OA = OQ/ γ AB = vt 8 t' x' t x P O B Q 9 t' x' t x P O B Q Consider u' x 10 Similarly, we arrive at t' x' t x P O B Q When u << c, we recover Galilean relativity 11 The temporal separation of events depends on the path taken between them and is greatest for an inertial, i.e., non-accelerating, path Super-luminal travel in a simply-connected spacetime would lead to temporal paradoxes The addition of velocities always yields a value less than the speed of light...
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