Relativity FAQ

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 definitive 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.

Sometimes people persist: What would the world look like in the reference frame of a photon? What does a photon experience? Does space contract to two dimensions at the speed of light? Does time stop for a photon? .... It is really not possible to make sense of such questions and any attempt to do so is bound to lead to paradoxes. There are no inertial reference frames in which the photon is at rest so it is hopeless to try to imagine what it would be like in one. Photons do not have experiences. There is no sense in saying that time stops when you go at the speed of light. This is not a failing of the theory of relativity. There are no inconsistencies revealed by these questions. They just don't make sense.

Despite these empty answers, nobody should feel too put down for asking such questions. They are 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 I pursue a beam of light with the velocity c (velocity of light in a vacuum) , I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the basis of experience or according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how, otherwise, should the first observer know, i.e., be able to determine, that he is in a state of fast uniform motion? One sees that in this paradox the germ of the special relativity theory is already contained. Today everyone knows, of course, that all attempts to clarify this paradox satisfactorily were condemned to failure as long as the axiom of the absolute character of time, viz., of a simultaneous, unrecognizedly was anchored in the unconscious. Clearly to recognize this axiom and its arbitrary character really implies already the solution to the problem"

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. On this basis Einstein constructed the theory of special relativity which has since been well confirmed by experiment.

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 towards the ultraviolet or beyond. 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).