Consider boosting a light ray at an arbitrary angle. Without loss o...

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Consider boosting a light ray at an arbitrary angle. Without loss of generality, you may assume the boost is in the .-direction and the ray is propagating in the xy-plane at angle A E [0, IT] with respect to the x direction in the original frame. (a) Boost the ray and verify that it moves at speed C in the x' coordinates. (b) What angle o' with respect to the '-direction does the light ray propagate at? (c) You are in a starship, at rest with respect to a field of fixed, distant stars. Looking out, you see a dusting of stars scattered uniformly over all 47 of solid angle. Now fire up your rocket and accelerate until you are moving at a relativistic velocity. Describe qualitatively what field of stars you see now (the quantitative effect is very interesting - it's called a special conformal transformation - but I won't ask you to work it out). (d) A lightbulb emits isotropically in its own rest frame. In your own in- ertial frame, the lightbulb is moving at a relativistic velocity. Describe, qualitatively, its pattern of emission in your frame.

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