I am a science teacher, and throughout my training, never found out
what would happen if you turned on your headlights while traveling at the
speed of light. In a really fast car of course.
You CANNOT travel at the speed of light.
Only massless particles can do so.
jasjeet s bagla
More importantly, to emit light you need to create electric
and magnetic fields, and this requires charged particles. But
no charged particle of zero mass exists. So charged particles,
and hence creation of light, can only happen at speeds that
are less than the speed of light. And what happens is completely
determined by the relativity principle - in your frame of
reference it looks just like normal light, but in a frame travelling
close to the speed of light relative to you the light is "blue-shifted"
or shifted to higher energy (such as X rays etc).
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Update: June 2012