# Aging in the Twin Paradox

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This is my first post, but I read most threads in the Relativity forum, and I still havent found a clear and explicit answer to the following question, concerning the Twin Paradox.

When one of the twins accelerates and travels near c and then gets back, it's said that he appears younger because he has undergone some "heavy acceleration", which has made the time rate for him to pass slower.

However, arent all reference frames equally valid? I know, you'd say it's not the same with acceleration and GR, but why wouldnt it be? Basically acceleration is defined as change of velocity vector in a period of time. We know that velocity is relative to the observer, so consequently change of velocity would be also. There's no way we can know which one of the two bodies has changed its velocity, dont you think?

NOte: I prefer to get only reasonable replies, and not the Matrix-Oracle type of prophesies, which not even the author understands what they mean.

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It works because the twins are not in the same inertial frame. Frames of refference are equally valid only when they are in the same inertial frame. Since one of the twins is accelarating, they are not in the same intertial frame.

Here is a detailed article on why this works.

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There´s another very simple explanation:

Eigentime -the ammount of time that the respective twin ages- is the length of his trajectory through spacetime. Since they don´t take the same path through spacetime the length of their paths differ (in this case) and hence they have aged differently when they meet again.

btw.: Didn´t bother reading the link provided above, so maybe it´s also said there - but I doubt it.

EDIT: Read it. Quite an ok explanation although they used the "twin two is no inertial frame all the time" argumentation which I don´t like because the concept of inertial frames is confusing at least, as Companiero allready showed.

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This is my first post' date=' but I read most threads in the Relativity forum, and I still havent found a clear and explicit answer to the following question, concerning the Twin Paradox.

When one of the twins accelerates and travels near c and then gets back, it's said that he appears younger because he has undergone some "heavy acceleration", which has made the time rate for him to pass slower.

[/quote'] No, this is not correct. From the Earth Frame it is only the Relative velocity of the traveling Twin that causes time dilation, his acceleration has no effect. From the traveling twin's frame, during the period of turnaround, he will measure the Earth's frame time rate as sped up.

However, arent all reference frames equally valid? I know, you'd say it's not the same with acceleration and GR, but why wouldnt it be? Basically acceleration is defined as change of velocity vector in a period of time. We know that velocity is relative to the observer, so consequently change of velocity would be also. There's no way we can know which one of the two bodies has changed its velocity, dont you think?

The one which changed velocities is the one that felt the forces of acceleration. If I'm driving down the road, and I hit the brakes, I will see the car next to me seemingly accelerate forward. However, anyone can tell which of the two of us actually changed velocities by watching to see which of us is either thrown forward into his seat belt or pushed back into his seat.

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Put simply, you can tell the difference between the twin's motion. The one who goes away and comes back again has to decelerate to turn round (and accelerate again afterwards). In his frame, that deceleration looks like a force (so he would feel like he has weight in the direction of motion). The other twin (who doesn't move) feels no force.

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Severian - When you talk about force are you neglecting the force of gravity on twin one? There has never been a clear difference between "force" through acceleration as opposed to "force" through gravitation. People get muddled quite a bit when this topic somes up. If twin one stays on earth, subject to 1g the entire time, and twin two rides a ship that accelerates at 1g up to the speed of light, decelerates at 1g, and turns around to head back under 1g acceleration, then they've both been subject to the same forces the entire time. How does force play into that scenario.

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Severian - When you talk about force are you neglecting the force of gravity on twin one? There has never been a clear difference between "force" through acceleration as opposed to "force" through gravitation.

Yes there is. They are indistinguishable. That was the whole point of GR' date=' that one cannot tell whether one is in an accelerating frame, or under the influence of a force.

People get muddled quite a bit when this topic somes up. If twin one stays on earth, subject to 1g the entire time, and twin two rides a ship that accelerates at 1g up to the speed of light, decelerates at 1g, and turns around to head back under 1g acceleration, then they've both been subject to the same forces the entire time. How does force play into that scenario.

The travelling twin's velocity is not in the same direction all the time. If he goes round in a wide loop he will feel a force to the left or right. Also, he has to reneter the potential well of the planet (or where-ever the first twin is) and will be aware of this extra force.

All that is required by the problem is to break the symmetry between the twins. As long as they experience something different, there is no paradox.

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what if they are speeding away from each other at the same speed?

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If they both move away at the same speed, turn around and come back, they will be the same age.

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what if they are speeding away from each other at the same speed?

By this description you are necessarily invoking a third observer. That observer would see both clocks as the same, if the speed and accelerations are the same.

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There's no way we can know which one of the two bodies has changed its velocity' date=' dont you think?

[/quote']

On the contrary - you can always tell if there is an acceleration. It's constant velocity you can't distinguish, which is why all inertial frames are valid.

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On the contrary - you can always tell if there is an acceleration. It's constant velocity you can't distinguish, which is why all inertial frames are valid.

actually, you can't always know if you are accelerating. you may just be in a gravitational field.

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Why does the direction of force matter? It seems like you're coming close to recognizing absolute space. Force is force. Acceleration is acceleration. Accelerating one way and then the next does not changes the fact that you are accelerating the whole time. Accelerating in one direction to the speed of light (slowing down the clock) and then turning around and accelerating the other way to the speed of light doesn't reverse the slowing of the clock. If it does, then you enter into the absolute space realm. Relativity doesn't like absolutes.

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Accelerating in one direction to the speed of light (slowing down the clock) and then turning around and accelerating the other way to the speed of light doesn't reverse the slowing of the clock.

The acceleration itself has no effect on the clocks, it is only the velocity which matters. But the twin who goes away and comes back again must change speed at some point. Even while in a closed spaceship with no windows he would know that he was the one who moved because he was the one who felt the acceleration.

Edit: I just noticed I had a typo in post 7. I said acceleration at one point when I meant velocity. Maybe this is the source of confusion. Apologies, I have corrected it now.

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anyway what if they are communicating with radiowaves and telling each other what the time is? I think I've heard some explanations but I'm still not sure...

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The acceleration itself has no effect on the clocks' date=' it is only the velocity which matters. But the twin who goes away and comes back again must change speed at some point. Even while in a closed spaceship with no windows he would know that he was the one who moved because he was the one who felt the acceleration.

[/quote']

But by the equivalence principle, you should have a redshift in any accelerating frame.

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actually, you can't always know if you are accelerating. you may just be in a gravitational field.

You know if you're in an accelerating frame of reference. (This is a bit of a non-sequitur, since my previous answer was context-dependent.)

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But by the equivalence principle, you should have a redshift in any accelerating frame.

Yes of course. Just like you have a redshift from a gravitational field. I meant that it is not the acceleration in the twin paradox which is causing the age difference since the transition from v to -v is supposed to be intantaneous...

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Forgive my lack of science but ive always found the scenario of the twin paradox impossible.We have mass and we know it would take an infinite amount of energy to propel us to LS so even theoretically we cannot ever go LS.I cannot see how you can do the correct mathematic formula that would take into account a mass bearing body,moving at LS and then forcasting its constraints on space-time.Surely it would contradict GR so you cannot calculate an outcome to an event with an invalid formula.

Help me if im totally wrong but if light photons take 8 minutes from sun to earth havent we only aged 8 minutes.Or another way if the we can see light from a star say at 10 billion years away,thats how long we have aged.

If the universe is 14.5 billion years old i cannot travel for a hundred years at light speed then come back and from my framepoint the universe is say when i arrive at earth an extra billion years old.Im sure it must be correct to say the universe is 14.5 billion years old and a photon from some sun regardless of how long it travels at the speed of light and then back to were it started from the universe is still only 14.5 billion years old.Or imaginary particles and such would make a mockery of our perceptions.

help me if im totally not getting this

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Forgive my lack of science but ive always found the scenario of the twin paradox impossible.We have mass and we know it would take an infinite amount of energy to propel us to LS so even theoretically we cannot ever go LS.I cannot see how you can do the correct mathematic formula that would take into account a mass bearing body' date='moving at LS and then forcasting its constraints on space-time.Surely it would contradict GR so you cannot calculate an outcome to an event with an invalid formula.

[/quote']

You don't need to accelerate to light speed. Any old speed will do. If the twin take a walk down to the shops and comes back, he will be younger than his twin who stayed at home. It is only that the effects become more pronounced with high speeds.

Help me if im totally wrong but if light photons take 8 minutes from sun to earth havent we only aged 8 minutes.Or another way if the we can see light from a star say at 10 billion years away,thats how long we have aged.

What do you mean 'how long we have aged'? The 8 minutes or 10 billion years is how long it has taken the light to reach us.

If the universe is 14.5 billion years old i cannot travel for a hundred years at light speed then come back and from my framepoint the universe is say when i arrive at earth an extra billion years old.

Why not? (Other than the fact that the Earth probably wouldn't be there anymore...)

Im sure it must be correct to say the universe is 14.5 billion years old and a photon from some sun regardless of how long it travels at the speed of light and then back to were it started from the universe is still only 14.5 billion years old.

You are correct that the universe is 14 billion years old or so, but I don't get why you say the photon has to go back to where it started?

Or imaginary particles and such would make a mockery of our perceptions.

What imaginary particles?

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You don't need to accelerate to light speed. Any old speed will do. If the twin take a walk down to the shops and comes back' date=' he will be younger than his twin who stayed at home. It is only that the effects become more pronounced with high speeds.

[/quote']

Thats what i am having a conflict with,to me the twin paradox only represents a perception.The photon from the sun takes 8 minutes to get here to my frame point were i observe it hitting my electrolite plate.Regardless of its velocity it has taken 8 minutes,from its framepoint it is 8 minutes old isnt it.hence we both are 8 minutes older from when it set off.now if the photon was my twin brother are we not both 8 minutes older

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Severian - When you talk about force are you neglecting the force of gravity on twin one? There has never been a clear difference between "force" through acceleration as opposed to "force" through gravitation. People get muddled quite a bit when this topic somes up. If twin one stays on earth, subject to 1g the entire time, and twin two rides a ship that accelerates at 1g up to the speed of light, decelerates at 1g, and turns around to head back under 1g acceleration, then they've both been subject to the same forces the entire time. How does force play into that scenario.

Yes, people do get muddled up, A part of the reason is that the "force" being experinced by each twin is only a part of the picture. The real difference in time dilation is more related to the difference in potential. (or the Amount of work that it would take to move a mass form point to point.)

For a person standing on the Earth, the time differential between himself and a object in space would be related to the amount of work it would take to lift an object to that distance against Earth's gravity. Since the Earth's gravity falls off with distance this energy does not increase very much once you get past the distance of the moon's orbit.

In the case of the person accelerating towards the Earth, the case is different. He could consider himself at rest within a gravity field (his engines are firng in order to keep him from falling.) if he looks out his window, he sees the whole universe falling by. If he looks "above" him, he sees the Earth falling towards him. If the Earth is falling, then it must be in response to the same gravity field he himself is stationary in. If he measures the Earth's rate of fall, he will note that it matches that as if the gravity field strength is the same for the Earth as it is for him. This indicates that the gravity field is uniform (does not decrease with distance) This means that to "lift" a mass to the Earth "height" at any given moment, you would have to fight the same force of gravity the whole way (as opposed to from on the Earth, where the field strength weakens with distance). Thus from his veiwpoint,there is a greater difference in gravitational potential between himself and the Earth, then what a person on the Earth would measure between them. This also means that he will see a different time differential, then the Earth observer would.

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Thats what i am having a conflict with' date='to me the twin paradox only represents a perception.The photon from the sun takes 8 minutes to get here to my frame point were i observe it hitting my electrolite plate.Regardless of its velocity it has taken 8 minutes,from its framepoint it is 8 minutes old isnt it.

[/quote'] No, form its frame, it hasn't age at all, because from its frame, the distance form Sun to Earth is zero, and it takes zero time to cross zero distance at c.

hence we both are 8 minutes older from when it set off.now if the photon was my twin brother are we not both 8 minutes older

Now your twin brother could not travel at c, but he could travel at .866c. In which case, you would would see him age at half speed and only age 4 min during the trip. He on the other hand, would measure the distance between Sun and Earth as only half that that you did (length contraction) and for him the trip would then take only 4 min. Thus both of you agree that he aged only 4 min during the trip.

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Thats what i am having a conflict with,to me the twin paradox only represents a perception.

No, it's real. Moving clocks run slower than stationary clocks. This has been confirmed by a number of experiments and is continually tested by GPS satellite atomic clocks. (There are also effects of general relativity to consider, but the special relativity effects are well-established)

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No, form its frame, it hasn't age at all, because from its frame, the distance form Sun to Earth is zero, and it takes zero time to cross zero distance at c.

so light doesnt take 8 minutes to get from the sun,from its frame point its instant.This doesnt make sense to me sorry i cannot see how from your frame point your instant when it takes me 8 minutes to observe you.help

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