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A source of light is traveling away from us at .95c. Its emr reaches us with a big redshifted wave pattern yet still arrives at the speed of light. So if our light source moves away from us at say 1.05c does the emr reach us with a reversed wave pattern (information is backwards) yet still arrives at the speed of light?

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The light source can't move at 1.05c That would violate causality. Say it did move at 1.05c. For you, everything might be happening well but for some observer moving pretty fast (you can calculate) it's space-time trajectory would be reversed. That is if you lorentz transform to a frame moving at some speed, it's space-like nature would be reversed in time. So effect would be preceding cause which has a lot of inconsistencies so it's not possible.

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