# Twin paradox? HA! I'm an only child.

1. Dec 14, 2005

### tribdog

Correct me if I'm wrong, please. If I travel at near the speed of light in my new spaceship then an observer here on earth would age 20 years while I'd only age a small fraction of that. I understand that (well, I believe that). Here's where I start running into questions. The observer on earth watches me go 20 light years from earth. If I just went 20 light years from earth and only felt a small amount of time pass doesn't that bring the problem of traveling to other stars down to the "simple" problem of engine power? I read once that some guy didn't think humans would ever go to another star system because of the huge travel times needed, but if I'm understanding relativity if I'm willing to cut myself off from the rest of the world and have a fast enough ship the entire universe is accessible. Even though I never go faster than light.

2. Dec 14, 2005

### Garth

You are not wrong - but that is not the twin paradox. (You can find plenty of posts on the actual so called twin paradox if you search in this Forum)

Have a safe short journey!

Garth

3. Dec 14, 2005

### JCCol

Yes it is true that it makes travel in space much better but your age according to your velocity is applied in the equation

sqrt [1-v^2/c^2]

were v is of course you velocity
this will give you a decimal answer that you multiply by the number of years you are traveling and that is your age when you get back to normal velocity
Hope this answers your question because I don't really understand the question.

4. Dec 14, 2005

### StatusX

That's true. The problems are 1) getting to that speed, which is a matter of finding out where to fit potentially millions of times the rest of the ship's mass in fuel, and keeping the acceleration at a tolerable level, and 2) it will still take at least 20 years for the people on earth to see you travel 20 light years away, so unless everyone goes together, or the trip is purely for your own purposes, this doesn't help things much.

5. Dec 14, 2005

### tribdog

Of course the trip is only for my purpose. I'm selfish and want to meet Alf.

6. Dec 14, 2005

### Ich

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html" [Broken] gives some examples.

Last edited by a moderator: May 2, 2017
7. Dec 14, 2005

### Staff: Mentor

Yes - while en route to your destination, you'd find that it is a lot closer than you had calculated it to be before you left. So you could travel interstellar-ly if you wanted to and didn't care about anyone you ever met on earth being alive to see you come home.

8. Dec 14, 2005

### dicerandom

Or coming home, for that matter.

The colonization of extrasolar systems will, sadly, likely be a one-way endeavor.

9. Dec 14, 2005

### DaveC426913

Which raises some interesting potential paradoxes. Subsequent colonies could well find faster ways of getting to a potential landing site than the first missions.

Can you imagine the let down of a colony ship travelling for generations to their new home, only to find it occupied by humans already?

10. Dec 14, 2005

### JesseM

Yeah, check out http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken], it shows the travel times to different destinations (as measured by someone onboard the ship) if you accelerate at 1G for the first half of the trip, then decelerate at 1G for the second half:

nearest star (4.3 ly) - 3.6 years
Vega (27 ly) - 6.6 years
Center of our galaxy (30,000 ly) - 20 years
Andromeda galaxy (2,000,000 ly) - 28 years
anywhere, but see next paragraph (n ly) - 1.94 arccosh (n/1.94 + 1) years

(the next paragraph says 'For distances bigger than about a thousand million light years, the formulas given here are inadequate because the universe is expanding. General Relativity would have to be used to work out those cases.')

Last edited by a moderator: May 2, 2017
11. Dec 14, 2005

### tribdog

I guess I need to go to ALFa Centari.

12. Dec 14, 2005

### Staff: Mentor

I would hope they'd be polite enough to offer a tow...

13. Dec 14, 2005

### dicerandom

Heh... "But it's only 5 light years out of our way, it would be rude not to help!"

14. Dec 15, 2005

### Crazy8s

You would also need to find some way for your body to survive the increased inertia in all of it's atoms, as well as all of the atoms in the ship you were on.

15. Dec 15, 2005

### Ich

No. You never ever feel anything of time dilation, length contraction or mass increase. That's what SR is all about.

16. Dec 15, 2005

### Wishbone

Wait I used to know a lil about SR, but now I am confused, if you are travelling to a star 5 light years away, does that mean to an outside observer at rest, it will take 5 years for them to see you reach your destination, it actually wont take you that long, right?

17. Dec 16, 2005

### JesseM

An outside observer will see it take more than 5 years because they will see you travelling at less than the speed of light. For you the time can be less than 5 years (if you are moving fast enough--your velocity would have to be over $$(\sqrt{2}/2)*c$$), because you see the distance from the earth to the star Lorentz-contracted to less than 5 light years, so even though you see the star approaching you at less than the speed of light, you can still make it there in under 5 years.

18. Dec 16, 2005

### dicerandom

A light year is simply a measurement of distance, it is the distance that light travels in a year. So saying that a star is 5 light years away means that it takes 5 years for the light from that star to reach us.

Think of it this way: To an observer standing at rest here on Earth, it takes a photon five years traveling at c to reach that star. Anyone who is in a ship will take longer than that to reach the star, since they must travel slower than c. The closer they get to c, the closer to five years it takes them to get to the star as observed in the Earth's frame. Simmilarly, the closer that the ship's velocity gets to c the less and less time it takes to reach the star in the ship's frame, this will be asymptotic to 0 as the velocity approaches c.