Peter and Paul are twins. Peter is on the Earth, to which our stationary frame of reference is attached. Paul is sitting at the controls of his spaceship out in space, far away from any gravitational fields. Paul is also at rest in the stationary frame. Peter’s clock and Paul’s clock are synchronized.

Paul now switches on the rockets on his spaceship and accelerates away into deep space at an acceleration of 1g (≈ 9.8 m/s^2). After 1 year he is travelling close to the speed of light and is benefiting from relativity’s time dilation effects.

5 years after the start of his journey (as measured by his own clock) Paul turns his ship around, but keeps his rockets firing. He is now slowing down at 1g relative to the Earth.

After another 5 years Paul’s ship comes to rest relative to the Earth. However, he keeps his rockets firing and now starts to accelerate back towards the Earth.

After another 5 years Paul’s ship is halfway back to Earth. Paul turns the ship around again, but once again he keeps his rockets firing. He is now slowing down at 1g.

After another 5 years Paul’s ship comes to rest relative to the Earth and Paul now switches off his rockets. He is now back where he began. But when he compares his clock with Peter’s he discovers that while he has aged only 20 years, Peter has aged 3348 years!

But this age difference must be due entirely to the effects of SR, because during the entire experiment Peter and Paul have been subject to exactly the same GR effects. Peter has been on the Earth, whose gravity has been accelerating him at 1g, while Paul has been subject to an identical acceleration of 1g in his ship. By GR’s Principle of Equivalence, these two accelerations are indistinguishable and produce identical effects. Ergo, the age difference at the end of the experiment must be caused entirely by the SR effects of Paul's travelling at high velocities.

QED …? :-k

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Erm. Not quite.

There is the Twin Paradox which is due to SR and involves no acceleration at all see http://www.hawaii.edu/suremath/SRtwinParadox.html

Then there is the issue of acceleration and the equivalence with gravity which is a postulate of GR.

What needs to be remembered in the example above is that each twin travels a different "world-line" through spacetime. The Paul twin undergoes two accelerations and two decelerations. The Peter twin undergoes one acceleration. The two are moving through different world-lines and therefore there will be a time dilation effect due to acceleration as well as motion near light speed relative to the inertial frame.

"Definitive Proof That It's SR?"

Why do you need to prove it? SR has it's time dilation effects--just read Einstein's original 1905 paper. That's where he calls it a "peculiar consequence," but not a paradox.

http://mentock.home.mindspring.com/twinrdux.htm
http://mentock.home.mindspring.com/twins.htm
http://mentock.home.mindspring.com/twin2.htm

According to SeanF, that's irrelevant:

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what about Mary? Sorry just had to ask.

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For the benefit of those people who won't accept that the Twin Paradox is an SR effect.

I know. SR's time dilation effects are what cause the age difference. That's the whole point of my thought-experiment.

I have, but to properly understand it one must do more than "just read" it.

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Ah. But read my third link above. It shows a time dilation that is not caused by SR effects.
Just a casual reader will notice that Einstein establishes the basic facts of the "twin paradox" in that paper.

Just thought I'd throw my 2¢ in here.

Eroica, I don't think you're example deals with SR at all. Since both twins are constantly experiencing 1g, neither one of them is ever in an inertial frame, are they?

I'm not as up-to-speed (ha!) on GR as I am on SR, but my prediction would be that Peter and Paul would both be the same age at the end of this experiment . . . could be wrong, though.

Now, it'd be different if you have Paul cut his engines at a given velocity and coast for a while before turning around and refiring the engines to slow (doing the same thing on the trip back, of course). Then I think Paul would be younger due to SR on the basis of how much time he spends coasting.

Like I said, though, I'm not clear enough on GR to say whether a 1g gravity well and 1g acceleration would produce equal dilations, but the equivalence principle does seem to suggest it.

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He may undergo the same accelerations, but at a different place in space, and that makes a difference. The space borne twin observes his sibling (nice touch of gender neutrality, don't you think ) as being very high up in the gravitational well. This mean he perceives the earth clock as running fast relative to his. This is a GR effect, not SR. To quote Stephen Hawking in "A Brief History of Time" (page 33)

Note that Hawking is saying that you get the twin paradox simply by having one twin walk to the top of a mountain. Nothing close to the speed of light or space here. The space and high speed simply make it a larger effect (years instead of nanoseconds). Even these small changes have been observed by taking atomic clocks up in airplanes and observing that the one that flew ran fast compared to the one on the ground.

I will admit that you can compute the outcome of the space thought experiment using only SR, but it requires that you treat the acceleration and the direction change as a sudden shift between two inertial reference frames. That is, you totally ignore what happens during that period. While this use of SR gives you an answer, it does not give you an explanation. That requires general relativity. If you don't believe me, check out the text books. You'll find that they support this position.

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He points out that you get a twin paradox here. I'm not sure that it's necessarily the same one.

The SR thought experiment can be set up in intergalactic space, where any gravity well is negligible, and you still end up with one younger twin.

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No, if you read the entire context of the discussion in the book you'll see it's the same one. And you're wrong to say that there is not a gravity well if you do the experiement in deep space. One twin undergoes acceleration to change direction and by the principal of equivalence that is indistinguishable from a gravitational field.

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"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli

What are you guys talking about? There is no equivalence here! The twin taking the space flight has to first accelerate to near the speed of light and then change acceleration to head back towards the earth. And then again he changes acceleration to slow down so he doesn't collide with the earth. His acceleration is not constant at all. The twin on the earth, on the other hand, experiences constant acceleration of 1g the entire time. There is no equivalence here and hence no problem.

The equivalence is between an accelerated reference frame and a gravitational field, not between the two twins. The principle of equivalence is one of the foundations of general relativity. It states that the laws of physics are the same in an accelerated reference frame as they are in a gravitational field. That's why one way of providing "artificial" gravity in a spacecraft is to continuously accelerate.

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"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." - William Thompson, 1st Baron Lord Kelvin

"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli

The original post said "By GR’s Principle of Equivalence, these two accelerations are indistinguishable and produce identical effects. " But the two accelerations are not indistinguishable, are they? Twin 1 is comforable, experiencing the earth's 1G as he sits on the beach sipping Pina Colada. In the meantime, twin 2 is being thrown from one end of his space ship to the other as the outbound rockets extingush and the inbound rockets ignite to change the spacecrafts direction back towards the earth.

One G in the spacecraft will be indistinguishable from 1 G on Earth. The difference, as I pointed out in my first post is that the space twin experiences this acceleration at a long distance away, and that makes a difference in how the two twins perceive each other's clocks.

In any case, Ryback, we're not really in disagreement here. The accelerations the space twin experiences place him in a very non-inertial frame while the earth twin can be considered to be in an inertial one for the purposes of the experiment. My disagreement with the person who originated the thread is that I (and other physicists) know that SR is not sufficient for a full description of the twin paradox. Because of the accelerations (indistinguishable from gravitational fields) that the space twin experiences a full explanation requires general relativity.

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"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli

I say that the acceleration does not change in magnitude, which is the important point. The GR effects of a gravitational field on one's clock are not dependent on the direction of the field, are they? I may be wrong, but I still contend that the GR effects on Peter's clock are identical to the GR effects on Paul's clock.

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[-X SeanF, SeanF, you surprise me! And to think that I was just waiting for you to leap to my defence

You're absolutely wrong here. Of that I'm sure. I stand over my figures. Peter (the traveller) will age just 20 years, while Paul will age 3348 years.

Neither of the twins is in an inertial frame of reference. That's correct. But if the GR effects are the same, then the age difference can only be explained by SR.

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Sorry, Eroica! I'm still working this one over in me little ol' mind here.

While Paul is rocketing away, experiencing his own little gravity well, wouldn't he say that since Peter is "below" him and getting farther and farther away, that Peter must be deeper in the gravity well? Now, when he's turned around and decelerating, Peter is "above" him and thus higher in the gravity well - but the difference in their heights (and thus the difference in Paul's opinion of the gravity well depth) is greater, so the GR-Paul-is-aging-faster wouldn't exactly cancel out the GR-Peter-is-aging-faster.

If that's right, wouldn't that mean that GR predicts different ages? Or am I still missing something?

Don't get me wrong, I still think the twin paradox can be dealt with entirely within SR. I'm just still working through this experiment of yours.

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I still say that the GR effects are not the same. If you wish to dismiss the obvious issue of acceleration change during the turn around segment of the trip, what about the initial part? As the twin is leaving the earth, he will experience >1g. That is, he will experience the force of the earth's gravity added to the 1G inertial force of the rockets acceleration. A similar argument could be made for the journey back. GR should be able to explain everything here. If I am not mistaken isn't GR a more "general" theory and hence it can explain everything SR can and more?