Relativity thought experiment

[Jim T]

Twins board identical space ships. They are each put to sleep for lift off. When they wake up, they are both accelerating at the same constant rate and they are traveling further and further away from each other. After a year by their respective shipboard clocks, they are again anesthetized. When they wake up, they are under the same rate of acceleration, but they are now moving closer towards each other. After a 2nd year, they are re-united.

Is one older than the other (due to relativistic effects)?

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Is one older than the other (due to relativistic effects)?

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I'm not sure I exactly follow you here, but I'm pretty sure the answer is maybe

It will depend on what happened when they were asleep.

I assume when you say 'accelerating at the same constant rate' you mean the same direction too

Whichever twin undergoes more acceleration overall will be the one who has aged less. This statement is not well defined, but under most interpretations this will be true most of the time

And yes it's possible they both age the same amount, it all depends on exactly which way they were accelerating throughout the whole trip

[Jim T]

Let's say that they were only under for 30 minutes each time, and that any differences in acceleration during those times are negligible (especially when considered over the length of time they are accelerating). The rest of the time they are at exactly the same acceleration.

With respect to their vectors, let's say that twin A is changing vectors constantly, while twin B only changes course once (when they begin to narrow the distance between them).

[Jim T]

Hell, I just realized I'm ignoring the need for "deceleration". It's late.

[Scotch78]

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it all depends on exactly which way they were accelerating throughout the whole trip

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Whichever twin undergoes more acceleration overall will be the one who has aged less.

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I'm pretty drunk right now, but I'm pretty sure that one of these statements must be false. If direction mattered, then reversing it would reverse the temporal distortion. However, Ferris Bueller proved that going backwards doesn't reverse the effects, so I'm going to guess that time isn't a vector.

Scott

Let me just state that I'm not an expert on the subject (which is sad, because I should be, but I skipped class too much) but here's what I reckon

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and that any differences in acceleration during those times are negligible

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The smaller you make the differences in acceleration, the closer the twins will be to aging the same amount of time.

So I guess the answer here would then be that the twins would have age the same amount of time, except for a negligible amount

The key here is acceleration is not relative, this is what breaks the symmetry

[Scotch78]

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The key here is acceleration is not relative, this is what breaks the symmetry

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I'm not sure what you mean by "relative", but I think we're saying the same thing. I'm saying that traveling for ten years in one direction, then reversing direction (but maintaining the same magnitude of acceleration) for another ten years to reach the same point in space does not mean that I will age the same as someone who stood at that same point in time for all twenty years.

Scott

edit: Conversely, I'm saying that if direction did matter, then the twins would be the same age (assuming they split and reunite at the same point in space).

Ok yeah I think I agree with you, I didn't read and comprehend your post correctly

I'm not sure why you think one of those statements is incorrect

[Scotch78]

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I'm not sure why you think one of those statements is incorrect

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Read the edit to my second post. Basically, the first passage that I quoted says that only direction matters. The second passage says that magnitude matters. If only direction matters, then magnitude cannot matter. Since time isn't a vector, I'm going to guess that magnitude does matter. In which case, the first passage was incorrect. Modus Tollendo Tollens, yeah baby!

Scott

ooooohhhhhhh, I think I get it now, it was my poor choice of words. I didn't mean to imply that only direction matters

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Modus Tollendo Tollens, yeah baby!


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Dude, just when I think I'm on the same wavelength as you, you confuse me even more /images/graemlins/tongue.gif

[Scotch78]

Modus Tollendo Tollens (http://www.informatik.htw-dresden.de/~logic/conclusions/rule8.html)

Sorry, that was the form of my counter argument, I like to do logic proofs when I get drunk.

Scott

[PairTheBoard]

[ QUOTE ]
Twins board identical space ships. They are each put to sleep for lift off. When they wake up, they are both accelerating at the same constant rate and they are traveling further and further away from each other. After a year by their respective shipboard clocks, they are again anesthetized. When they wake up, they are under the same rate of acceleration, but they are now moving closer towards each other. After a 2nd year, they are re-united.

Is one older than the other (due to relativistic effects)?

[/ QUOTE ]

The thing is, A could be travelling out and back while B is just sitting on a nonrotating planet, moving from one side to the other to match or mirror A's acceleration. If B's acceleration due to gravity is made to match A's then it seems strange that A's clock should be different from B's when he returns. From inside their windowless crafts they have both experienced identical forces of acceleration.

I'm not sure this has ever been satisfactorily explained to me. If it was, I've forgotten.

PairTheBoard

I don't know the answer to your question, but I do know that time dialation occours sitting on a planet due to gravity, which may mean that if they matched accelerations there clocks would be the same

[PairTheBoard]

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I don't know the answer to your question, but I do know that time dialation occours sitting on a planet due to gravity, which may mean that if they matched accelerations there clocks would be the same

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Really! I never even considered that possibility.

PairTheBoard

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I don't know the answer to your question, but I do know that time dialation occours sitting on a planet due to gravity, which may mean that if they matched accelerations there clocks would be the same

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Really! I never even considered that possibility.

PairTheBoard

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You're missing out on some of the coolest physics!

Near the event horizon of a black hole the time dialation get's real crazy. If a ratio of say .5 means for every second we experience, some dude experiences .5 seconds, then if this some dude is on the event horizon the ratio would be 0 (although not exactly, some even more quantum weirdness happens that I'm not sure exactly how it changes things)

But think about that for a second.

If you were to look at some one falling towards a black hole, he would never actually make it there, since the time he experiences will be less and less a fraction of how much we experience. Now think about it from the some dude's perspective, looking out, as he falls through, he should theoretically see the Universe speed up and up and up and then see the Universe experience an infinite amount of time as he passes through an event horizon, this will all happen in a very short time for him.

Btw, if we could get a spaceship to a quasar (a big black hole), the tidal forces will be weak enough not to crush us as we pass through the event horizon (tidal forces are inversly proportional, maybe squared not sure, to the radius of the event horizon)

Also I'd like to ask a question to any one who know's about this stuff:

How do black holes grow? (since it takes and infinite amount of time for something to fall into it)

And if they do grow, does something near the surface of the event horizon fall through, or does it get 'pushed back' (It wouldn't actually get pushed back I know, I guess I'm asking does the black hole 'swallow some space-time')?

[PairTheBoard]

So if you could hang out on the edge of a Black Hole's event horizen you could watch the Universe come to an end.

hmmmmm.


PairTheBoard

[Jim T]

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If B's acceleration due to gravity is made to match A's then it seems strange that A's clock should be different from B's when he returns. From inside their windowless crafts they have both experienced identical forces of acceleration.

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Yes, that was the point in my poorly constructed thought experiment.

[Jim T]

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I don't know the answer to your question, but I do know that time dialation occours sitting on a planet due to gravity, which may mean that if they matched accelerations there clocks would be the same

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Yes, that has always been my thought, but that effect has always been ignored when I have seen anyone contemplate the problem. I guess I just need to get into some advanced physics.

[PairTheBoard]

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I don't know the answer to your question, but I do know that time dialation occours sitting on a planet due to gravity, which may mean that if they matched accelerations there clocks would be the same

[/ QUOTE ]

Yes, that has always been my thought, but that effect has always been ignored when I have seen anyone contemplate the problem. I guess I just need to get into some advanced physics.

[/ QUOTE ]

The thing is, if the clocks are the same like HotPants suggests, consider this. We have been on this planet for something like 4 billion years. If a spacecraft were to accelerate at 1 g for even a few thousand years it would be travelling so close to the speed of light with respect to it's original reference frame that it's on board clock would be nearly standing still compared to the original frame. In 4 billion years the universe would have aged googolplexes of years. Yet that has clearly not happened for the occupants of planet Earth.

Ok, so we're rotating and a spacecraft who's g vector kept rotating would max out on it's speed. But there's got to be a planet around someplace that doesn't rotate. Do the grains of sand on the surface of that planet virtually never age? I don't think so.

I think there's an expert explanation for this but I don't know what it is.

PairTheBoard

Let me just clarify that the time-dialation due to gravity is constant

I'm guessing that some one in space experiences around 1.000000001 as much time as we do, so it's not a huge effect (at least for planets)

[PairTheBoard]

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Let me just clarify that the time-dialation due to gravity is constant

I'm guessing that some one in space experiences around 1.000000001 as much time as we do, so it's not a huge effect (at least for planets)

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ok. Then it would not provide a solution for the paradox of one windowless craft accelerating at 1 g out and back while the other stays at home with 1 g supplied by gravity. 1g for the travelling craft will get it going pretty fast in just a few dozen years. Besides, the travelling craft doesn't even need to maintain the 1g the whole time. Once it gets up to speed it can just coast fast as lightning as long as it wants. The stay at home craft would have to go off planet to stay acceleration-equal and then it would have No time dilation due to gravity.

PairTheBoard

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ok. Then it would not provide a solution for the paradox of one windowless craft accelerating at 1 g out and back

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The direction of acceleration is important here I think

[PairTheBoard]

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ok. Then it would not provide a solution for the paradox of one windowless craft accelerating at 1 g out and back

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The direction of acceleration is important here I think

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The stay at home craft could duplicate the g directions the whole way by just moving to one side of the planet and then to the other. Theoretically it could go via a corridor through the center of the planet to keep things simple.

PairTheBoard

[Jim T]

[ QUOTE ]
Whichever twin undergoes more acceleration overall will be the one who has aged less. This statement is not well defined, but under most interpretations this will be true most of the time

[/ QUOTE ]

So what if twin A is under a constant 1G acceleration on Earth, while twin B is at a constant 1G acceleration until some point when, let's say, she reached a relative velocity of .25C away from twin A at which point her ship begins coasting at that constant velocity and has 0G acceleration.

Your answer above indicates that it is the Earthbound twin, who is still experiencing acceleration, that ages less.

[runner4life7]

I'm lazy, but did you even state a frame of reference because they can all be different "ages" from different frames of reference. Granted I slept through modern physics, but the little I remember is that A) these are not going fast enough and B) You must state a frame of reference

[usmhot]

[ QUOTE ]
So what if twin A is under a constant 1G acceleration on Earth, while twin B is at a constant 1G acceleration until some point when, let's say, she reached a relative velocity of .25C away from twin A at which point her ship begins coasting at that constant velocity and has 0G acceleration.

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In this case the twin on board the spaceship would age less than the twin on the planet.
During the time when her acceleration is 1G her clock and that of the twin on the planet would pass time at the same rate. However, when the spaceship is coasting - experiencing 0G - her clock would be slower than the planet-bound twin.

Special Relativity is not a factor here as from either one's frame of reference it is the other who is moving. So, when you say [ QUOTE ]
she reached a relative velocity of .25C away from twin A at which point her ship begins coasting at that constant velocity and has 0G acceleration

[/ QUOTE ] you have to account for the appropriate frames of reference. Twin B is traveling at a velocity 0.25G away from the planet as measured by twin A on the planet, BUT twin A is traveling at a velocity of 0.25G away from the spaceship as measured by twin B in the spaceship.

The only factor at this point is the acceleration due to gravity of the planet-bound twin.

And, incidentally, a rotating vs non-rotating planet really have nothing to do with anything.

[PairTheBoard]

[ QUOTE ]
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So what if twin A is under a constant 1G acceleration on Earth, while twin B is at a constant 1G acceleration until some point when, let's say, she reached a relative velocity of .25C away from twin A at which point her ship begins coasting at that constant velocity and has 0G acceleration.

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In this case the twin on board the spaceship would age less than the twin on the planet.
During the time when her acceleration is 1G her clock and that of the twin on the planet would pass time at the same rate. However, when the spaceship is coasting - experiencing 0G - her clock would be slower than the planet-bound twin.

Special Relativity is not a factor here as from either one's frame of reference it is the other who is moving. So, when you say [ QUOTE ]
she reached a relative velocity of .25C away from twin A at which point her ship begins coasting at that constant velocity and has 0G acceleration

[/ QUOTE ] you have to account for the appropriate frames of reference. Twin B is traveling at a velocity 0.25G away from the planet as measured by twin A on the planet, BUT twin A is traveling at a velocity of 0.25G away from the spaceship as measured by twin B in the spaceship.

The only factor at this point is the acceleration due to gravity of the planet-bound twin.

And, incidentally, a rotating vs non-rotating planet really have nothing to do with anything.

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That can't be right. I'm thinking the g force has nothing to do with it. It's the speed relative to the initial frame of reference that determines the slow down of the clock. Gotta be.

PairTheBoard

[usmhot]

Nope ... fraid not.

Special Relativity accounts for different frames of reference which are in motion relative to each other. In Special Relativity gravity is not taken into account.
Special Relativity was subjected to a number of thought experiments which highlighted paradoxes - the best known of which is the 'Twin Paradox' which is effectively what the original post of this thread exemplifies.

It wasn't until Einstein formulated General Relativity that these questions were properly addressed. He pointed out that acceleration and gravity were, to all intents and purposes, the same thing. So, if you are in a box and feel a force pulling you to one side of the box (which you can call 'the bottom') then there is absolutely no way of knowing whether the force is gravity or acceleration.
He also showed that time dilation occurs when accelerating - which is the same as saying that time dilation occurs in a gravity field. This has been verified by experiment.


Incidentally, sincere apologies - I got it backwards in my original post - the twin on Earth would age more slowly than her space-faring counterpart. Time slows down in a gravity field relative to another point in space.

[usmhot]

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It's the speed relative to the initial frame of reference that determines the slow down of the clock.

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Incidentally, to answer this point more succinctly ... there is no favoured frame of reference. We often fall into the trap of automatically thinking in terms of our postion (i.e. on planet Earth) as being THE frame of reference to which all others are measured - but that's wrong.
To see this more clearly, take two spaceships, A and B, which are traveling apart at some velocity v. What would you expect to see if you were on ship A? And what would you expect to see if you were on ship B?

Answer in white

<font color="white">If you are on ship A your clocks would measure time as normal, but the clocks on ship B would appear to be slower.
BUT
If you are on ship B your clocks would measure time as normal, but the clocks on ship A would appear to be slower.</font>

The paradox of each twin seeming have aged more slowly than the other is due to the fact that special relativity applies only when the two observers are moving at constant linear speeds relative to each other. Special relativity doesn't handle acceleration. Unlike velocity, acceleration is not relative.

At least one of the twins must undergo acceleration/deceleration in order for them to be reunited. Once that happens, special relativity no longer applies. That is why the paradox arises.

Bob Feduniak

[PairTheBoard]

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usmhot --


Incidentally, sincere apologies - I got it backwards in my original post - the twin on Earth would age more slowly than her space-faring counterpart. Time slows down in a gravity field relative to another point in space.

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I don't think so. The time dilation due to gravity is minimal. The time dilation due to velocity is the main thing. And we have proof with clocks sent into orbit. They no longer feel the force of gravity, but due to their speed they come back to earth having aged slower than their earth bound counterparts.

The Twin that travels out and back and spends time close to the speed of light is younger when he returns than his earthbound brother. And he never has to exceed 1g to do it. The more time he spends coasting near the speed of light the younger he will be than the earth he left behind when he returns. This is well known in relativity.

PairTheBoard

[PairTheBoard]

[ QUOTE ]
The paradox of each twin seeming have aged more slowly than the other is due to the fact that special relativity applies only when the two observers are moving at constant linear speeds relative to each other. Special relativity doesn't handle acceleration. Unlike velocity, acceleration is not relative.

At least one of the twins must undergo acceleration/deceleration in order for them to be reunited. Once that happens, special relativity no longer applies. That is why the paradox arises.

Bob Feduniak

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I was with you until the second paragraph. What does the acceleration/deceleration have to do with anything. The twin on earth can experience identical acceleration in both directions due to gravity. I think the acceleration is irrelevant. It's the velocity of the traveler that causes him to age slower.

PairTheBoard

It is the velocity. The problem is that the two twins can't be brought back together without at least one of them experiencing acceleration/deceleration. Once that happens, special relativity ceases to apply. Without introducing acceleration/eeceleration into the picture, it's not possible to verify whether the twins have aged differently, so there's no paradox.

The fact that special relativity can't handle this sort of thing is one of the reasons that general relativity was developed. I don't recall how to apply general relativity to the twin paradox, and it's not even close to being intuitively clear to me.

Bob Feduniak

[Moon Double Comb]

The acceleration/deceleration is fundamental here, since it breaks the symmetry and special relativity is not applicable anymore. You need general relativity.

And although I'm not an expert on the subject, I think you're misinterpreting the gravity/acceleration relation. Gravity curves spacetime, so that an otherwise straight worldline through flat spacetime is seen as a curved worldline from a rest frame. While acceleration is a curved worldline in itself. So seen from a rest frame both are interchangeable.

I would venture to guess that if you apply general relativity to the twin paradox the twins either have the same age and are not spatially seperated OR have a different age and ARE spatially seperated.

[PairTheBoard]

Ok, the reason no one has ever been able to give me a simple explanation for this is because the explanation is not simple. This link goes into various explanations. It looks to me like the determining factors are the speed of the craft and the two directions - ie. "away from" and "back toward". But you guys can figure it out.

Twin Paradox (http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html)


PairTheBoard