## Monday, June 29, 2009

### Near the speed of light

What happens when we travel near the speed of light?

Let's say you're traveling at 99.5% the speed of light. That's 299792458 meters per second, or 185351 miles per second. You're heading straight towards Proxima Centauri, the nearest star besides the Sun. Proxima Centauri is about 4 light years away, meaning that it takes a beam of light four years to get from here to there. 4 light years is about 2.3 x 1013 miles.

Large numbers, eh?

It might seem as if you would get to Proxima Centauri in about 4 years. After all, you're practically like a beam of light yourself now. But things are not so simple when we get close to the speed of light. To continue with our calculations, we will need something known as the Lorentz factor. The Lorentz factor is just some number, symbolized with (the letter gamma).
= 1/sqrt( 1 - (v/c)2)
v is the velocity, and c is the speed of light. In our example, is approximately equal to 10.

One of the things that happens when you travel near the speed of light, is that all distances in the direction of travel get shortened by a factor of . The Earth will seem like a squashed spheroid to you. It will also seem as if Proxima Centauri is not 4 lightyears away, but 0.4 lightyears away. So you will get there in 0.4 years without ever breaking the speed limit set by Relativity!

I would be on Earth, watching you. I would see you arrive at Proxima Centauri 8 years later. From my perspective, it took you 4 years to get there, and 4 more years for your signal to return to me. Let's say that you decided to return home, and sent a message to me saying so. It would take the message 4 years to get to me, and you will appear about one week later, since you travel at nearly the same speed as your own message.

By the time you returned, about 8 years would have passed on Earth. From your perspective, the entire trip only took 0.8 years. From your perspective, Earth has skipped ahead in time by about 7.2 years. From my perspective, it seems like you hardly aged over that long trip.

Let's say that you're about 100 kg (220 lb). Once you start moving near the speed of light, your mass increases by a factor of , so you will appear to be 1000 kg. Since your mass increased by 900 kg, guess how much energy it required to mobilize you? That's right, E=mc2. In your case, this will be 8.1 x 1019 Joules, or about twenty thousand megatons. And that's just you by yourself. If you're in some kind a space ship, the space ship might carry about a million more megatons of energy. You would probably make quite an explosion if you hit one of Proxima Centauri's planets, if it has any. Not that we were planning to do anything like that.

You and your spaceship will appear to be flattened by a factor of . You will seem as flat as a pancake. You will probably look quite absurd, a massive, flying, pancaked person. What's more, your colors would be all shifted. When you're flying away, you will be redshifted by about a factor of 20. Basically, I will only see what little ultraviolet light you emit. But when you're flying towards me, you will be blueshifted by a factor of 20. Much of that infrared light which you normally radiate will now be blueshifted into visible light and x-rays. I'm not sure what color you would appear, but I estimate about the color of a star of 6,000 degrees, like the sun--a yellowish white.

You, while on your journey, will see something even more exciting. Everything behind you will be redshifted by a factor of 20. You would see the extreme ultraviolet range. In the ultraviolet range, most stars will seem much dimmer, except for the hotter ones, including white dwarfs. If you look in front of you, light is blueshifted by a factor of 20, so you will see part of the middle infrared spectrum. You can see giant dust clouds and nebula in this range. Some of these dust clouds are where stars will form. And as you swing your head around, looking from front to back, you will see all the ranges between middle infrared and extreme ultraviolet. I'm sure it would be quite an experience.

Eduard said...

Anonymous said...

Most people don't realize that while relativity prohibits a spaceship from traveling faster than the speed of light, it doesn't prohibit it from getting anywhere in an arbitrarily short amount of time, according to the spaceship's clock. Like you said, the distance becomes shorter with the speed of the spaceship, according to the spaceship's measure of distance. Am I right?

miller said...

Yes, you can get anywhere in an arbitrarily short amount of time in your own reference frame. However, from the reference frame of an observer on earth, your journey must take at least four years.

Secret Squïrrel said...

Nice explanation. Should be 100kg.

You might be able to clear up a small misunderstanding of mine (save me looking it up ;-)

If there is no preferred frame of reference, why is it that the greater amount of time elapses for the Earth-bound observer? This seems to tag them as being definitely stationary (and you as moving). Surely, from your perspective, the Solar System first recedes at 99.5c while Proxima Centauri approaches at the same speed, then SS approaches while PC recedes. Is it to do with your spacecraft being a non-inertial ref frame because it is accelerates for part of the trip?

Thanks.

miller said...

Thanks for the correction!

The twin paradox has everything to do with the fact that you are not in the same inertial reference frame for the two-way trip. If you pick any single reference frame, you will see that the traveler is moving at least 99.5% the speed of light for at least half the trip.

Secret Squïrrel said...

Ok, it's the act of you returning (and obviously experiencing acceleration while turning around) that "tags" you as moving very fast for at least part of the journey.

If we use the out-bound ship as the ref frame and accept that the Earth is receding at 0.995c, then when the ship returns, it will be observed (from the outbound frame) to be travelling at some velocity greater than 0.995c (nearly 0.999c if I understand things correctly). So if you could see clocks on both the returning ship and the Earth, the Earth clock would be seen to still be faster than the ship clock, because the Earth is travelling at "only" 0.995c compared with the ship's 0.999c.

Is that correct?

Thanks again.

miller said...

Yes, that is correct.

Scott said...

Pushing Secret Squïrrel's question a little further -- I take it the "magic" happens when the ship decelerates? From the perspective of the ship, the whole universe must "squish up" during acceleration, and must "stretch back out" during deceleration, so that the distance between the ship and earth suddenly seems much greater than it had in transit. Then on the way home again, the universe squishes up again, making for a zippy trip, but then again stretches out, making it look like the trip took longer than it did...

Does that sound right?

miller said...

I would say that the acceleration is not in itself particularly important. It would't matter, for instance, if you somehow accelerated instantaneously. What's important is that you are not in the same inertial reference frame after you turn around, no matter how it is you turned around.

Scott said...

Yes, that makes sense -- I'm just trying to visualize as concretely as possible the experience of the astronaut.

Serghei Ignat said...

If i will weight 1000kg, will I be able to breath the air inside my starship, move my body, etc? Wouldn't I "collapse" under my own gravity? For a speed very close to light will I and my starship turn into a tiny neutron star?

miller said...

No, because there isn't any gravity.

If there were gravity, I think you would experience it ten times stronger when moving so fast, because in your own reference frame, the source of gravity is ten times more massive. I haven't worked it out though.