# Simultaneous birth of two people in an inertial frame

1. Apr 11, 2015

### samirgaliz

Suppose two people separated by some distance, were simultaneously born in an inertial frame that is moving at some velocity with respect to a stationary frame.
For an observer in the stationary frame the two events are not simultaneous. The stationary observer will see one person is born before the other as they are separated by distance in the moving frame.

What would happen when the moving frame decelerates and comes to rest? Do they have different ages? It seems there is a paradox that i can not resolve!

2. Apr 11, 2015

### FactChecker

Do you mean different ages in the frame that decelerated or in the "stationary" frame? (The "stationary" frame being the one that did not decelerate). I believe that the decelerating frame would still think they are the same age. Remember that the stationary frame would observe the deceleration rate of the two twins to be different.

3. Apr 12, 2015

### samirgaliz

I meant in the stationary frame. My problem is that the decelerating frame once it stops becomes identical to the the stationary frame. Say, the moving frame was a spaceship that landed back in the stationary frame.

Last edited: Apr 12, 2015
4. Apr 12, 2015

### Orodruin

Staff Emeritus
What do you even mean by decelerating frame? If it is an inertial frame it does not decelerate. If it is not you need to be more specific. Also you cannot refer to a frame as the stationary frame. Observers can be stationary in a frame, but frames are not stationary. There is no such thing as absolute rest, not even in classical mechanics.

5. Apr 12, 2015

### samirgaliz

The inertial frame was initially moving at a constant velocity and then decelerated and came to rest. The other stationary frame was already at rest relative to the moving one. So both at the end are at rest with respect to each other.
Thanks.

6. Apr 12, 2015

### Ibix

You might like to read the thread on clocks in Bell's spaceships, since it covers this topic.

The short answer is that the age of each child is the interval along its worldline. In this case, that will depend on the specifics of the acceleration profiles used. If the two children are in one spaceship, but at different places, then their acceleration profiles will be different as the spaceship changes length as seen from any inertial frame. If they are in separate spaceships they can decelerate at different rates at different times, and the results entirely depend on how they choose to do that.

Part of your confusion, I suspect, stems from the idea that one frame changes to be like the other. Don't think like that. A frame is just a set of coordinates that it is convenient for people at rest in that frame, and when the children decelerate they simply pick a different set of coordinates. That perhaps makes it clearer that what happens depends on how each child chooses to change speed. It's a matter of their personal choices, not some global change of frame.

7. Apr 12, 2015

### samirgaliz

Thanks Ibix I will check the thread. But do the twin have the same age once they come to rest or different?

Last edited: Apr 12, 2015
8. Apr 12, 2015

### Orodruin

Staff Emeritus
If it decelerated it is not an inertial frame. Being at rest is also not something definite but only defined relative to something else.
As already state: This depends on the world lines of the twins. You need to specify how they move. You simply cannot say that their inertial system "comes to rest" as this makes no sense (inertial systems do not accelerate). You need to specify the deceleration of the twins.

9. Apr 12, 2015

### stevendaryl

Staff Emeritus
You have to give more information about how the twins decelerate. What the Lorentz transformations tell us is that if two events are simultaneous in the traveling frame, then in the stationary frame, the event at the front takes place later than the event at the rear.

So if according to the traveling frame, the two twins are born at the same moment, and decelerate at the same moment, then according to the stationary frame, the front twin is born later (making him younger than the rear twin) and the front twin decelerates later. So the front twin will be younger when they come to rest.

10. Apr 12, 2015

### samirgaliz

Thanks stevendaryl, that makes sense. I guess I missed the fact that the front twin decelerates later.
So my other question is whether at the moment of deceleration, the twins do age differently in the moving frame?

11. Apr 12, 2015

### FactChecker

There will be disagreement. Remember that the observers in the stationary frame did not agree that the two were born simultaneously. So when the frames reach identical speeds, people who were in different frames will still disagree about their ages.

12. Apr 12, 2015

### samirgaliz

Thanks FactChecker.
Do the twins within the decelerating frame, disagree as well about their ages?

13. Apr 12, 2015

### Ibix

The answer is "it depends on the way you do the deceleration". There is no universal answer to this question.

It is true that the twins will agree about their age before the acceleration phase. It is also true that they will agree about their age difference after the acceleration and that difference will not change if they do not accelerate again. However, the difference in age (which might be zero, but might not be) depends on how they decelerate. You will need to specify the deceleration rates of the twins, and the times and places that they start decelerating.

14. Apr 12, 2015

### FactChecker

I think we can assume the simplest case where the positions of the twins in the decelerating frame is constant wrt that frame. That is, there is no relative velocity between the two twins in the decelerating frame. In that frame, the two remain the same age throughout. When the decelerating frame reaches the same velocity as the "stationary" frame, the two men still believe that they were born at the same time and are the same age. To observers in the "stationary" frame, the two were born at different times and are different ages. Since the frames are now at the same velocity, there is no disagreement about simultaneous events now, but there was disagreement when the two were born. So the observers in the "stationary" frame still say that the two were born at different times.

Last edited: Apr 12, 2015
15. Apr 12, 2015

### Ibix

The problem with this is that you need to define the simultaneity convention you are using in your decelerating frame. There's only one that isn't obviously contrived for inertial observers, but there are multiple options for non-inertial observers. Depending on what you pick, the world line associated with "no relative velocity between the twins" will be different, and the age difference after the acceleration will be different.

This must be wrong. If the twins finish up at rest with respect to me and the twins say they are the same age then so must I. Otherwise I could stand next to one of the twins and look at the other one, and the twin I'm standing next to would be seeing the other one as the same age as him, while I see him as a different age. That's contradictory.

16. Apr 12, 2015

### samirgaliz

Thanks to everyone and yes FactChecker, the assumption is that the distance between them remains constant wrt the decelerating frame. Sorry for not making it clear!
Does the rear twin looks physically older than the front one when both frames reach the same speed?

17. Apr 12, 2015

### samirgaliz

That was my original reason for this question, this contradictory situation when both frames come to rest!

18. Apr 12, 2015

### FactChecker

Assume that there is no rotation of the decelerating coordinate system. Pick one of the "twins". He is fixed in a decelerating coordinate system where time and distance are changing (to an outside observer in the "stationary" coordinate system) as his coordinate system decelerates. There is one coordinate that the other twin was at before the deceleration began. If that twin remains at those coordinates in the decelerating coordinate system, then by definition he is not moving wrt the decelerating coordinate system. Neither twin is moving in that coordinate system and their separation distance remains constant. Those positions and that coordinate system are uniquely defined throughout the deceleration.

19. Apr 12, 2015

### FactChecker

Not really. The decelerating twins think that they were born simultaneously and remained the same age. An observer in the stationary frame says that one twin was born before the other, but he observes that the twins decelerate at different rates and their decelerating clocks drifted versus each other. So he believes that the twins aged differently. So even though one twin is older by the stationary time, he understands why their deceleration brought them to the same age in the decelerating times.

20. Apr 12, 2015

### Staff: Mentor

Not according to the description you gave. At least, not if I'm understanding it correctly.

As I understand it, here is what happens: both twins are born simultaneously according to the "moving" frame (they are initially both at rest in this frame, but it's moving relative to the frame in which they will both end up at rest). They both start decelerating simultaneously in the moving frame. They decelerate in such a way as to maintain constant spatial separation as seen by them; this means that the twin in the "rear" (where "front" is the direction in which the force that decelerates them is exerted) must decelerate harder (i.e., he feels a greater force). Finally, both twins stop decelerating simultaneously according to their momentarily comoving frame, which is also the "rest" frame.

If the above is correct, then the twin that is in the "rear" of the two will age less during the deceleration, so the two will not be the same age once the deceleration stops; the "rear" twin will be younger than the "front" twin.

21. Apr 12, 2015

### FactChecker

I stand corrected. I think you are right. To clear up one question from the OP, a stationary observer would see those changes happening and understand why. They would just measure it differently. One says they were born simultaneously and the other says not so. They agree on the final result, only for different reasons.

22. Apr 12, 2015

### samirgaliz

Why does the rear twin experience more deceleration than the front one? What if both were seat belted to chairs at a constant distance, then they both experience the same deceleration!

23. Apr 12, 2015

### Staff: Mentor

"Constant distance" is trickier than it sounds when relativistic effects matter. A "constant distance" between two things means that if you find the location of one thing, then find the location of the other thing at the same time, the distance between those two location will always be the same.

However, the bolded text above points to the problem: because of the relativity of simultaneity, "at the same time" in one frame is not "at the same time" in another, and therefore the notion of "constant distance" is frame-dependent. If your two twins remain at a constant distance in one frame, they won't remain at a constant distance in other frames.

Google for "Born rigid motion". Also be sure that you understand Bell's spaceship paradox; it's not exactly the situation we're describing here, but knowing how to resolve Bell's paradox is essential to working out this problem as well.

Last edited: Apr 13, 2015
24. Apr 12, 2015

### samirgaliz

Thanks Nugatory. My question is that in the moving decelerating frame where both twins are at a constant distance, why does the rear one experience more deceleration than the front one. I understand that their distance is not constant as seen by an observer in an inertial frame. I will check Bell's paradox.

25. Apr 15, 2015

### Alan McIntire

The moving frame would appear SHORTER to us than when it is stationary with respect to us in the stationary frame. To be stationary with respect to us, the moving fram will have to decelerate. As it does so, the frame will appear to lengthen. The twin in the rear of the decelerating frame will decelerate LESS than the twin in the front, so will age more. When the frame comes to rest with respect to us, the distance between the twins will have lengthened, and the front twin age less.

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