Time Travel in Special Relativity

[yinfudan]

Since I only learned special relativity but not yet general relativity, please bear with me that our discussion will be limited to the scope of special relativity, that is, suppose we would not utilize special spacetime topology, such as worm hole and black hole.

I ran into some video about time machine on Discovery Channel. You can watch it on youtube at , which talks about the time travel to the past and the actual time machine is being built. However, I doubt this idea very much, with my knowledge of special relativity.

In special relativity, time travel to the future is believed possible and exemplified by the twin paradox. The twin paradox is well resolved. When the traveling brother returns to the earth, his brother is older and more time has passed on the earth. This looks as if the traveling brother manages to time travel to the future. But this so called time travel has the following nature. Please confirm:

1. Suppose the traveling brother has a powerful telescope on the spaceship, he would see the time on the Earth passes slower, during his trip away from the earth.
2. He could not interact with his brother or anything else on the earth, except sending radio signal back.
3. He would only see the time on the Earth passes much faster, during his trip back to earth.
4. Once he is back to the earth, he can interact with his brother again.
5. Both of them are older than when they separated and commerced the trip.

Because of this, some people argue that time travel to the past is also possible. Now let us think of this scenario: the traveling brother wants to age faster than the brother on earth. There are probably two ways to achieve this: send his family for high speed travel, or he stays up high up in the space where gravity is lower than on the earth. In this case, when the brothers unite, the aging faster brother claims he has traveled to the past because his family is younger.

I think the above scenario is possible. But it is still not time travel to the past. It is merely that the time passes in different rates. Both of the brothers are still older than when they separated. Either of the brother can ever go back to any time before they separated.

This can also be very easily seen from a spacetime diagram. No matter how much the speed is, the time axis is always warped in a way that, it is still pointing to the positive direction in time, and positive or negative direction in space. This indicates that time can only move forward but pass in different rates.

As for the grandfather paradox, found at http://en.wikipedia.org/wiki/Grandfather_paradox, I think it is also easy to explain. The man simply is not able to travel back to kill his grandfather. If the grandfather is still alive, say 60 years old and the man is 10 years old, it is possible that when the man meets his grandfather, the grandfather is 70 years old and the man is 80 years old, but, even now, if the man kills his grandfather, he will still be alive, and his grandfather still did give birth to his father before and his father to him.

 

[JesseM]

Since I only learned special relativity but not yet general relativity, please bear with me that our discussion will be limited to the scope of special relativity, that is, suppose we would not utilize special spacetime topology, such as worm hole and black hole.

I ran into some video about time machine on Discovery Channel. You can watch it on youtube at , which talks about the time travel to the past and the actual time machine is being built. However, I doubt this idea very much, with my knowledge of special relativity.

This video is talking about the ideas of a physicist named Ronald Mallett (see the last section of the article for some objections to his ideas from other physicists), and his scheme definitely does depend on a special spacetime geometry similar to wormholes and black holes (specifically he is proposing that the energy from circulating light beams could distort spacetime in such a way as to allow closed timelike curves, i.e. time travel), it can't be undestood with special relativity alone.

1. Suppose the traveling brother has a powerful telescope on the spaceship, he would see the time on the Earth passes slower, during his trip away from the earth.
2. He could not interact with his brother or anything else on the earth, except sending radio signal back.
3. He would only see the time on the Earth passes much faster, during his trip back to earth.
4. Once he is back to the earth, he can interact with his brother again.
5. Both of them are older than when they separated and commerced the trip.

Yes, all these things are true, although the key is that the traveling brother has aged less than the brother on Earth, because he was the one who turned around to return to Earth (if two clocks start at the same place and end at the same place, the clock that moved with constant speed and direction will always have aged more than the clock that accelerated to turn around).

Because of this, some people argue that time travel to the past is also possible.

I don't think anyone argues that travel to the past would be possible based on the twin paradox in special relativity, all the time travel schemes that have been proposed depend on distortions to the geometry of spacetime (although if there were particles that could move faster than light--tachyons--then they could be used to send messages to the past in special relativity, but physicists are doubtful that tachyons exist, and there certainly has been no evidence for them).

 

[yinfudan]

This video is talking about the ideas of a physicist named Ronald Mallett (see the last section of the article for some objections to his ideas from other physicists), and his scheme definitely does depend on a special spacetime geometry similar to wormholes and black holes (specifically he is proposing that the energy from circulating light beams could distort spacetime in such a way as to allow closed timelike curves, i.e. time travel), it can't be undestood with special relativity alone.

Thanks Jesse for your quick reply!

General relativity says that mass can curve the spacetime fabric around it. I do not have a very deep mathematic background, but I suppose that, although the spacetime can be curved, its topology cannot change. Think of a 2-D scenario, no matter how you warp the surface of a sphere, it cannot become donut.

So if the spacetime we live in is regular 4-D, or at least it is locally regular 4-D in the lab, without circles or loops in it, no matter how Ronald Mallett curves it, no matter how powerful the laser is, the tolopogy preserves. Thus, only time passing rate changes. Time travel to the past is impossible.

 

[JesseM]

So if the spacetime we live in is regular 4-D, or at least it is locally regular 4-D in the lab, without circles or loops in it, no matter how Ronald Mallett curves it, no matter how powerful the laser is, the tolopogy preserves. Thus, only time passing rate changes. Time travel to the past is impossible.

I don't know that closed timelike curves would require a topology change--if we think of an analogy with 2D surfaces, in a flat plane all geodesics are straight lines and thus never form loops, but if you distort the surface without changing the topology I think you can make it so that some geodesics are loops (imagine creating a bulge in the surface that looked like the top 3/4 of a sphere--wouldn't the equator still be a geodesic?) Kip Thorne also mentions on p. 497 of Black Holes and Time Warps that it's possible to create a wormhole (which in pure GR should mean it's possible to create closed timelike curves) without a topology change, although it can only be constructed in a way that violates causality:

Is there no way out? Is there no way to make a wormhole without getting entangled with the ill-understood laws of quantum gravity--no perfectly classical way?

Somewhat surprisingly, there is--but only if one pays a severe price. In 1966, Robert Geroch (a student of Wheeler's at Princeton) used global methods to show that one can construct a wormhole by a smooth, singularity-free warping and twisting of spacetime, but one can do so only if, during the construction, time also becomes twisted up as seen in all reference frames. More specifically, while the construction is going on, it must be possible to travel backward in time, as well as forward; the "machinery" that does the construction, whatever it might be, must function briefly as a time machine that carries things from late moments of construction back to early moments (but not back to moments before the construction began).

There is also the Tipler cylinder, a solution of GR which requires a massive rotating cylinder of infinite length and thus cannot actually be constructed by any finite collection of beings (although maybe it could be constructed in a universe that didn't already contain it if an infinite set of beings at regular intervals all coincidentally decided to construct a section of it, and all the sections lined up)--however impractical this solution may be, I'm not sure the topology of a universe with a Tipler cylinder is different than one without it. And Mallett's solution was rather similar to a tipler cylinder in that it involved light being caused to circulate by the distorted spacetime around an infinite line singularity--the controversial part was Mallett's assertion that this would still work if the line singularity were removed and the light was caused to circulate by non-gravitational means, which I don't think he ever demonstrated mathematically.

 

[Crazy Tosser]

3. He would only see the time on the Earth passes much faster, during his trip back to earth.

What?
I do believe that he would see time pass a lot faster only during his acceleration back to earth... If it will start running faster at all...

 

[JesseM]

What?
I do believe that he would see time pass a lot faster only during his acceleration back to earth... If it will start running faster at all...

yinfudan was referring to what he would see visually through his telescope, which is influenced by the Doppler effect (see this section of the twin paradox page), not what would be true in an inertial frame where he was at rest during the return journey (and your statement about 'seeing' time pass a lot faster during the acceleration would only make sense in a non-inertial frame, but there is no single 'correct' way to construct a rest frame for a non-inertial observer, there would be some non-inertial frames where your statement would be correct and others where it wouldn't be).