class08

# class08 - Announcements Reading for Monday Chapter 2.6-2.11...

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Announcements Reading for Monday: Chapter 2.6-2.11 First Mid-term is in 11 days (Feb. 9 th , 7:30pm). It will cover Chapters 1&2. Review: Lorentz & velocity transformations (relativistic version of Galileo) Transformations (in 1D) If S’ is moving with speed v in the positive x direction relative to S, then the coordinates of the same event in the two frames are related by: Galilean transformation (classical) Lorentz transformation (relativistic) Note: This assumes (0,0,0,0) is the same event in both frames. vt x x = ) ( vt x x = γ ) ( 2 x c v t t = γ 2 / 1 c uv v u u = v u u = t t = Some examples Suppose a spacecraft travels at speed v=0.5c relative to 2 / 1 c uv v u u = 2 / 1 c v u v u u + + = 2 2 / 1 ' ) ( ) ( c uv v u u x c v t t vt x x = = = γ γ Relativistic transformations Q1 the Earth. It launches a missile at speed 0.5c relative to the spacecraft in its direction of motion. How fast is the missile moving relative to Earth? (Hint: Remember which coordinates are the primed ones. And: Does your answer make sense?) a) 0.8 c b) 0.5 c c) c d) 0.25 c e) 0 Velocity transformation: Which coordinates are primed? y y' (x,y,z,t) u u is what we were looking for! (i.e. velocity measured in S) S x z S' x' z' v (x',y',z',t') Spacecraft Earth

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The “object” could be light, too! Suppose a spacecraft travels at speed v=0.5c relative to 2 / 1 c uv v u u = 2 / 1 c v u v u u + + = Q2 the Earth. It shoots a beam of light out in its direction of motion. How fast is the light moving relative to the Earth? (Get your answer using the formula). a) 1.5c b) 0.5 c c) c d) d e) e George has a set of synchronized clocks in reference frame S, as shown. Lucy is moving to the right past ... -3 -2 -1 0 1 2 3 ... v ? George Lucy ) ( ) ( 2 x c v t t vt x x = = γ γ Q3 George, and has (naturally) her own set of synchronized clocks. Lucy passes George at the event (0,0) in both frames. An observer in George’s frame checks the clock marked ‘ ? ’. Compared to George’s clocks, this one reads A) a slightly earlier time B) a slightly later time C) same time The event has coordinates (x = -3, t = 0) for George.
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