# What did I miss on this one?

## Main Question or Discussion Point

I missed something when I learned about Relativity.
Everyone knows that story about twins. If one takes off in a rocket and travels near the speed of light, when he returns he won't have aged but his twin would be an old man.
The part I don't understand is this: since there is no absolute reference frame why can't the twin in the rocket be considered to be standing still and the earth flying away at near the speed of light? That would make the twin on Earth the young one and the rocket guy aged.

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OneEye

Okay, let's simplify the model: Consider a spacecraft passing earth at .99c, making its perigee at 1 km distance. At perigee, a clock is started on the spacecraft. At the same (Lorentz-adjusted) time, a clock is started on the earth.

The spacecraft continues in a straight line at .99c on a course which (capitalizing on the Riemannian structure of the cosmos) will have it passing the earth again at some time in the future.

At the time of the second passing, the clocks are read. Which one is dilated?

In this scenario, we have excluded acceleration as a factor. Instead, we have only v to deal with. We are now able to consider time dilation as a factor of v alone.

So, which clock experiences the time dilation?

tribdog said:
The part I don't understand is this: since there is no absolute reference frame why can't the twin in the rocket be considered to be standing still and the earth flying away at near the speed of light? That would make the twin on Earth the young one and the rocket guy aged.
Apparently that's not correct.

[13:41:39] (Chen): Can't you think of it like Earth accelerated away from the ship?
[13:41:49] (Chen): Why not?
[13:41:51] (cookiemonster) The Earth person wouldn't feel the acceleration.
[13:41:54] (cookiemonster) The ship person would.
[13:42:07] (cookiemonster) Therefore the frames are distinguishable.

Janitor
Neat question, OneEye

As a minor detail, I think it needs to be added that you are assuming the universe is gravitationally closed (meaning there will be a Big Crunch in our future). Otherwise, I don't believe that the Riemann structure you speak of allows the geodesic trajectories to converge.

My own guess is that the two clocks in this case, where neither clock gets accelerated by any forces, will match one another as they pass by for the second time.

Another minor detail: they won't pass all that closely if there is even the slightest lumpiness to the universe.

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OneEye
Chen said:
Apparently that's not correct.
I have no desire to be disagreeable, but I just got a major case of heartburn over this.

SR and GTR both tell us that any frame of reference is equally valid (equally "at rest"). In GTR, the spaceship acceleration can be regarded as a gravitic field, thus the astronauts may regard themselves as at rest. I cannot propose the analogy for the landlubbers on the earth, but it was my impression that GTR was meant to do for acceleration what SR did for velocity - hence, disarming any claims for one frame of reference being specially favored over another.

Now you seem to be telling me that this isn't so.

How can this be?

OneEye
Reality is for people who can't handle Relativity

Janitor said:
As a minor detail, I think it needs to be added that you are assuming the universe is gravitationally closed (meaning there will be a Big Crunch in our future). Otherwise, I don't believe that the Riemann structure you speak of allows the geodesic trajectories to converge.

My own guess is that the two clocks in this case, where neither clock gets accelerated by any forces, will match one another as they pass by for the second time.

Another minor detail: they won't pass all that closely if there is even the slightest lumpiness to the universe.
Don't bother me with facts! I am theorizing!!!! ( ).

Just noodling, but I suspect that there may be trajectories which converge even in an open or relatively flat model of the universe, because of the unbounded qualities of all non-Euclidean models. In an "expanding" or "flat" model, those trajectories would be much more limited, but (maybe) should still be there. I think. Maybe.

OneEye said:
SR and GTR both tell us that any frame of reference is equally valid (equally "at rest"). In GTR, the spaceship acceleration can be regarded as a gravitic field, thus the astronauts may regard themselves as at rest. I cannot propose the analogy for the landlubbers on the earth, but it was my impression that GTR was meant to do for acceleration what SR did for velocity - hence, disarming any claims for one frame of reference being specially favored over another.

Now you seem to be telling me that this isn't so.
For starters, I'm not the one telling you this. I too though the same as you this morning. Second of all, I believe you forgot one keyword in this sentence: "SR and GTR both tell us that any frame of reference is equally valid". SR talks about inertial frames of reference.

OneEye
Chen,

I would appreciate some elaboration on this. I have just finished Relativity, and, as you, would have hotly denied that Einstein allowed for any "specially favoured" frame of reference such as cookiemonster seems to be commending. Mind you, this leads us to the sort of difficulty which cookiemonster proposes, but I had thought the denial of any specially-favored inertial or gravitational frame of reference was not only essential relativistic doctrine, but a de fidei proposition - even an axiom - of fundamental nature to the theory. To deny this seems to me (though a dilettante, I admit), to be an essential denial of relativity.

OneEye
Janitor said:
My own guess is that the two clocks in this case, where neither clock gets accelerated by any forces, will match one another as they pass by for the second time.
If I understand SR properly, that's not possible. The existence of a relative velocity difference is in itself the cause of the time dilation. Imagine a closed Riemannian universe which contains only two spaceships with a relative velocity of (say) .9c. Each spaceship will see the other spaceship as having dilated time and distance. Both spaceships are "at rest" WRT themselves; both are "in motion" WRT the other. To which does the time dilation happen? Both! Right?

This is a problem that I have been noodling with as well. It ties into some other questions I have regarding relativity. Perhaps this board is a place to discuss my questions.

You guys are making this problem WAY to hard. It's covered in rigorous detail in most SR intros by assuming only that the time interval during which the space ship turns around can be made arbitrarily short with an arbitrarily great acceleration. No GR is needed.

You can show the same result (the traveller DOES end up younger) with a slightly different scenario that doesn't have quite the psychological wollop that seeing your twin be younger than you would. Here's how this version goes.

A space ship with one guy on it flies past a crowd of people on the earth. The lone traveller holds up a sign saying that he's 30 years old. Somebody in the crowd who's also 30 sticks around, and everybody else goes home. Twenty years later (on the space ship), the lone traveler passes another space ship with a crowd of people on it heading toward earth. He holds up another sign that says, "I'm 50 years old, and I'd appreciate it if someone on your ship who is also fifty will give a message to a guy on earth that you saw the guy he saw when they were both thirty and when you saw me we were both 50, and then tell him how old you are when you meet him." The guy in the crowd who's 50 opens a hatch and throws everybody else out, and continues on toward earth. When he arrives, he holds up a sign that says "I saw that guy who was 30 when he passed here years ago, and when I saw him he was 50, and now I'm 70. The guy who stayed on earth is shocked to hear this because he's a lot older than 70.

How's that for a paradox? No doppler shifted radio signal frequencies to screw around with and no acceleration. Just do the LTs back and forth.