original by Philip Gibbs 24-Mar-1997

I am driving my car at the speed of light and I turn on my headlights. What do I see?

Sadly this question and all others about experiences at the speed of light do not have a definitive answer. You cannot go at the speed of light so the question is hypothetical. Hypothetical questions do not have answers. Only massless particles such as photons can go at the speed of light. As a massive object approaches the speed of light the amount of energy needed to accelerate it further increases so that an infinite amount would be needed to reach the speed of light.

Despite this empty answer, nobody should feel too put down for asking such a question. It is exactly the kind of question that Einstein often asked himself from the age of 16 until he discovered special relativity ten years later. Einstein reported that in 1896 he thought "If one runs after a light wave with light velocity, then one would encounter a time-independent wavefield. However, something like that does not seem to exist!" In 1905 he realised how it could be that light always goes at the same speed no matter how fast you go. Events which are simultaneous in one reference frame will happen at different times in another which has a velocity relative to the first. Space and time can not be taken as absolute.

Questions of relative velocity in relativity can be answered using the velocity subtraction formula v = (w - u)/(1 - wu/c²) (see relativity FAQ: velocity addition). If you are driving at a speed u relative to me and you measure the speed of light in the same direction (w = c in my frame), the formula gives v the speed light in your reference frame as, v = (c-u)/(1 - u/c). For any speed u less than c this gives v = c so the speed of light is the same for you. But if u = c the formula degenerates to zero divided by zero; a meaningless answer.

If you want to know what happens when you are driving at very nearly the speed of light, an answer can be given. Within your car you observe no unusual effects. You can look at yourself in your mirror which is moving with the car and you will look the same as normal. Looking out of the window is a different matter. The light from your headlights will always go at the speed of light in your reference frame. It will strike any object in its path and be reflected back. Everything else will be coming towards you at nearly the speed of light so the light reflected off it will be Doppler shifted to very high frequencies. If you have a suitable camera you could take a snapshot. The objects passing are contracted in length but because of the different times of passage for the light and effects of aberration, the snapshot will show the objects you pass rotated (see relativity FAQ Penrose-Terrell Rotation).