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If you are traveling at the speed of light and attempted to turn on your headlights, will they still come on?

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JoyfulSilence · 46-50, M
Yes, because from the point of view of you and the lamp, it is no different than if you were stationary. That is, if you were stationary relative to a frame or moving close to the speed of light relative to a frame (you cannot move at the speed of light), you and the lamp would still behave the same, from your point of view.

From another object, what is sees will vary. If you are moving away from another object, that object will see your time as slowing down. The electrons in the lamp will slow, the events will slow, but the photons will still emerge at the speed of light, no matter what. Time will never stop, though, so the lamp eventually comes on.

Here I am assuming no gravity. Near black holes the time can appear to freeze so the light may never come on.