Twin paradox: telling who accelerates (why isn't it arbitrary?)

[Confusedent]

I'm going to test my understanding by taking a crack at this one... plus I'd already been thinking about this situation some...

When the twins pass very close by each other (say, within 10 meters) at Galaxy B they can communicate with each other and see into the other ship's window. Will they agree that their ship clocks are synchronized with each other then?

Special Relativity says that an observer in any inertial frame will measure her own clock ticking slower than a clock in an inertial frame which is in motion relative to the observer's rest frame (at relativistic speed). So is there a paradox when the ships pass by each other and each twin can look in the window of the other ship and observe that the other twin has not aged differently than herself?

Yes, they are the same age, and its not inconsistent because of relative simultaneity. Events happening simultaneously for observers in the galaxies reference frame will happen non-simultaneously and in opposite orders for the two observers (since the Lorentz transformation between two events depends on v and not v^2, the sign reverses the order of t1 and t2). So a greater amount of time can pass for one observer between one event and when they meet than for the other and the same event, allowing for each to determine that the other is the slower aging one. For example, observers in the reference frame of the galaxies would determine that each traveller was born (or passed their starting galaxy) at the same time, while each traveller in their reference frame would determine the other had "started" at an earlier time, in order to have aged at a slower rate and been the same age when meeting. I believe this makes sense because each traveller, seeing themselves as stationary, would determine the other traveller to be the one suffering from relativistic addition of velocities relative to the galaxies (each sees the galaxies as moving at .8c, while seeing the other observer moving at some .8c < v < c), hence each sees the other observer as "losing" some speed relative to the galaxies (moving slower relative to them than himself). If one observer sees the other as having traveled the same distance, but having taken longer to do it, then he must judge that the other observer moved slower relative to the galaxies than he did (since in that reference frame he started earlier).

I hope that was atleast halfway correct and somewhat readable.

During the inertial (constant speed) phase of the trip did both twins age less than the residents of the 3 relatively "stationary" galaxies?

I'm going to say no, because again each sees themselves as the stationary one, so each sees the others as aging slower. They cannot meet and determine that each is actually younger, so on meeting at Galaxy B all will determine they are the same age, but will disagree about who passed their starting galaxy first. The reasoning was all explained in the last paragraph.

 

[Confusedent]

Incidentally, yes I was mainly asking the more fundamental question of what's different about the accelerating observer when the situation appears the same to both. In more detail, supposing the twins were just two particles without internal structure and they were the only objects in their universe, it would be indistinguishable which one had accelerated, and each would seem to determine the other had accelerated while they had not.

The answers seemed to be (if I remember correctly):
1) One actually would have accelerated, and the end result would determine who it had actually been
2) Certain spacetime paths (geodesics) are just special in that they are inertial, or another way of saying that accelerations are not relative in the same way velocity is. [Edited this to make it more accurate]
3) Just because the situation appears the same to each observer doesn't mean that it is.
4) SR says that no experiment can distinguish between two inertial frames, but experiments can distinguish between inertial and accelerating frames. So while the situation is mirrored for observers in inertial frames (from their own points of view), it isn't between different non-inertial frames.

I wasn't questioning whether the effect actually occurred, just asking how since it seems logically that each would return being younger than the other (since each determines the other was the one who accelerated).

 

[matheinste]

Hello confusedent

Quote:-

---In more detail, supposing the twins were just two particles without internal structure and they were the only objects in their universe, it would be indistinguishable which one had accelerated, and each would seem to determine the other had accelerated while they had not.----

Don't forget that in SR for a particle to accelerate an applied force is required. This will distinguish them. The one which had a force applied to it will be the one that underwent acceleration.

Matheinste.

 

[Mentz114]

Incidentally, yes I was mainly asking the more fundamental question of what's different about the accelerating observer when the situation appears the same to both. In more detail, supposing the twins were just two particles without internal structure and they were the only objects in their universe, it would be indistinguishable which one had accelerated, and each would seem to determine the other had accelerated while they had not.

The answers seemed to be (if I remember correctly):
1) One actually would have accelerated, and the end result would determine who it had actually been
2) Certain spacetime paths (geodesics) are just special in that they are inertial, or another way of saying that accelerations are not relative in the same way velocity is. [Edited this to make it more accurate]
3) Just because the situation appears the same to each observer doesn't mean that it is.
4) SR says that no experiment can distinguish between two inertial frames, but experiments can distinguish between inertial and accelerating frames. So while the situation is mirrored for observers in inertial frames (from their own points of view), it isn't between different non-inertial frames.

I wasn't questioning whether the effect actually occurred, just asking how since it seems logically that each would return being younger than the other (since each determines the other was the one who accelerated).

Yes, I wouldn't argue with that. Especially point 4).