[Physics FAQ] - [Copyright]

Original and updated by Philip Gibbs, 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 have no definitive answer.  You cannot travel at the speed of light, and so the question is hypothetical.  Hypothetical questions do not have definitive answers.  Only massless particles (such as photons) can travel at the speed of light.  As a massive object approaches the speed of light, more and more energy is needed to accelerate it further, and so it will need an infinite amount of energy to reach the speed of light.

Sometimes people persist, asking such questions as: 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 such attempt is bound to lead to paradoxes.  There is no inertial frame in which a photon is at rest, and so it is hopeless to try to imagine what things would be like in such a frame.  Photons do not have experiences.  There is no sense in saying that time stops when you travel at the speed of light.  This is not a failing of the theory of relativity.  There are no inconsistencies revealed by these questions; they simply 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.  But 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 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, or of simultaneity, was rooted unrecognized in the unconscious.  To recognize clearly this axiom and its arbitrary character already implies the essentials of the solution of the problem."

In 1905, Einstein realised how it could be that an observer can measure light always to travel at the same speed no matter how fast he moves.  Events that are simultaneous in one reference frame will happen at different times in another frame that has a non-zero velocity relative to the first.  Space and time cannot 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 velocity addition in the relativity FAQ).  Set w to be the speed of light in my frame: w = c.  If you are driving at a speed u relative to me and you measure the speed of light in the same direction, the formula gives the speed of light in your reference frame as v = (c − u)/(1 − cu/c2) = (c − u)/(1 − u/c).  When u < c, the denominator is non-zero, and then we have v = c(c − u)/(c − u) = c.  So, for any speed u less than c, this gives v = c, and so the speed of light is the same for you as for me.  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 rear-view mirror, which is attached to and thus moving with the car, and you will appear the same as usual.  Looking out of the window is a different matter.  The light from your headlights will always travel 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, and so the light reflected from it will be Doppler shifted to very high frequencies—towards the ultraviolet or beyond.  With a suitable camera you could take a snapshot.  The objects passing would be contracted in length, but because of the different times of passage for the light and effects of aberration, the snapshot would show the objects you pass as rotated.  See Penrose-Terrell Rotation in the relativity FAQ.

Reference: Quote from Einstein's biographical notes in Albert Einstein, Philosopher Scientist, ed. Schilpp.