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

#### JesseM

OK JesseM, then there's a paradox, because in SR each twin is supposed to observe that the clock of the other twin, who is in motion relative to the first twin's rest frame, is ticking slower.
No, in SR the normal time dilation rule only applies in inertial frames. Both twins accelerate to turn around at the midpoint of the journey, so neither remains in a single inertial frame. If you analyze the problem from start to finish in an inertial frame--any inertial frame, not necessarily one where their speeds were symmetrical--you'll always get the same conclusion, that they will have aged the same amount when they reunite.

#### Fredrik

Staff Emeritus
Gold Member
OK JesseM, then there's a paradox, because in SR each twin is supposed to observe that the clock of the other twin, who is in motion relative to the first twin's rest frame, is ticking slower.
If you check out the links in post #7 and make an effort to understand those resolutions of the twin paradox, you won't have any problems with scenarios such as the ones you describe.

There was nothing wrong with the first scenario other than that we would have to ignore the effects of gravity and that it would take millions of years to separate the twins to begin with, and then millions of years of synchronize all the clocks. They'd be really old twins. There's no paradox in that scenario either. When you understand simultaneity in SR, you'll understand why.

#### RandallB

OK RandallB, but I think you are dismissing my alternative "paradox" based on technicalities (fair enough), which I shall try to remedy in this updated version:
It is not a technicality, it is a requirement that you analyze SR issues from one and only one frame at a time.
You just have not learned to spot when you are not holding to that rule.
Many have a problem with that for a long time before they get it.

You do not need to worry about the accelerations – in SR just focus on the frames. (save acceleration and gravity for when you get to GR).
Let’s take a closer look at your new problem.
Twins 1 and 2 begin their journey located together, and synchronize their clocks. Each twin's ship quickly accelerates away from each other to a speed of .8c (relative to their common starting rest frame) and then travel apart a distance of 25 LY each at that constant identical speed. Then they decelerate identically (all pre-arranged), stop, and immediately reaccelerate identically toward each other quickly to a constant speed of .8c at which they continue at until they pass by each other (10 meters apart).

When they pass by each other on the return trip and look in each other's window:

(1) Will the other twin's clock show (approximately, say within 1 second) the same time as theirs? They pass by each other only 10 meters apart, so the light travel time from ship to ship is insignificant.

(2) Will they observe each other to have aged by about the same amount? Or will each twin observe the other twin to have aged about 50 or 100 years less?
You have Three frames of reference:
Base: Defined with a start point and two points 25 LY away as measured in the Base Frame.

Frame A: Twin 1 uses to depart on Twin 2 uses to return in.

Frame B: Twin 2 uses to depart on Twin 1 uses to return in.​

Sure the twins see each other’s clocks as running even slower than the base clock during both the outbound and inbound trips. But they were both in two different frames.
And both traveled 25LY in both frame A & B.
From the view of ANY observer remaining in ANY one frame there had the same experience, just in different orders! Which one had had slow time first and faster time second?
Depends on your POV, but no matter what reference frame POV you use (for the entire round trip) after the math is done the Twins (in this example) will have the same time and Little brother back at Base Frame Start will likely now be the older brother.

Remember: You cannot use a POV from just Twin 1; unless it is from only one of the two frames A or B which means Twin 1 must use the POV of that one frame to figure the time traveled during the other hallf of the trip.

Hope you are doing the math on these – it will help you understand why it is so important to work though the whole problem in each of the three frames. See what happens here when you send one Twin out at 0.5c to turn around at 15.625 LY to meet back with the other Twin at the Start point.

A

#### Al68

Hello Al68.

Quote:-

--- Surely you wouldn't suggest that the ship's voyage is non-inertial just because its coordinate velocity relative to earth changed. ----

I think the suggestion is that the ship's voyage is non inertial because it underwent acceleration.

There is nothing profound about the twin paradox it is just a consequence of the axioms of SR.

The OP asked how we would know which twin accelerated without him/her measuring or feeling any acceleration. Under these circumstances the only way of knowing is by looking at the end result.

Matheinste
Well, there is certainly nothing profound about the aspect of the twin paradox that is normally addressed.

And, it seems like your last statement is basically saying that we can determine which frame is inertial by observing which frame has the greatest elapsed proper time, and we know which frame has the greatest elapsed proper time because it will be the inertial frame.

True enough, but not really an answer to the OP's question. But we could determine which frame is non-inertial without measuring proper acceleration, and without looking at the end result. Just determine which twin changed velocity relative not only to the other twin, but also relative to the other masses in the universe.

Even in Newtonian physics, if you have to conjure up fictional forces to explain the relative motions of every other mass in sight, then you must be in an accelerated frame.

In the paper I referenced earlier, http://hem.bredband.net/b153434/Works/Einstein.htm [Broken] , Einstein suggests that it is the presence of these distant masses that causes inertia to exist in the first place, since otherwise you could never explain local effects such as the bulging equator in his example, or why Dish Network's satellite doesn't fall to earth, since it's stationary relative to earth's surface, along with many other things that just can't be explained as a closed system, separate from the rest of the universe.

I know many people think that physics only needs to describe such things, not explain them, but the OP asked for a reason why, not just for a simple description of what happens.

Al

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#### matheinste

Hello Al68.

I think i will have to leave this thread because i have obviously not understood the OP's question or incorrectly thought the question had been answered.

Matheinste.

#### Confusedent

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 travelled 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).

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#### 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

Gold Member
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).

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