Relativity in Ender's Game

[splashpot]

Pretty basic relativity questions. Have any of you read Ender's Game by Orson Scott Card? Great book by the way. But I'm questioning if the issues with relativity in the book are accurate.

In the book, a military legend, Mazer Rackham, defeated an army of alien bugs 80 years ago. Realizing that his expertise would be needed in the future when starships are ready to attack the alien homebase, they decide to put Mazer in a spaceship, send him off at near light speed, and then have him return, just in time to train the next military genius, Ender Wiggins. Mazer says only eight years passed for him on the ship, but 80 years passed for everyone else. 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?

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.

At the end of the book, Ender decides to leave on a ship with his sister. He leaves behind his brother on Earth. For Ender, only 2 years passes on the ship. But for his brother, 50 years passes. Ender uses the communication device to talk with his brother who is 77 years old, while Ender is still young. Is this possible? This seems wrong to me because Ender flew away from Earth, which could also be viewed as the Earth flying away from Ender. It doesn't make sense to me that Ender should stay young while his brother gets old.

I know the book is fiction and that an instantaneous communication device is probably impossible, but are these other relativity concepts flaws in his book?

[oneeye13]

google "twin paradox"

and there is something different about the frames

[Andrew Karpinski]

Would a device that communicated slightly faster than the speed of light be instanteous?

[Sharkey]

That’s the famous Twin Paradox.

A variation I’ve wondered about is where both twins go on identical voyages except in opposite directions then return to their common starting point and compare ages.

[chrisnice]

[ QUOTE ]
That’s the famous Twin Paradox.

A variation I’ve wondered about is where both twins go on identical voyages except in opposite directions then return to their common starting point and compare ages.

[/ QUOTE ]

The direction of travel makes no difference. Think of it like this. You are allways travelling through space and time at a speed equal to the speed of light. Whenever you increase your speed through space you decrease the speed at which you move through time. Directtion is irrelevant.

[Sharkey]

What is the difference in age between the twins in the version I described?

[chrisnice]

[ QUOTE ]
What is the difference in age between the twins in the version I described?

[/ QUOTE ]

None.

[Sharkey]

[ QUOTE ]
[ QUOTE ]
What is the difference in age between the twins in the version I described?

[/ QUOTE ]

None.

[/ QUOTE ]

Yet each twin saw the other aging slower than himself during their voyages.

[KeysrSoze]

For part of the trip each sees the other twin aging slower, but for the rest of the trip they each see each other catch up.

[Sharkey]

[ QUOTE ]
For part of the trip each sees the other twin aging slower, but for the rest of the trip they each see each other catch up.

[/ QUOTE ]

For which part of the trip does each twin see the other’s clock appear to be going faster than the normal rate?

[KeysrSoze]

When they start moving back towards one another. Their frame of reference to each other gets blue shifted, instead of red shifted when they were traveling apart.

[Sharkey]

Sorry, but time dilation is not necessarily related to shift in wavelength. It’s possible to observe time dilation for a frame of reference moving perpendicularly to the line connecting you.

[KeysrSoze]

Just a figure of speech.

[oneeye13]

[ QUOTE ]
For part of the trip each sees the other twin aging slower, but for the rest of the trip they each see each other catch up.

[/ QUOTE ]
...?

[ChromePony]

[ QUOTE ]

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.

[/ QUOTE ]

This part is definitely fiction, but the Rackham age part is legit assuming they have a ship that can travel that fast which I get to be about .995c...thats pretty fast.

[ChromePony]

[ QUOTE ]
Just a figure of speech.

[/ QUOTE ]

Its just confusing when worded like that because its not like time slows for Rackham for example when he's traveling away from earth and then speeds up again when he approaches to cancel out the previous effect.

One way to look at it is that the velocity term is squared in the equations so the sign/direction doesnt matter, and its really not like redshift/blueshift at all.

[Matt R.]

I think the explanation for Sharkey's version lies in the fact that both twins obviously must accelerate to meet back up with each other. They don't start to "catch up" with each other during the return voyage -- during any constant velocity part of the trip the clocks will appear slow relative to the other twin (as Chrome said, direction doesn't matter).

I have no idea how to deal with the acceleration though (probably involves general relativity), but I would think this has to be the explanation?

[Requin]

[ QUOTE ]
I think the explanation for Sharkey's version lies in the fact that both twins obviously must accelerate to meet back up with each other. They don't start to "catch up" with each other during the return voyage -- during any constant velocity part of the trip the clocks will appear slow relative to the other twin (as Chrome said, direction doesn't matter).

I have no idea how to deal with the acceleration though (probably involves general relativity), but I would think this has to be the explanation?

[/ QUOTE ]
Ya, it depends on who accelerates (decelerates, negative accelerates, whatever) to meet up with the other twin to exchange information. Or, if they send a message in order to establish who is older, then that the message must at some point match speeds (by acceleration) with one twin. The reason you get a paradox in the book is that with instantaneous communication, there is no need for the message to accelerate, it just magically appears. So it is impossible to determine who has actually accelerated, and so its impossible to know if it is Ender or his brother who has experianced a slower passage of time.

[IronDragon1]

[ QUOTE ]
Would a device that communicated slightly faster than the speed of light be prohibited by the laws of physics?

[/ QUOTE ]

Seriously, I'm a physics donk-I have no idea.

Please enlighten me

[Sharkey]

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.

[Requin]

[ QUOTE ]
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.

[/ QUOTE ]
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:

[ QUOTE ]
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]

[ QUOTE ]
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?

[/ QUOTE ]
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.


[ QUOTE ]
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.

[/ QUOTE ]
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.


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

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

[Requin]

[ QUOTE ]
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.

[/ QUOTE ]
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.

[ChromePony]

[ QUOTE ]

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.


[/ QUOTE ]

This is partially true if youre talking about quantum teleportation, but unlike it sounds there is actually no way for any information to travel faster than light. If you separate particles that have are quantum entanlged then it is true that a measurement on one with instantaneously affect the results of a measurement on the other no matter how far away it is. However, in order to convey useful information you need to know the states of each particle and this can only be shared classically and such classical information is limited by the speed of light.

Of course without this fancy communication thing Card's plots would have completely broken down and the books wouldnt be nearly as entertaining, so Im alright with granting him a freebie here.

[Requin]

[ QUOTE ]
No. Radio waves always travel at the same speed.

[/ QUOTE ]
I don't know the exact physics of it, but anything on your ship must be travelling in the direction that your ship is traveling. You want to send it back to earth. So clearly you must chance its current velocity. The fact that light always travels at the same speed makes this hard to explain, but trust me whatever you use to send information must undergo acceleration.

[Sharkey]

What precisely do you think is changing velocity, and in which frame of reference?

[bunny]

[ QUOTE ]
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.

[/ QUOTE ]
They are the same age - as they recede from each other they witness their twin's clock running slow. At the furthest point of separation each of them thinks they are older than their twin. They then turn around and speed back together - here it seems their twin's clock is running faster than their own and they "catch up". When they return to Earth they will be the same age.

[Sharkey]

[ QUOTE ]
They then turn around and speed back together - here it seems their twin's clock is running faster than their own and they "catch up".

[/ QUOTE ]

Caused by what specific physical phenomenon?

(If that’s not an impolite question.)

[bunny]

It's a consequence of the speed of light being constant for all observers.

[Sharkey]

Clarify something if you would. Do you mean time dilation is dependent on relative direction? If that is the case, then how can several observers positioned all around a linear accelerator observe the same lengthening of lifespan for an unstable relativistic particle?

[bunny]

[ QUOTE ]
Clarify something if you would. Do you mean time dilation is dependent on relative direction? If that is the case, then how can several observers positioned all around a linear accelerator observe the same lengthening of lifespan for an unstable relativistic particle?

[/ QUOTE ]
Dont they observe it using the same instruments at rest in the accelerator? I havent thought about this and dont know the answer, hopefully metric/borodog or someone clever will stick their nose in soon...

In the twins example it doesnt seem a problem to me as the spacetravellers have heaps of photons all "banked up" waiting to hit them as they speed back to earth, the only way I can understand this is that they see time running faster on the other ship (as they have to observe the light moving at constant speed).

Edit: I guess I am claiming time dilation is dependant on relative direction but I dont know if perhaps the solution isnt actually the periods of acceleration...it's been too long since relativity courses I'm afraid. I'll have to withdraw from answering. /images/graemlins/confused.gif