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

[Confusedent]

I'm sure this question has been asked thousands of times before, but I can't see how nature determines which twin accelerates (or is subject to a gravitational field) and which one doesn't. People say one twin will feel the acceleration and the other won't, but suppose neither twin had an accelerometer present (internal or otherwise). All they can tell is that the separation between twins was increasing at a constant rate, and then changes at the moment of the acceleration. The twin in a spaceship sees the Earth moving away and then turn around, while the twin on Earth sees the spaceship moving away and then turn around.

If we use the gravitational time dilation explanation, it would seem to still be completely arbitrary who we treat as being in an inertial frame, and the gravitational field would seem to each observer to simply be acting on the opposite observer with an opposite direction.

I feel I understand everything else about what's going on here with SR, except that this seems completely arbitrary, and even scarier, each one actually should be younger than the other one because each one has seen the other one switch frames (which is truly impossible). If someone can explain this it'll seriously help alleviate my headache, and probably save me days of worrying about it.

 

[matheinste]

Hello confusedent.

In the unlikely situation that the traveling twin cannot detect acceleration by any means, if he knows his special relativity, he can conclude that because he is younger than his twin when they meet again, then it is he, the traveller, who has undergone the acceleration.

Matheinste.

 

[robphy]

I'm sure this question has been asked thousands of times before, but I can't see how nature determines which twin accelerates (or is subject to a gravitational field) and which one doesn't. People say one twin will feel the acceleration and the other won't, but suppose neither twin had an accelerometer present (internal or otherwise). All they can tell is that the separation between twins was increasing at a constant rate, and then changes at the moment of the acceleration. The twin in a spaceship sees the Earth moving away and then turn around, while the twin on Earth sees the spaceship moving away and then turn around.

Since we are dealing with special relativity (a flat spacetime), it is probably best to not consider any "gravitational fields" (which is associated with spacetime curvature).

I don't think it's best to think that it is "nature [that] determines which twin accelerates".
Rather, it is that nature (via the Einstein Field Equations, presumably) determines which spacetime paths are inertial and which are not. It is the "traveling twin" (by some mechanism whether he is aware of it or not) that has chosen a non-inertial path between two events.

By the way, a simple accelerometer that can be used in the experiment is simply an object on a frictionless table. If you wish to deny that apparatus to the traveller, I think it should be possible to distinguish the two twins by the results of radar experiments. The spacetime maps that each makes from radar experiments will differ.

 

[Mentz114]

I'm sure this question has been asked thousands of times before, but I can't see how nature determines which twin accelerates (or is subject to a gravitational field) and which one doesn't.

Nature doesn't determine it - the twins do. This is very hard to understand - what do you mean ? If my twin and I decide to travel by different routes from A to B what's to determine ? I go on the motorbkie and my twin walks. When we meet my clock shows slightly less elapsed time that my twins. What's scary about that ?

 

[Dale]

Hi Confusedent, welcome to PF,

Expanding on robphy's point, here is an arXiv paper I really liked called http://arxiv.org/abs/gr-qc/0104077v2" . Note in particular figures 8 and 9 which show the situation in the traveling twin's frame. Also note the metrics on page 7 and 8

The key point to remember is that the acceleration does not cause time dilation, it only serves to indicate an asymmetry of the two reference frames. While an accelerometer reading is one such asymmetry it is not the only asymmetry. Another is the difference in radar experiments, or the differece in Doppler shifts. However, at a fundamental level, if you do not have enough information to calculate the metric along each worldline then you do not have enough information to calculate the relative aging.

 

[Confusedent]

Thanks for the help all. I'm still pondering these answers...

-Matheinste: Sorry but that kind of seems like circular logic. It says that nature favors one observer as having "really" accelerated, while treating the other as having been inertial, when it could have just as easily treated them oppositely.

-robphy: I kind of see what you're saying about spacetime paths, but I don't see why one path needs to be considered inertial and the other non-inertial. Wouldn't each observer, from their point of view, see their own spacetime path as being the inertial one? Or am I misunderstanding how spacetime geometry works?

I tried to get past using feelings of acceleration since that just goes back to the idea of making one observers reality seem more real than the others. Plus, if the twins were particles without charge they shouldn't feel anything, each would think itself in an inertial frame.

 

[Fredrik]

People say one twin will feel the acceleration and the other won't, but suppose neither twin had an accelerometer present (internal or otherwise).

Do you think that SR predicts a different result in that case? That would be like walking off a cliff and expecting not to fall if you don't look down

I feel I understand everything else about what's going on here with SR, except that this seems completely arbitrary, and even scarier, each one actually should be younger than the other one because each one has seen the other one switch frames (which is truly impossible). If someone can explain this it'll seriously help alleviate my headache, and probably save me days of worrying about it.

My standard answer: "Check out #3 and #142 (page 9) in this thread."

 

[Confusedent]

The key point to remember is that the acceleration does not cause time dilation, it only serves to indicate an asymmetry of the two reference frames. While an accelerometer reading is one such asymmetry it is not the only asymmetry. Another is the difference in radar experiments, or the differece in Doppler shifts.

But it is the acceleration that causes the asymmetry, and it should be indistinguishable who accelerated, so I still don't get why each twin doesn't return being younger than the other (besides that it is impossible).

Is it just that while there is no absolute rest with respect to velocity, there is an absolute rest with respect to acceleration (an absolute reference frame in at which everything else's acceleration is judged against)? Even though we could pick a different frame and treat the absolute frame as undergoing acceleration, nature would somehow know the difference?

I do appreciate your guys help in this, and apologize if I sound like a broken record parroting the same question.

 

[Mentz114]

Sorry but that kind of seems like circular logic. It says that nature favors one observer as having "really" accelerated, while treating the other as having been inertial, when it could have just as easily treated them oppositely.

Nature doesn't have your problem with symmetry. The situation is not symmetrical.

One observer 'really' did accelerate !

 

[Confusedent]

Nature doesn't have your problem with symmetry. The situation is not symmetrical.

One observer 'really' did accelerate !

However, at a fundamental level, if you do not have enough information to calculate the metric along each worldline then you do not have enough information to calculate the relative aging.

Does this mean that if we aren't told which one accelerated we can't determine which one is will be younger when they meet? For example, if the situation was stated that the distance between them was increasing at 0.8c, and then after the turn around the distance is decreasing by 0.8c, we would still determine that one will be younger than the other (since there was an acceleration) but we couldn't know which one (since the problem didn't specify)? As the first response said, only when they got back together could they determine that the younger one must have been the one to accelerate.

Assuming that's correct, I think I'm starting to get this now...

 

[Mentz114]

Yes, you are getting it. The 'twin' effect has been confirmed experimentally by flying accurate clocks around the globe. Have a look at this sticky thread.

https://www.physicsforums.com/showthread.php?t=229034

 

[Fredrik]

But it is the acceleration that causes the asymmetry, and it should be indistinguishable who accelerated, so I still don't get why each twin doesn't return being younger than the other (besides that it is impossible).

You may have overlooked the fact that this can't be explained just by logical arguments. SR is a theory of physics. It consists of a mathematical model (Minkowski space) and a set of postulates that identify things we can measure with things in the model. The point is that there must be some way to interpret mathematical statements as predictions about the results of experiments, and it's impossible to derive an interpretation. It must be postulated.

The relevant postulate in this case is that what a clock measures is the proper time of the curve in spacetime that represents its motion. The curves that minimize the proper time (i.e. the time measured) are called timelike geodesics. They represent inertial motion. That can be considered a postulate too. (It may be optional in the sense that we can choose to postulate something else instead and derive this thing from that).

We can imagine "n-tuplets" instead of twins, and let n go to infinity. Have them move on all the different paths from start to finish. The one that's the youngest when they meet again is by definition the one who did inertial motion.

Is it just that while there is no absolute rest with respect to velocity, there is an absolute rest with respect to acceleration (an absolute reference frame in at which everything else's acceleration is judged against)?

Not a "frame", but there's a set of curves (the timelike geodesics) with a special significance. (They represent inertial motion).

Even though we could pick a different frame and treat the absolute frame as undergoing acceleration, nature would somehow know the difference?

You can e.g. choose to use a coordinate system such that the time axis coincides with the accelerating twin's world line. His coordinate acceleration in such a frame is of course 0 since his position is 0 at all times, but that doesn't change the fact that he's going to be younger than his brother when they meet. Nature doesn't care about what coordinate systems we're using.

Also, the acceleration measured by an accelerometer is equal to the coordinate acceleration in a co-moving inertial frame. (It obviously can't be equal to the coordinate acceleration in an arbitrary frame). That's another postulate.

Does this mean that if we aren't told which one accelerated we can't determine which one is will be younger when they meet?

Yes.

 

[Dale]

But it is the acceleration that causes the asymmetry, and it should be indistinguishable who accelerated

This is a contradictory pair of statements. If X causes some physical asymmetry then X must be physically distinguishable, otherwise X would not be capable of breaking the symmetry.

For example, if the situation was stated that the distance between them was increasing at 0.8c, and then after the turn around the distance is decreasing by 0.8c, we would still determine that one will be younger than the other (since there was an acceleration) but we couldn't know which one (since the problem didn't specify)?

Essentially, yes.

 

[Al68]

But it is the acceleration that causes the asymmetry, and it should be indistinguishable who accelerated, so I still don't get why each twin doesn't return being younger than the other (besides that it is impossible).

Is it just that while there is no absolute rest with respect to velocity, there is an absolute rest with respect to acceleration (an absolute reference frame in at which everything else's acceleration is judged against)? Even though we could pick a different frame and treat the absolute frame as undergoing acceleration, nature would somehow know the difference?

I do appreciate your guys help in this, and apologize if I sound like a broken record parroting the same question.

Hi Cunfusedent,

The issue of why must we treat the inertial frame as a "preferred" frame is not addressed in the standard resolutions. As you have seen, they presuppose their conclusion (that the inertial frame is "special") and show the math, which is good, but that doesn't answer your question.

One thing I would point out is that while relative velocity is not absolute, and therefore its derivative, coordinate acceleration cannot be absolute, proper acceleration is absolute in the sense that when a ship accelerates due to a force acting on it, its acceleration (and change in velocity) is relative to every other massive body in the universe, not just the other twin. These distant masses, and their relationship to (local) inertia, was discussed by Einstein, Mach, and others.

I would recommend searching the net for Einstein's writings. His way of thinking about these things is very different from anything I've read on the subject by others. And he takes the issue of why inertial frames are special seriously, instead of just accepting the fact and not worrying about why it's true. Einstein's writings may not satisfactorily answer your question, but you will find your point addressed and discussed.

You could even read Einstein's own Twins Paradox resolution, it's the only one I'm aware of that considers it from the point of view of an accelerated reference frame (in which the ship is at rest) during the turnaround. But while interesting, it still doesn't answer your question.

Also, Einstein claimed, in reference to one liquid sphere rotating relative to another, that the cause of the bulging equator on one sphere instead of the other, ie the "cause" of inertia itself, cannot be local, but must be due to distant masses. http://hem.bredband.net/b153434/Works/Einstein.htm

Al

 

[Confusedent]

This makes things considerably clearer. I guess its hard to accept the idea that you get different answers depending on who accelerated, when it doesn't work this way for velocity (e.g. if they're traveling apart at constant velocity, each sees the other aging slower). I need to study up more on Minkowski space and these geodesics too, the two SR books I've read didn't cover this.

Thanks again for the help everyone.

 

[RandallB]

This makes things considerably clearer. I guess its hard to accept the idea that you get different answers depending on who accelerated, when it doesn't work this way for velocity (e.g. if they're traveling apart at constant velocity, each sees the other aging slower). I need to study up more on Minkowski space and these geodesics too, the two SR books I've read didn't cover this.

But the issue in SR Twins is not, "relative to every other massive body in the universe".
Nor is it due “if they're traveling apart at constant velocity, each sees the other aging slower”
Because: when they're travelling toward each other at constant velocity, each still sees the other aging slower.

What you need to be clear on is how whoever changes reference frame [and they can always tell if the just set out a trackable buoy to float next to them in “stationay” inertial motion with them]. When you change direction you have to know your away motion (the frame the buoy stays in) is a different frame than your return frame motion; (if you still stationary wrt to the buoy you put out the only way you could see the other twin now coming toward you is they are now in a different frame of motion)

The thing that makes all the difference is what is the rate of time difference is, between the two frames used by the clock that changed frames. Inorder to figure the total time on that clock you must include when it runs MUCH slower in the other frames than the one you pick as a reference. Enough slower to more than make up for the slow time you see on the stay at home twin clock - that net total be slow comared to the stay at home twin clock - to match exactly how that clock POV saw both versions of your clock (outbound & inbound) run slow.

The point is not to mess up and use BOTH frames (outbound & inbound) as part one master reference ie. No “Time Line” of a clock accelerating into a second frame!
You must do all calculations and observations from just one Frame.
Although all frames will disagree about which clocks are going fast or slow – they all agree and give the same times when the two clocks are next to each other (at departure and return). Seeing that is just a matter of doing the SR math completely from each one of the three different frames point of view.

It is clear that all frames must be wrong because none can agree on which one has the correct rate of time. BUT since all can produce and agree on one net solution to such a twin problem – all must be defined as correct in some way when used as a sole reference point “as if preferred”.

The net result was to establish relativistic solutions that were to be applied only wrt a single reference frame – but any one reference frame is OK; which required assuming that the idea of a Newton Absolute Time & Absolute Space be abandoned.
That shows up in GR too, with what is called an indeterminate background – you will learn more about that when you read Smolin (Perimeter Institute).
But before you do that be sure to “do the SR math” yourself enough times from different frames to understand why “Aboslute” was rejected in SR & GR.

 

[matheinste]

Hello Confusedent

Quote from Al68:-

----You could even read Einstein's own Twins Paradox resolution, it's the only one I'm aware of that considers it from the point of view of an accelerated reference frame (in which the ship is at rest) during the turnaround. But while interesting, it still doesn't answer your question.-----

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As RandallB says so well, it does not matter whose point of view or (single) frame you do the calculation in, they will all, of necessity, give the same END result.

Matheinste.

 

[nutgeb]

Here's a variation on the twins paradox:

Each twin travels in her own spaceship. The twins synchronize their clocks at the start. One twin starts on the far side of galaxy A, the other starts on the far side of Galaxy C. Each ship accelerates rapidly to .8c past its own starting galaxy, and the paths of the two ships are directly toward each other. By the time each ship actually passes the centerline of its own starting galaxy A or B, it has finished accelerating and thereafter continues on at constant speed for many years. Eventually, both ships simultaneously pass Galaxy B traveling in opposite directions. Galaxy B is located exactly at the midpoint between Galaxies A and C.

As each ship passes its starting Galaxy A or C, each twin communicates with residents of her starting galaxy and synchronizes her ship clock with the galaxy residents' local clock. The galaxy residents of Galaxies A, B and C all have synchronized their own clocks with each other just before then.

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?

During the voyage, the twins approach each other at a relative speed higher than .8c but less than c. They are in separate and distinct inertial frames after passing their starting galaxy.

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?

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

 

[Al68]

Hello Confusedent

Quote from Al68:-

----You could even read Einstein's own Twins Paradox resolution, it's the only one I'm aware of that considers it from the point of view of an accelerated reference frame (in which the ship is at rest) during the turnaround. But while interesting, it still doesn't answer your question.-----

------------------------------------------------------------------------------------

As RandallB says so well, it does not matter whose point of view or (single) frame you do the calculation in, they will all, of necessity, give the same END result.

Matheinste.

Yes, Einstein's resolution does give the same result as the standard resolutions. But the end result is not the only thing that matters. The OP was not asking what the end result is, presumably he knew that already.

Al

 

[Al68]

But the issue in SR Twins is not, "relative to every other massive body in the universe".

Well, this issue relates to the "cause" of inertia itself that leads to accelerated bodies being distinguishable from inertial ones. Which is relevant if you care about the more profound aspect of the Twins case, instead of just how to get the end result. Surely you wouldn't suggest that the ship's voyage is non-inertial just because its coordinate velocity relative to Earth changed.

And the OP was not asking how to just get the right answer. He was asking how we determine which twin to consider inertial. Most of the responses explained how to solve the problem after this determination is made.

Al

 

[RandallB]

Here's a variation on the twins paradox:

The twins synchronize their clocks at the start. One twin starts on the far side of galaxy A, the other starts on the far side of Galaxy C.

No they cannot. They must be next to each other and directly looking at each others clocks to know all agree that what time is on each clock. This cannot be done if the are apart from each other

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.

You stated that backwards, any observer will see all moving clocks as running slow.

However, because that obsever also sees each clock in a moving frame as not being correctly set; such that by reading the times on the clocks as they pass by thet are set out of sync in such a way that although each one is running slow - by only reading the time displayed only when the clocks pass by it will seem to show time there running faster than the observers clock. Just remember, is from reading many diffent clocks passing by as if showing a movie of many snapshots of time.

In SR no paradox at all, just the realization that each frame can think of itself as "correct and prefered"; but no one of them can prove they are abosolutly preferred to any other frame.

 

[matheinste]

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

 

[nutgeb]

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:

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?

 

[JesseM]

(1) Will the other twin's clock show (approximately, say within 1 second) the same time as theirs?

Yes.

(2) Will they observe each other to have aged by about the same amount?

Yes.

 

[nutgeb]

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.

 

[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]

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.

 

[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 , 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

 

[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]

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).