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Twin Paradox (yet again!)


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Have I got this correct? The Twin Paradox can be resolved by showing that only one of the twins undergoes acceleration in order to return to base. So what has the value of their relative velocity got to do with the paradox?

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Yes for a system at rest there are no relativistic effects.

Take a train and a station; before the train takes off there

is an absolute quantity of space between them. Give the

train speed; especially alot of speed and relativistic effects

come into play; for the train distances have shrunk and

the station's clock is running fast.

 

There is no reciprocal effect as some claim.

Only one clock goes slower.

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Tom Mattson wroye

The value of the relative velocity determines the exact age difference. The faster the rocket travels, the greater the age disparity when it returns to Earth.

If there was no one-sided acceleration (the two didn't meet again) would the assymetrical aging still apply?

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If there was no one-sided acceleration (the two didn't meet again) would the assymetrical aging still apply?

 

If there is no acceleration how will you compare their ages? One or both must be in a different frame from the observer so you cannot do a fair comparison. For example, if the observer is on the Earth's frame, the travelling twin will appear younger, but if he is travelling with the spacefaring twin, the twin on Earth will appear younger. If he is travelling at the average velocity of the 2 twins, they will appear to be the same age.

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Originally Posted by Severian

For example, if the observer is on the Earth's frame, the travelling twin will appear younger, but if he is travelling with the spacefaring twin, the twin on Earth will appear younger. If he is travelling at the average velocity of the 2 twins, they will appear to be the same age.

 

I am confused by the use of the word appear in (will appear younger) and when the twins are compared (one is younger). How do we get from appear to is?

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I am confused by the use of the word appear in (will appear younger) and when the twins are compared (one is[/i'] younger). How do we get from appear to is?

 

I am using "appear" because age is not a frame invariant quantity. They have different ages depending on the frame of the observor. Feel free to us 'is' if you like but I tend to think of true age of a person as being in the person's frame ('rest age' if you like).

 

If both twins accelerate back to meet would there still be a difference in their ages?

 

That depends on who does the accelerating. Basically, if you can't distinguish the motions of the two brothers (so they do the same accelerations) they should be the same age when they meet.

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The value of the relative velocity determines the age difference. There will be an age difference only if there is a difference in the type of motion (acceleration) of the twins.

 

Therefore, essentially, the twin's relative velocity generates the possibility of an age difference and a one-sided acceleration makes this an actuality. Is this basically correct?

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That depends on who does the accelerating. Basically, if you can't distinguish the motions of the two brothers (so they do the same accelerations) they should be the same age when they meet.

 

 

What about in the following scenario:

 

Where > and < depict acceleration...

 

and each # depicts one year of coasting with no acceleration.

 

We have a pair of twins in Spaceships - A and B They are starting at rest wrt Earth.

 

 

A - >>>>><<<<<<<<<<>>>>>

 

B - >>>>>#####<<<<<<<<<<#####>>>>>

 

 

So both A and B undergo the exact same amount of acceleration which results in their return to the rest frame of Earth. We'll say that >>>>> is equal to an acceleration that brings a ship to a velocity of 0.5c wrt Earth. So B has coasted at this speed (150,000 km/s) for 10 years longer than A (Because A didn't coast at all, he just turned around immediately when he reached this velocity)

 

So using the formula: T1 = T0/SqRt[1-(v^2/c^2)]

 

B will be about 1.55 years younger than A when they are together again... even though they both underwent exactly the same amount of acceleration.

 

Or do I have this wrong?

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Originally Posted by Severian

I would rather say that the velocity makes the age difference and the acceleration lets you see it.

The relative velocity on its own can't make the age difference: the system is symmetrical. An asymmetry has to be introduced for the age difference to become actual.

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B will be about 1.55 years younger than A when they are together again... even though they both underwent exactly the same amount of acceleration.

 

Or do I have this wrong?

 

I agree. Their accelerations weren't identical because there were different pauses between them. Sorry, maybe I explained that badly before - what I was trying to say was that the acceleration lets you tell the brothers apart. If the accelerations are such that you cannot tell them apart then they must have aged the same amount.

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The value of the relative velocity determines the age difference. There will be an age difference only if there is a difference in the type of motion (acceleration) of the twins.

 

Therefore' date=' essentially, the twin's relative velocity generates the possibility of an age difference and a one-sided acceleration makes this an actuality. Is this basically correct?[/quote']

 

I'd say that what "makes" the time difference depends on which twin you ask.

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Originally Posted by Janus

I'd say that what "makes" the time difference depends on which twin you ask.

Thanks Janus. That's solved the problem. I wish I'd thought of that.

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The relative velocity on its own[/i'] can't make the age difference: the system is symmetrical. An asymmetry has to be introduced for the age difference to become actual.

 

The relative velocity does make the age difference.

According to Brother A in space, his brother B is experiencing time dilation due to earth moving near the speed of light, and therefore is aging slowly. Brother A is absolutely correct.

According to Brother B on earth, his brother A is experiencing time dilation due to his spaceship moving near the speed of light, and therefore is aging slowly. Brother B is absolutely correct.

There is nothing to distinguish A from B at this point.

Theoratically, they CAN observe each other with a telescope. The information moving between the spaceship and earth is at the speed of light. No problem there.

When A experiences an acceleration or deacceleration to make a stop on earth, which is the exact same thing as gravity in relavity, A will experience time dilation. When A reaches earth, he will be younger than his twin brother B.

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Originally Posted by Lethalfang

When A experiences an acceleration or deacceleration to make a stop on earth, which is the exact same thing as gravity in relavity, A will experience time dilation.

Agreed. The relative velocity on its own can't make the age difference.

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Theoratically' date=' they CAN observe each other with a telescope. The information moving between the spaceship and earth is at the speed of light. No problem there.[/quote']

 

But that is a different measurement. To specify a measurement you have to specify what you are measuring and which frame you are measuring from. The twin paradox is supposed to demonstrate that you can have an age difference even when measuring both twins' age in the same frame.

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Agreed. The relative velocity on its own[/i'] can't make the age difference.

 

Yes it can. According to brother B, it is only the relative velocity that causes A to age less.

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