Overheard In Providence

Last night some friends mentioned the recent news coverage of two German scientists claiming to have measured photons traveling faster than light. Ars Technica provides some informed debunking of these claims, but true or not, my friends wanted to know why super light speed travel was such a big deal. In particular, they had heard that traveling faster than light allows one to travel backwards in time. I wanted to give them a simple explanation, but my time at the Hot Club had dulled my intellectual reflects, and by the time I had one, we had moved on to other things. Here’s the explanation as promised.

Sound moves through air at 340 meters per second (m/s). That means that if I yell “Go!” then you move away from me at 400 m/s, you can catch to the sound I’ve made. As you catch up to the sound, however, you’ll hear it backwards. First you’ll catch up to the “o!”, than the “G”. The same logic applies to light. If you could travel faster than the speed of light, you’d see things happening backwards. But so what? What’s so special about seeing this happen backwards? If your a fast moving blind person, and you hear things backwards, we don’t say that you’re traveling back in time. Is light special?

Well according to special relativity, yes, light is indeed special. Sound travels through air at 340 m/s, but if you’re moving relative to the air, sounds speed relative to you changes. Also, if you get rid of the air (as in space) there’s no more sound. In the end of the 19th century scientists desperately wanted to find the stuff light used to travel though space. They called this stuff ether, but since if didn’t actually exist, they had a heck of a time trying to find it.

If light were traveling through the ether of space, then as we moved through space in different directions at different speeds, we’d measure the speed of light differently. Special relativity states that this doesn’t happen. Anyone moving at a constant velocity will measure light as traveling at 299,792,458 m/s. As a result, if you and I are floating towards each other in space at a constant speed, and we each a have a flashlight, and we each measure the speed of light reaching us from the other person’s flashlight, we will each be equally justified in claiming that we are stationary, while the other person is moving. In fact, special relativity says that the laws of physics (including the speed of light) will be exactly the same for each of us.

At first glance, this all seems very confusing. If I am moving towards you, and you toss a few photons in my direction, how can you and I possibly both see those photons as moving at the same speed? In particular, suppose I’m holding a measuring stick, and you and I both record the time at which the photons are at each end of the stick. If we agree on the times and the length of the stick, you will conclude that the photons are moving slower than I do. I will have seen them move one stick-length in one time-unit, but you will see them travel less than one-stick length (since the stick is moving toward you) in the same time-unit. The conclusion: for special relativity to hold true, people moving at different speeds must perceive lengths and times differently. In particular, if I am moving towards you, the only way we can measure the same speed of light is if we measures times and lengths differently.

It turns out that as we travel towards each other, we observe a time dilation (as well as a length contraction). If you are holding a watch, I will see it running slow. If I am growing a beard, you will see it growing slow. No matter what each of us does, the other will perceive it as happening more slowly than if we were both standing still next to each other. It’s pretty wild stuff I know, but trust me, it’s been tested many times. It also means that in theory a person can travel many light years on a spaceship traveling near the speed of light, but only age a few days along the way. If the spaceship goes faster than the speed of light however, all bets are off (and as a result, special relativity states that it takes an infinite amount of energy for a spaceship to reach the speed of light).

This brings us back to time travel. Since observers moving at different speeds always agree about the speed of light, but disagree about things like durations of time and the lengths of objects, they also disagree about when events take place simultaneously. In particular, if two stars explode, two people moving towards each other can disagree about which exploded first, and neither can be accurately viewed as incorrect.

Now suppose that in edition to the photons leaving the exploding stars, a message was sent at super light speed to a nearby space station. Upon receiving that message, the station sounds its “exploding star” alarm. An observer moving at a certain speed could accurately perceive the alarm as sounding before the stars exploded. In this way, super light speed travel allows information to travel backwards in time. This poses a problem for the laws of physics, and special relativity forbids it.

Ok, enough of this confusion. In my defense, I’m a computer scientist and haven’t taken a physics class since I got a “C” in thermodynamics my junior year.