Relativity in Ender's Game

[Requin]

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A different version of the Twin Paradox:

1. The twins begin at rest on Earth.

2. They embark on separate voyages which are identical except in opposite directions.

3. Both voyages include accelerating to near the speed of light from the point of view of Earth.

4. They meet again back on Earth.

5. They compare ages.

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Actually, I was looking back at what I said, and I meant that the message must meet up with, not match speeds with, the other traveller. It works out the same though, because it will be impossible for the message to get to the traveller without either experiancing some acceleration, or having the traveller experiance acceleration.

Anyways.

In your example, the answer is that they both have the same age. Why? Because you have both twins accelerating. They must experiance some acceleration to return to Earth, and so take they take this into account when measuring the passage of time. They will each think the other has experianced acceleration, and so logically must be younger than someone who has stayed still. But since they have BOTH accelerated, there is no paradox: they both underwent the same relativistic effects.

[Sharkey]

Yet each twin saw the other aging slower than himself the whole time.

[Matt R.]

Not during the part of the journey where they are accelerating. When they change directions for their return journeys, they can no longer claim to be in a stationary reference frame. (I'm not exactly sure how the passage of time looks during the accelerating part of the journey in each reference frame, but I do know that one can no longer claim to be the stationary observer once he accelerates. This is what breaks the "symmetry" of the problem and allows the twins to actually be the same age when they meet back up.)

[Sharkey]

As I recall the equations, they don’t require zero change in velocity for time dilation to occur, only that there be a velocity. (Acceleration causes its own time dilation, but that can be ignored here.) Either way, even ignoring the effect altogether during periods of acceleration, whatever happens to one twin happens to both, because their voyages are identical except in opposite directions.

So, if each twin sees the other aging slower than himself during some part of their voyages and never sees the other aging faster than himself during any part of their voyages, then each must expect the other to be younger that himself when they meet again to compare ages.

[kevyk]

It's easier to consider this by just adding another sibling to the traditional twins paradox.

Twin A leaves Earth at 0.8c headed in the +x direction.
Twin B leaves Earth at 0.8c headed in the -x direction.
Twin C stays on Earth.

The 3 twins reunite on Earth in 20 years (by Twin C's clock). A and B will have experienced the passage of only 12 years, while C will have aged 20. The fact that they move in opposite directions doesn't matter.

[Matt R.]

I'm pretty sure one of the assumptions for the derivations of Lorentz's original equations is constant velocity. If that assumption isn't met, all bets are off (until you use general relativity of course).

The thing about this:

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So, if each twin sees the other aging slower than himself during some part of their voyages and never sees the other aging faster than himself during any part of their voyages, then each must expect the other to be younger that himself when they meet again to compare ages.

[/ QUOTE ]

is that they can't instantaneously compare their relative ages during their journey. They must either wait until they meet back up, or wait for some type of signal to relay the information (which can only travel less than or equal to the speed of light). I'm sure it would be much easier to "see" this with the mathematics, but I have no idea how to handle accelerations. Basically, you cannot ignore the accelerations in this case, and even though their journeys are identical, they can't instantaneously compare their ages due to the speed restrictions on transmitting the information. Once you take this stuff into account, the observations from any reference frame work out correctly.

[Sharkey]

Let’s avoid acceleration altogether. The twins pass each other at the origin already going in opposite directions at close to +c and –c respectively. When each reaches a certain distance, he sends a signal back to the origin indicating how much time he has observed transpire on the other’s clock and elapsed time on his own ship, with all time scales using the instant they passed each other as t=0.

[atrifix]

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This does not sound right to me because on the return trip, any time that was gained for Mazer would have been lost. Am I wrong?

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In a word, yes.

Because Mazer turns around at some point, he needs to accelerate. Thus special relativity cannot be used to compare the two frames and general relativity predicts the correct result, that Mazer will be younger. Assuming he is travelling at -.995c, that means he needs to accelerate first to 0 and then to .995c, which is quite a substantial shift in space-time.


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Second. In the book, they have a device that is capable of instantanous communication across the universe. While I don't expect that to be possible because it is way faster than the speed of light, they use this device which makes me wonder about another age question.

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This is partly science fiction, and definitely goes against the theory of relativity, but there is also a point where relativity breaks down. Quantum mechanics predicts that there are things which "travel" faster than light.


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It doesn't make sense to me that Ender should stay young while his brother gets old.

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This is the paradox, but again you have the acceleration problem. Google Twin Paradox for more information.

[Requin]

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Let’s avoid acceleration altogether. The twins pass each other at the origin already going in opposite directions at close to +c and –c respectively. When each reaches a certain distance, he sends a signal back to the origin indicating how much time he has observed transpire on the other’s clock and elapsed time on his own ship, with all time scales using the instant they passed each other as t=0.

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You're not ignoring acceleration here. To send the signal back to the origin, the signal must undergo acceleration.

[Sharkey]

No. Radio waves always travel at the same speed.