Time Dilation in General Relativity: Twins Paradox Explained

[Niramas]

I have always been confused about time dilation in General Relativity.

In the twins paradox, it is the traveling twin that ages slower. However, could you not just as easily say that it is the non-traveling twin that is moving away from the other?

So why is it the traveling twin and not the non-traveling twin that experiences the slowing of time relative to the other.

One difference I can see between the two is that the traveling twin accelerated away from non-traveler. However, the time dilation continues even after the acceleration ceases (i.e. based on velocity, not acceleration).

Another difference would have to do with velocity through an absolute space, but I thought that did not exist.

Please forgive my ignorance, but clearly I am missing something fundamental here. Can anyone enlighten me?

 

[Niramas]

This may be a Special Relativity issue... if so sorry!

 

[ghwellsjr]

I have always been confused about time dilation in General Relativity.

In the twins paradox, it is the traveling twin that ages slower. However, could you not just as easily say that it is the non-traveling twin that is moving away from the other?

Yes, you can say that, at least until the traveling twin turns around.

So why is it the traveling twin and not the non-traveling twin that experiences the slowing of time relative to the other.

Time Dilation is a coordinate effect so whatever coordinate system you use determines the speed of each twin and thus the Time Dilation of each twin.

One difference I can see between the two is that the traveling twin accelerated away from non-traveler. However, the time dilation continues even after the acceleration ceases (i.e. based on velocity, not acceleration).

That is a difference but it is insignificant because as you say Time Dilation is based on velocity, actually speed.

Another difference would have to do with velocity through an absolute space, but I thought that did not exist.

Please forgive my ignorance, but clearly I am missing something fundamental here. Can anyone enlighten me?

What you have missed is that the traveling twin has to fire his rockets to get back to the non-traveling twin so that means you can use a coordinate system based on the rest frame of the non-traveling twin, who will experience no Time Dilation, while the traveling twin will experience Time Dilation for the whole trip.

If on the other hand you want to consider a coordinate system where the traveling twin is at rest after he accelerates away, then the "non-traveling" twin will be the only one that experiences Time Dilation for a while. But then the "traveling" twin has to fire his rockets even more than he did at first in order to be able to get back to the first twin and that will produce a greater Time Dilation for him so that when he reaches the first twin, he ends up with less accumulated time than the first twin had during the trip.

Does that make sense?

 

[pervect]

I have always been confused about time dilation in General Relativity.

In the twins paradox, it is the traveling twin that ages slower. However, could you not just as easily say that it is the non-traveling twin that is moving away from the other?

You can

So why is it the traveling twin and not the non-traveling twin that experiences the slowing of time relative to the other.

If you analyze the problem carefully, you'll see that it depends on how the twins reunite. If you have two twins A and B moving away from each other in the flat space-time of special relatiavity they will never reunite. But if A turns around by accelerating to rejoin B, then when they rejoin B's clock will have the most elapsed time, similarly if B turns around by accelerating to rejoin A, then A's clock will have the most elapsed time.

The fundamental principle here is that a non-accelerating observer maximizes (or more accurately extremizes) his proper time.

One difference I can see between the two is that the traveling twin accelerated away from non-traveler. However, the time dilation continues even after the acceleration ceases (i.e. based on velocity, not acceleration).

Another difference would have to do with velocity through an absolute space, but I thought that did not exist.

Please forgive my ignorance, but clearly I am missing something fundamental here. Can anyone enlighten me?

What you are most likely missing is the relativity of simultaneity. See any of the numerous threads on "Einstein's train paradox" for a more complete description of the issue. The short version is that when A and B compare clocks, they need a notion of simultaneity in order to do it. They need to be able to answer "What distant event is simultaneous with the local event that happens now".

And simultaneity is not independent of the observer in special relativity, thus A and B have _different_notions of simultaneity. THis explains how A's clock can be slow in B's coordinate system, and B's clock can be slow in A's coordinate system - the two coordinate systems have different notions of what "at the same time" means.

 

[Niramas]

First thank you for taking the time to answer.

ghwellsjr:

"What you have missed is that the traveling twin has to fire his rockets to get back to the non-traveling twin so that means you can use a coordinate system based on the rest frame of the non-traveling twin, who will experience no Time Dilation, while the traveling twin will experience Time Dilation for the whole trip."

I still don't see the why based on whatever frame I use.

I think I need a more fundamental explanation.


pervect:

"The fundamental principle here is that a non-accelerating observer maximizes (or more accurately extremizes) his proper time."

So you are saying the acceleration does have something to do with it?

"What you are most likely missing is the relativity of simultaneity..."

But if say the clock is at the non-traveling observer, it seems to me that the traveler frame of reference will come back in sync with the non-travelers as he returns and he will not have aged any differently at all. That cannot be right can it?

THis explains how A's clock can be slow in B's coordinate system, and B's clock can be slow in A's coordinate system - the two coordinate systems have different notions of what "at the same time" means.

Are you saying that both A & B are aging slower relative to each other?

When I think of this in terms of the speed of light is constant for all observers, it seems to me that both observers would experience slower-time relative to the other. But then it would seem that the twins would be the same age when they meet again.

 

[Jonathan Scott]

At a very simplified level, changing velocity in space-time is like turning a corner in space and instantly changes the definition of what other things are "level" with you in the direction you are travelling.

So when you are walking along, someone who is walking at the same speed but in some other direction is always going slower in your direction than you are, but the same applies from their point of view as well. But if you change direction and turn towards where someone else is going, they are suddenly further ahead in that direction.