If nothing goes faster than the speed of light and you were in a car going at the speed of light, what happens when you turn the headlights on?
The simplest way to answer this is to say that only massless particles can go at the speed of light in a vacuum, so the scenario is impossible, but that wouldn’t be any fun. So instead, by trying to answer this, we can look at the very core of Einstein's theory of special relativity.
The first thing to know is a concept called “inertial frame of reference”, which Galileo Galilei came up with four centuries ago. Each frame is either still or moving at a constant velocity with respect to each other.
The usual example involves two observers: one passenger on a train moving at a constant speed in a straight line and another person standing near the tracks. If the train passenger were to shoot a bullet at a certain speed, the bullet would move faster for the person outside the train, as you would add the velocity of the train to the bullet.
But things are different if the passenger shone a flashlight. The speed of light measured by the passenger and by the trainspotter would be the same. This happens because the speed of light is constant. It's a limit that cannot be passed. The previous example with the bullet and train is an approximation of the relativistic reality, and it is only correct because both the train and the bullet are moving very slowly compared to the speed of light.
Even if you could have a car or spaceship moving almost at the speed of light, its headlight would still be moving at the speed of light.
Unfortunately, we can’t get much more information than that. Relativity is an extremely well-built theory and when you push its limits, like a car moving at the speed of light, it simply tells you that it’s impossible.
Now, this might seem like a disappointing answer, but it isn’t. Physics is good like that. Before you get to your "impossibles", a lot of crazy things go down.
As you’re moving at a speed comparable to the speed of light, the light will be shifted by the Doppler effect. In the same way, the siren of an ambulance seems to change pitch if it’s approaching or moving away from us. If a source of light is moving fast enough, the light waves will actually be pushed closer together and the light will seem to change color.
Imagine your car is moving at 10 percent the speed of light, with your headlights emitting a nice yellow hue. The light will bounce off the road and will be reflected back to you. But surprisingly, it is not yellow anymore – it will be violet.
As your velocity increases, so does the frequency of the light. At 50 percent, you’ll get UV light back. At 99.9 percent of the speed of light, the reflected light will only be observable by an X-ray detector.
The change in light is not the only curious effect you’re about to experience in your relativistic car. The rules of special relativity clearly suggest that time dilates and lengths contract as one moves close to the speed of light.
But this doesn’t mean that by looking outside your windscreen everything will appear squashed. As you're covering a large distance in a short period of time, objects you pass by will appear to change angles as if they are rotating. This phenomenon is called the Lampa-Terrell-Penrose effect, and although it doesn’t change the maths of the theory, it tells us what we should be seeing at those speeds.
It’s unlikely we’ll be able to experience those effects with our naked eyes, as not only is it impossible to reach the speed of light, but also a car moving at relativistic speed can’t be made. We have no way to power it and make it stick to the ground. And even if we could, the sheer friction from the air molecules will quickly heat up, either melting both the car and the passenger in the best case scenario or worse, generating a tremendous nuclear explosion once you go beyond a certain speed.
So, please respect the speed limits. It’s for all our sakes.