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Unformatted text preview: 2. Consider a process where an event at P causes an event at Q . Let’s choose the sepa- ration coordinates to be Δ x = x 2- x 1 > 0 and Δ t = t 2- t 1 > 0, and V = Δ x/ Δ t is the speed of the “signal”. Then Δ t ′ = t ′ 2- t ′ 1 = γ bracketleftbigg ( t 2- t 1 )- u ( x ′ 2- x 1 ) c 2 bracketrightbigg (61) = γ Δ t bracketleftbigg 1- uV c 2 bracketrightbigg (62) (63) If V > c , it might be possible to choose u (i.e. choose a frame of reference) where Δ t ′ is negative : that is, the e ff ect at Q preceeds the cause at P . This means cause and e ff ect are reversed, which leads to all sorts of logical problems. We can retain causality in special relativity by requiring that no signal can travel faster than light. This can also be forced upon the relative velocity u : we can alternatively prove that u < c by deriving the transformation of velocities, below. 1.4 Relativistic Doppler e ff ect Consider a source of light (e.g. a star) and a receiver approaching one another with relativeConsider a source of light (e....
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This note was uploaded on 09/20/2010 for the course AMATH 261 taught by Professor Rogermelko during the Spring '10 term at Waterloo.
- Spring '10