The twin paradox

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Humberto

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The twin paradox is as follows:

One of a twin stays on Earth while the other sets off in a spaceship traveling close to the speed of light and eventually returns to Earth after many years.

According to relativity theory, the twin in the spaceship should have aged less compared to the twin on Earth. Yet since there is no absolute reference frame, then from the perspective of the twin in the spaceship, it is actually the reference frame of Earth that traveled close to the speed of light, hence compared to the twin in the spaceship, the twin on Earth should have aged less. When returning to Earth, both of the twins should therefore have aged the same.

The paradox is resolved by noting that relativity theory does not consider all reference frames as equal in status, but only inertial reference frames (roughly those reference frames that don't accelerate) as equal in status.

The twin in the spaceship is not in an inertial reference frame since his reference frame changes direction back to Earth. There are three inertial reference frames in the problem:
  1. Earth's reference frame (there is actually acceleration, but Earth's speed is not of relativistic significance).
  2. The reference frame of the outgoing spaceship (once it reaches cruising speed).
  3. The reference frame of the incoming spaceship (once it reaches cruising speed).

Hence the twin on the spaceship changes inertial reference frames when returning to Earth and there is therefore no reference frame symmetry. The twin on Earth has indeed aged more.

This has been experimentally confirmed.

My question is: suppose the twin on the spaceship didn't turn around back to Earth. Hence he did not change his inertial reference frame. Would he and the twin on Earth then age the same?
 
What do you use to calculate age? If you use time as we know it then yes they'll be the same age as our time is measured by a constant(revolutions around the sun).

Or I could be talking complete crap.

*subscribes*
 
Not quite how I understand it. For the twin traveling in the spaceship time slows down locally so everything outside of this local reference frame appears to happen more quickly. If backwards observation was possible it would look like everything was moving at the speed of light and aging just as fast.

The twin on earth would have aged more regardless of if the one in the spaceship returned or not. But if he does return at light speed again it would be a round trip and the age difference would be double.
 
Swa said:
Not quite how I understand it. For the twin traveling in the spaceship time slows down locally so everything outside of this local reference frame appears to happen more quickly. If backwards observation was possible it would look like everything was moving at the speed of light and aging just as fast.
Click to expand...

To the twin on the spaceship time will appear normal to him just as it would have if he'd been on earth, 1hr would still be an hour and day still a day. In relation to each other though time slows down for the twin on the spaceship. In relation to each other the twin on earth would still age faster even if the other one does not return due to different reference points.

It's all relative :D

http://en.wikipedia.org/wiki/Time_dilation
http://www.pbs.org/wgbh/nova/einstein/hotsciencetwin/
http://science.howstuffworks.com/science-vs-myth/what-if/what-if-faster-than-speed-of-light1.htm
http://science.howstuffworks.com/science-vs-myth/everyday-myths/time-dilation1.htm
http://stargazerslounge.com/topic/93960-age-slow-when-approaching-light-speed/#entry937148
 
Suppose twins are born aboard a spaceship which, in Earth's reference frame, is traveling close to the speed of light. One of the twins is then ejected from the spaceship and comes back to Earth. Will the twin on Earth then age less than the twin in the spaceship?
 
Humberto said:
Suppose twins are born aboard a spaceship which, in Earth's reference frame, is traveling close to the speed of light. One of the twins is then ejected from the spaceship and comes back to Earth. Will the twin on Earth then age less than the twin in the spaceship?
Click to expand...

I would think that the twin still aboard the spaceship would age more slowly. But this is a fascinating topic...
 
Maverick Jester said:
How so? The twin on Earth would have a different spacetime path, but would be moving at less than the speed of light away from the spaceship upon returning to Earth?
Click to expand...

Sorry I did not read his question properly so it should be no. I was talking about the twin on the spaceship, same rules apply as before.
 
ponder said:
Sorry I did not read his question properly so it should be no. I was talking about the twin on the spaceship, same rules apply as before.
Click to expand...

In the second problem, the starting reference frame F[SUB]0[/SUB] is that of the spaceship. It's velocity in F[SUB]0[/SUB] is zero. Relative to F[SUB]0[/SUB] the twin who has returned to Earth is travelling close to the speed of light. Hence I think the twin on Earth will age less this time.
 
Humberto said:
In the second problem, the starting reference frame F[SUB]0[/SUB] is that of the spaceship. It's velocity in F[SUB]0[/SUB] is zero. Relative to F[SUB]0[/SUB] the twin who has returned to Earth is travelling close to the speed of light. Hence I think the twin on Earth will age less this time.
Click to expand...

Ja but you never said all that stuff before, you mentioned a spaceship travelling close to c and a twin being ejected.

Is this a new problem now? You just reversed everything, rules still apply, twin on earth ages 'slower' due to travel back while spaceship is stationary.
 
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Where people seem to have a problem is in their thinking of time and the age problem violating causality. Think of the universe having a clock that ticks by and with every tick the state of matter and energy advances. Now the faster you travel the more of these ticks "miss" so the effect of time slows down. The same thing happens in the presence of a large body of matter. Now in the local reference frame everything seems to happen at the normal rate because everything is equally slowed down but outside of this they happen relatively faster. Stars will for instance appear to go by at multiple times the speed of light.

There is no violation of causality as the state of matter still advances in all reference frames. It can thus not change any events that already happened. For a true violation of causality bring quantum entanglement into the picture. Of course this assumes that our perception and consciousness is governed only by physics. There's indications it's not in which case expect to see quite a few interesting phenomena like being able to experience reality in real time while seeing everything happen in slow motion. Actually expect a few interesting phenomena regardless.
 
Humberto said:
My question is: suppose the twin on the spaceship didn't turn around back to Earth. Hence he did not change his inertial reference frame. Would he and the twin on Earth then age the same?
Click to expand...
They would not due to the gravitational time dilation. See comment about clocks @ different heights here

http://en.wikipedia.org/wiki/Gravitational_time_dilation

Or maybe I have no idea wtf I'm talking about...you decide.
 
Humberto said:
Suppose twins are born aboard a spaceship which, in Earth's reference frame, is traveling close to the speed of light. One of the twins is then ejected from the spaceship and comes back to Earth. Will the twin on Earth then age less than the twin in the spaceship?
Click to expand...

The twin who was ejected from the spaceship would be dead. Space is pretty hostile to life :)
 
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