peapod said:
If you are driving down the highway at light speed and turn on your headlights, what happens?
Um... your headlights come on? :wink:
Pointless question, really, because you can't go that fast, but that's also a useless answer. We can, however, speculate a bit. It depends on the observer's state of motion with respect to the car. The basic principle of relativity, that the speed of light is the same for all observers, suggests you in the car would see your headlights illuminate the road in front of you as they normally would, because you're not moving with respect to your headlights. The speed of light as it leaves your headlights is what it always is, relative to your point of view. Assuming it's dark, of course. If it's daylight, you won't notice any difference.
So what would people standing by the road as you zoomed by see? They'd see an infinitely massive, infinitely short car go by, emitting great gobs of cerenkov radiation, as Nascar_James explained, and frying everybody in the neighbourhood. Ever seen a photo of the containment water in a nuclear power reactor? It glows blue because of all the high energy nuclear particles zipping through it at faster than the speed of light in water.
Somebody standing in front of your speeding car would see an infinitely massive object approaching, emitting very high energy radiation. I haven't done the calculation, but it'd be up there in the hard gamma ray range. The doppler effect, as #jaun's tinyurl links show, shifts the wavelength of light from your headlights way over into the shorter wavelength end of the spectrum. And somebody behind the car might see a massive black hole receding into the distance and sucking up everything in its path...
The real answer is that nobody knows, all the equations break down when you consider a massive object travelling at light speed. Frankly, I didn't do the calculation because I can't; nobody can. As you approach light speed, you get increasingly massive and more and more energy input is required to get another increment of speed, you shrink in the direction of motion, and your clocks run progressively more slowly. That's from the perspective of somebody watching you zoom by, you wouldn't notice a thing. When you actually get to light speed, certain quantities (notably your mass and energy content) become infinite in the equations, and you find yourself doing forbidden mathematical operations, like dividing by zero. Which is why physics says you can't do this and it's a pointless question.
But if ya wanna talk about what happens if you get your car up to 99.9999999999999999999999999999% of the speed of light, that we can deal with.