Understanding the Twin Paradox: A Quick Question Answered

[analyst5]

Hey guys, I just want to ask a quick question that confuses me a bit regarding the twin paradox. During acceleration, the moving twin very quickly 'runs over' across a large segment of the worldtube of the stationary twin. But, what is the perspective of the stationary twin during the acceleration of the moving twin (or during its change of frames). Does the stationary twin also run over across the part of the worldtube of the moving twin that is accelerating?

Sorry if my English is bad, I hope you understand the meaning behind this.
Cheers.

 

[mfb]

What is a "worldtube"?

During acceleration, the calculated time for the non-accelerating twin is changing quickly for the accelerating twin if this acceleration happens far away from earth. It does not happen in the other direction. This is not relevant for observations, however.
If you walk towards the Andromeda galaxy, the definition of "now" for events there changes by 1 day for you relative to someone standing on the ground next to you. You still see the same stars in the same way.

 

[analyst5]

What is a "worldtube"?

During acceleration, the calculated time for the non-accelerating twin is changing quickly for the accelerating twin if this acceleration happens far away from earth. It does not happen in the other direction. This is not relevant for observations, however.
If you walk towards the Andromeda galaxy, the definition of "now" for events there changes by 1 day for you relative to someone standing on the ground next to you. You still see the same stars in the same way.

So what happens from the perspective of the Earth twin? I mean how come the time isn't changing quickly from his perspective when the acclerated twin undergoes acceleration? Does the calculated time on the accelerated observer change from his perspective?

 

[Ibix]

The situation is loosely comparable to changing timezones. The traveling twin is re-writing her definition of "now" as she accelerates. That has no more physical effect than me setting my watch to GMT+1.

 

[JesseM]

Hey guys, I just want to ask a quick question that confuses me a bit regarding the twin paradox. During acceleration, the moving twin very quickly 'runs over' across a large segment of the worldtube of the stationary twin.

Not in any objective physical sense, only if she uses a particular type of non-inertial coordinate system which has the property that its definition of simultaneity at any point on her worldline must agree with the definition of simultaneity used in the inertial frame where her instantaneous velocity is zero at that that point. She is quite free to use some different type of coordinate system which doesn't work this way.

 

[analyst5]

So what can be said for the definition of 'now' of the stationary, Earth observer? Regarding the events on the traveling twin's worldtube? If the moving twin is moving away from Earth at first, then the stationary twin must conclude that the now from his perspective consists of the past of the moving twin, relative to another observer who is at rest with the moving twin. Then after acceleration, on the way back, the Earth twin can conclude that his 'now' consists of the future of the moving twin. So how does this jump in time occur during acceleration. Or does it occur? How do events of the moving twin occur in the stationary twin's reference frame? And thanks for the previous answers.

 

[PeterDonis]

So what can be said for the definition of 'now' of the stationary, Earth observer?

If the stationary, Earth observer uses the standard definition of "now" for an inertial frame (see further comments on that at the end of this post), then his definition of "now" never changes; only the traveling twin's does. More precisely, the "now" surfaces of the stationary twin always remain parallel (whereas the "now" surfaces of the traveling twin, if he uses the definition you are assuming, the one JesseM described, do *not* remain parallel; they change when he turns around).

If the moving twin is moving away from Earth at first, then the stationary twin must conclude that the now from his perspective consists of the past of the moving twin, relative to another observer who is at rest with the moving twin. Then after acceleration, on the way back, the Earth twin can conclude that his 'now' consists of the future of the moving twin.

Yes, but all that is because the moving twin changed his state of motion. The stationary twin did not. With the definition of "now" that you're using, changing your state of motion is what changes your definition of "now". So the moving twin's definition changes; hence the relationship between the moving twin's definition and the stationary twin's definition also changes. But that relationship is not what determines "now" for either one, with the definition you're using; each particular twin's definition of "now" only depends on his own state of motion, not on how his state of motion relates to the other twin's.

So how does this jump in time occur during acceleration. Or does it occur?

Not for the stationary twin, because his state of motion never changes.

How do events of the moving twin occur in the stationary twin's reference frame?

Just like you'd expect: the moving twin moves out to the turnaround point, turns around, and comes back again. Everything looks very simple from the stationary twin's reference frame, since it's a single inertial frame for the entire scenario.

Regarding the definition of "now": in relativity, "now" is not a fundamental concept; it's a convention. If you are moving inertially forever, the obvious convention to choose is the standard one, the one that matches the "now" surfaces of the inertial frame in which you are always at rest. But if you ever change your state of motion (meaning, if you ever feel acceleration), there is no unique way for you to define "now", and every possible way to do it has some counterintuitive properties. These counterintuitive properties can cause a lot of confusion if you don't realize that "now" is just a convention; but that in itself is counterintuitive, so it's not surprising that it takes a while to really understand how it works. It took me a while too when I was first learning about it.

 

[Ibix]

A slightly tricky thing to understand in relativity is that "now" for any remote location is just a convention. So the fact that the traveling twin "now" (by the stay-at-home twin's definition) thinks that now on Earth (by the traveling twin's definition) is yesterday (by the stay-at-home twin's definition) isn't really significant of anything. They could both define "now" in a different way and come to a different conclusion - which is what is happening when the traveling twin accelerates.

So - there is no "jump in time". There's just the traveling twin resetting her clocks at turn around, in order to match her new choice of "now".

Edit: I think that's just a paraphrase of Peter Donis' last paragraph. Must type quicker...

 

[analyst5]

If the stationary, Earth observer uses the standard definition of "now" for an inertial frame (see further comments on that at the end of this post), then his definition of "now" never changes; only the traveling twin's does. More precisely, the "now" surfaces of the stationary twin always remain parallel (whereas the "now" surfaces of the traveling twin, if he uses the definition you are assuming, the one JesseM described, do *not* remain parallel; they change when he turns around).



Yes, but all that is because the moving twin changed his state of motion. The stationary twin did not. With the definition of "now" that you're using, changing your state of motion is what changes your definition of "now". So the moving twin's definition changes; hence the relationship between the moving twin's definition and the stationary twin's definition also changes. But that relationship is not what determines "now" for either one, with the definition you're using; each particular twin's definition of "now" only depends on his own state of motion, not on how his state of motion relates to the other twin's.



Not for the stationary twin, because his state of motion never changes.



Just like you'd expect: the moving twin moves out to the turnaround point, turns around, and comes back again. Everything looks very simple from the stationary twin's reference frame, since it's a single inertial frame for the entire scenario.

Regarding the definition of "now": in relativity, "now" is not a fundamental concept; it's a convention. If you are moving inertially forever, the obvious convention to choose is the standard one, the one that matches the "now" surfaces of the inertial frame in which you are always at rest. But if you ever change your state of motion (meaning, if you ever feel acceleration), there is no unique way for you to define "now", and every possible way to do it has some counterintuitive properties. These counterintuitive properties can cause a lot of confusion if you don't realize that "now" is just a convention; but that in itself is counterintuitive, so it's not surprising that it takes a while to really understand how it works. It took me a while too when I was first learning about it.

Peter, thank you very much for your answer, I'll analyze it a few times and reply if anything else occurs in my mind. I appreciate the help both from you and other guys, I like the answers.

 

[analyst5]

Just like you'd expect: the moving twin moves out to the turnaround point, turns around, and comes back again. Everything looks very simple from the stationary twin's reference frame, since it's a single inertial frame for the entire scenario.

Regarding the definition of "now": in relativity, "now" is not a fundamental concept; it's a convention. If you are moving inertially forever, the obvious convention to choose is the standard one, the one that matches the "now" surfaces of the inertial frame in which you are always at rest. But if you ever change your state of motion (meaning, if you ever feel acceleration), there is no unique way for you to define "now", and every possible way to do it has some counterintuitive properties. These counterintuitive properties can cause a lot of confusion if you don't realize that "now" is just a convention; but that in itself is counterintuitive, so it's not surprising that it takes a while to really understand how it works. It took me a while too when I was first learning about it.

So can you please explain the time dilation regarding the moving twin from the stationary twin's reference frame. I know that during the intertial motion the moving twin's clock is slowed down, but what happens when the moving twin accelerates? Does the stationary twin 'perceive' (and by that I don't mean see, but has a specific segment of the other twin in his reference frame) the increase of time dilation when the moving twin is accelerating to get from the position of rest to the position of motion relative to the stationary twin?

 

[PeterDonis]

So can you please explain the time dilation regarding the moving twin from the stationary twin's reference frame.

IMO, the best way to conceptualize what's going on is to discard the concept of "time dilation" altogether. But before going into that, I'll answer your question as you asked it; see below.

I know that during the intertial motion the moving twin's clock is slowed down, but what happens when the moving twin accelerates? Does the stationary twin 'perceive' (and by that I don't mean see, but has a specific segment of the other twin in his reference frame) the increase of time dilation when the moving twin is accelerating to get from the position of rest to the position of motion relative to the stationary twin?

If you are using the concept of "time dilation", then yes, the moving twin's time dilation, as "perceived" by the stationary twin, depends on the moving twin's velocity in the stationary twin's rest frame; the higher the velocity, the more time dilation.

However, there are a number of issues with looking at things this way, which I won't go into in detail, but just summarize as follows: "time dilation", as a concept, does not generalize well, because it's not fundamental; it's a derived concept that works OK for certain scenarios, but that's all. So trying to analyze things using "time dilation" as your fundamental concept doesn't work well.

The fundamental concept is that spacetime is a 4-dimensional geometric object, and different curves in this geometry will have different lengths. The stationary twin follows one curve between the two points where the two twins meet; the moving twin follows another, different curve. Since the curves are different, their lengths are different;, and the length of a timelike curve (i.e., of the worldline of an object with nonzero rest mass, like either twin) is just the proper time experienced by an observer who follows the curve. So different lengths of curves means different proper times experienced.

This concept is completely general; it covers all the different variations on "twin paradox" type scenarios in flat spacetime, and it also generalizes to curved spacetime, when gravity is present (i.e., to general relativity as well as special relativity). Also, once you have a scenario analyzed in terms of spacetime geometry and lengths of curves, you can easily "read off" the usual stuff people talk about with relativity from the analysis: time dilation, length contraction, relativity of simultaneity, etc. You can also easily see the limitations of all those other concepts.

A good presentation of all this with regard to the twin paradox is given in this Usenet Physics FAQ article:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

The "Spacetime Diagram Analysis" is the geometric viewpoint I have described above; the FAQ article also shows how this analysis serves as a common framework for deriving all the other concepts.

 

[analyst5]

The basic thing I don't understand is the relative simultaneity in this case. In the last part of the 'out-trip' the stationary twin has the past of the moving twin as his present, from his reference frame, relative to another observer which is at rest with the moving twin. But after the u-turn, the present moment for the stationary twin (regarding the rocket and the twin that is moving) becomes the future of the moving twin, relative to the observer that is at rest with the moving twin. I don't really understand how this can happen, how does the time dilate from the perspective of the Earth twin during each acceleration of the trip, especially during the u-turn?

For example, if the moving twin is heading away from the twin (like in the outbound trip) then of course the moving twin can conlude that his present is filled with past moments of the moving twin. So let's imagine that the moving twin decides to slow down, deaccelarate, to the state of rest relative to the starionary twin after the outbound trip. After he comes to rest, the stationary twin must conclude that his present is the same as the present for another stationary observer that underwent deacceleraiton with the moving twin. From this it follows that at one point in time the stationary twin's present was the past of the moving twin, and after deacceleration it seems that the time went straight-forward a lot.

I cannot oversimplify what's been bothering me, but please try to understand. I just don't understand how can the stationary observer 'perceive' first the past and during deacceleration the present of the other twin, so I don't understand how does the time dilate during acceleration/deacceleration from the perspective of the stationary twin.

 

[ghwellsjr]

I cannot oversimplify what's been bothering me, but please try to understand. I just don't understand how can the stationary observer 'perceive' first the past and during deacceleration the present of the other twin, so I don't understand how does the time dilate during acceleration/deacceleration from the perspective of the stationary twin.

Time dilation refers to the rate at which a moving clock ticks. It doesn't refer to the time displayed on any clock. An instantaneous acceleration does not affect the time displayed on the clock. If you take the original scenario of the moving twin instantly changing direction from going away at one speed to coming back at the same speed, his clock is unaffected by the change in direction. It is always ticking at the same slower rate than the stationary twin during the entire trip.

 

[analyst5]

Time dilation refers to the rate at which a moving clock ticks. It doesn't refer to the time displayed on any clock. An instantaneous acceleration does not affect the time displayed on the clock. If you take the original scenario of the moving twin instantly changing direction from going away at one speed to coming back at the same speed, his clock is unaffected by the change in direction. It is always ticking at the same slower rate than the stationary twin during the entire trip.

But the measurements of simultaneity are?

Could you please explain how does he then switch from the past of the moving twin to its future? On the outward trip he 'perceives' his past and the on the inbound he 'perceives' his future, of course relative to what the observer that is accelerating with the moving twin 'perceive'

 

[ghwellsjr]

But the measurements of simultaneity are?

Could you please explain how does he then switch from the past of the moving twin to its future? On the outward trip he 'perceives' his past and the on the inbound he 'perceives' his future, of course relative to what the observer that is accelerating with the moving twin 'perceives'

Simultaneity is an issue concerning the Coordinate Time of an Inertial Reference Frame (IRF) and has nothing to do with the Proper Time on any clock at any particular event. If you analyze the twin situation from the IRF in which the stationary twin is at rest during the entire scenario, then you will have one definition of simultaneity. If you then use the Lorentz Transformation (LT) process to get to a different IRF moving at a constant rate with respect to the original IRF, you will get a whole new set of Coordinate Times for the same events (like the turn-around) and therefore a whole new set of simultaneity issues.

There is no IRF in which the moving twin remains at rest during the entire scenario so the best you can do is consider the IRF in which he is at rest during the outbound trip or the IRF in which he is at rest during the inbound trip. Both will yield a different set of speeds, time dilations, simultaneities, and distances for and between events but they all will yield exactly the same results for the Proper Times at those events and what each twin sees of the other ones clock compared to their own during the entire scenario.

The other option you have is to apply a non-inertial reference frame to the moving twin but there is no standard way to do this and no transformation process that takes care of everything automatically for you like the LT. You have to say how you want to build such a frame. In that case, all the issues of speeds, time dilations, simultaneities, and distances become quite fickle.

 

[analyst5]

Simultaneity is an issue concerning the Coordinate Time of an Inertial Reference Frame (IRF) and has nothing to do with the Proper Time on any clock at any particular event. If you analyze the twin situation from the IRF in which the stationary twin is at rest during the entire scenario, then you will have one definition of simultaneity. If you then use the Lorentz Transformation (LT) process to get to a different IRF moving at a constant rate with respect to the original IRF, you will get a whole new set of Coordinate Times for the same events (like the turn-around) and therefore a whole new set of simultaneity issues.

There is no IRF in which the moving twin remains at rest during the entire scenario so the best you can do is consider the IRF in which he is at rest during the outbound trip or the IRF in which he is at rest during the inbound trip. Both will yield a different set of speeds, time dilations, simultaneities, and distances for and between events but they all will yield exactly the same results for the Proper Times at those events and what each twin sees of the other ones clock compared to their own during the entire scenario.

The other option you have is to apply a non-inertial reference frame to the moving twin but there is no standard way to do this and no transformation process that takes care of everything automatically for you like the LT. You have to say how you want to build such a frame. In that case, all the issues of speeds, time dilations, simultaneities, and distances become quite fickle.

That's a great answer, and I appreciate it, but can you describe me the sequence of events on the worldtube of the moving twin from the stationary twin's perspective. I still haven't found out how does he perceive time flowing from his perspective during the u-turn, and how can he first 'perceive' the past of the moving twin, and after the turnaround his future, relative to another observer which is at rest with the moving twin.

 

[ghwellsjr]

That's a great answer, and I appreciate it, but can you describe me the sequence of events on the worldtube of the moving twin from the stationary twin's perspective. I still haven't found out how does he perceive time flowing from his perspective during the u-turn, and how can he first 'perceive' the past of the moving twin, and after the turnaround his future, relative to another observer which is at rest with the moving twin.

I have made a lot of spacetime diagrams to depict twin scenarios. Do a search on my name with the word "diagram" and you will find lots of threads that discuss these issues. Let me know which ones help the most.

 

[analyst5]

I have made a lot of spacetime diagrams to depict twin scenarios. Do a search on my name with the word "diagram" and you will find lots of threads that discuss these issues. Let me know which ones help the most.

How can I do the search? I'm very inferior in using the tools on this forum. Could you maybe post them in this thread with some explanation, that would help a lot.

 

[PhoebeLasa]

[...]
But, what is the perspective of the stationary twin during the acceleration of the moving twin
[...]

According to the home twin, the traveler's age is increasing linearly, during the ENTIRE trip, at a constant rate that is slower than the home twin's ageing. According to the home twin, the traveler's instantaneous turnaround has no effect at all on how he (the traveler) ages. And the home twin certainly doesn't think that the traveler's acceleration has any effect on her (the home twin's) ageing.

 

[ghwellsjr]

How can I do the search? I'm very inferior in using the tools on this forum.

At the top of this page you will see:

Physics Forums > Physics > Special & General Relativity

Click on Special & General Relativity

Off to the right click on:

Search this Forum

When the little box pops up, click on:

Advanced Search

Under "Search by Keyword" type "diagram".

Under "Search by User Name" type "ghwellsjr".

Scroll down to "Show Results as" and click on "Threads".

Click on "Search Now".

Could you maybe post them in this thread with some explanation, that would help a lot.

I did a search and found a thread that I think might address your issues:

https://www.physicsforums.com/showthread.php?t=671398&page=2

Look at my posts #35 and #36.

 

[analyst5]

At the top of this page you will see:

Physics Forums > Physics > Special & General Relativity

Click on Special & General Relativity

Off to the right click on:

Search this Forum

When the little box pops up, click on:

Advanced Search

Under "Search by Keyword" type "diagram".

Under "Search by User Name" type "ghwellsjr".

Scroll down to "Show Results as" and click on "Threads".

Click on "Search Now".



I did a search and found a thread that I think might address your issues:

https://www.physicsforums.com/showthread.php?t=671398&page=2

Look at my posts #35 and #36.

Thanks for the help, but I still don't see anything that has to do with the stationary twin's perspective and the sequence of events from his perspective that relate to the interval when the other twin changes frames. I still don't understand the hypotethical scenario in which he concludes that he 'perceives' (has in its present plane of simultaneity) the past of the moving twin relative to the perspective of the observer that is at rest with the moving twin. After deccleration to the state of rest relative to Earth, an observer which is at rest with the moving twin and the stationary twin must have the same temporal slice as their present. How is that possible and what happens during acceleration to balance the views from these frames?

 

[ghwellsjr]

Thanks for the help, but I still don't see anything that has to do with the stationary twin's perspective and the sequence of events from his perspective that relate to the interval when the other twin changes frames.

Instead of thinking in terms of a twin's perspective, you should think in terms of a reference frame. If you mean the IRF in which the stationary twin is at rest during the entire scenario, then you shouldn't be thinking in terms of any other frame, including any frames in which the other twin is at rest during part of the scenario.

The other twin doesn't change frames. You could say that the other twin is at rest at different times in two different frames but he is always in all frames as is the other twin. Both twins are in all frames all the way through the scenario, they just are at different speeds in the different frames.

I thought it was obvious in the three frames in post #35 of the above link that both twins were in all three frames. Nobody has to jump frames.

I still don't understand the hypotethical scenario in which he concludes that he 'perceives' (has in its present plane of simultaneity) the past of the moving twin relative to the perspective of the observer that is at rest with the moving twin. After deccleration to the state of rest relative to Earth, an observer which is at rest with the moving twin and the stationary twin must have the same temporal slice as their present. How is that possible and what happens during acceleration to balance the views from these frames?

Can you state one of the diagrams and what issues of simultaneity you are asking about. Remember, all events on the same horizontal line in any diagram are simultaneous in that diagram. The same events in another diagram are not simultaneous.

Simultaneity is not "preceived' by any observer. It can only be the result of making radar measurements and observing Proper Times and applying Einstein's second postulate (that the signals travel at c) and construction of a Coordinate System. Do it any way you want. You can either follow the well established conventions of Special Relativity or make up your own. It's not an issue of nature. It's a man-made construct. Let Einstein do it for you for IRF's or you can follow the construct of the radar scheme that I show in the last diagram of post #36 or tell us what you have in mind. Those are your options. There's no right way or best way or preferred way. It's all because time (and space) are relative.

 

[PeterDonis]

The basic thing I don't understand is the relative simultaneity in this case.

"Simultaneity" is another concept like "time dilation" which is not fundamental, and IMO is better discarded until you have a good understanding of the scenario using the spacetime viewpoint. A particular problem with simultaneity is that it tempts you to think of "present", "past", and "future" as being "real", instead of just conventions. In relativity, these are just conventions; they depend on the coordinates you choose. The only invariants are causal relationships: timelike, spacelike, or null (lightlike) separation between events.

I just don't understand how can the stationary observer 'perceive' first the past and during deacceleration the present of the other twin, so I don't understand how does the time dilate during acceleration/deacceleration from the perspective of the stationary twin.

This illustrates the problem with focusing on "simultaneity" instead of on spacetime. What the stationary twin "perceives" here is not "real"; it's just a convention. When the moving twin turns around, his simultaneity lines change orientation relative to the simultaneity lines of the stationary twin; but those lines are just imaginary lines drawn in order to assign coordinates to events. The changes in those lines are not "real" any more than the lines themselves are.

 

[analyst5]

"Simultaneity" is another concept like "time dilation" which is not fundamental, and IMO is better discarded until you have a good understanding of the scenario using the spacetime viewpoint. A particular problem with simultaneity is that it tempts you to think of "present", "past", and "future" as being "real", instead of just conventions. In relativity, these are just conventions; they depend on the coordinates you choose. The only invariants are causal relationships: timelike, spacelike, or null (lightlike) separation between events.



This illustrates the problem with focusing on "simultaneity" instead of on spacetime. What the stationary twin "perceives" here is not "real"; it's just a convention. When the moving twin turns around, his simultaneity lines change orientation relative to the simultaneity lines of the stationary twin; but those lines are just imaginary lines drawn in order to assign coordinates to events. The changes in those lines are not "real" any more than the lines themselves are.

Ok, I get it from the perspective of the moving twin, that his lines of simultaneity change orientation. But what happens from the stationary twin's perspective? I still don't understand it. How come his lines of simultaneity do not change orientation, since we can consider him to move away during the first leg of the trip, and therefore having events that are past (or that preceded others) in his present, and after that he has future events of the moving twin that can be considered to be his present. I still don't understand it. This disbalance confuses me.

 

[WannabeNewton]

How come his lines of simultaneity do not change orientation, since we can consider him to move away during the first leg of the trip, and therefore having events that are past (or that preceded others) in his present, and after that he has future events of the moving twin that can be considered to be his present. I still don't understand it. This disbalance confuses me.

The simultaneity lines for a given observer will depend only on features of that observer's world line, which is absolute-one observer is accelerating and the other one isn't there is no symmetry in this regard. The simultaneity lines aren't determined by the physical trajectories of observers as represented in different coordinate systems, which is relative and can be symmetrical in the manner of which you speak.

 

[JesseM]

So what can be said for the definition of 'now' of the stationary, Earth observer? Regarding the events on the traveling twin's worldtube? If the moving twin is moving away from Earth at first, then the stationary twin must conclude that the now from his perspective consists of the past of the moving twin, relative to another observer who is at rest with the moving twin.

I don't understand this phrase "consists of the past of the moving twin, relative to another observer who is at rest with the moving twin". Maybe a simple numerical example would help clarify things. Say the twin who leaves Earth moves away at 0.6c in the Earth twin's rest frame. Then in the Earth twin's reference frame, the event of his celebrating the 25th anniversary of his twin's departure is simultaneous with the event of the traveling twin's celebrating the 20th anniversary of the departure. In the inertial frame where the traveling twin has been at rest during the journey away from Earth, the event of the traveling twin celebrating the 20th anniversary is simultaneous with the event of of the Earth twin celebrating the 16th anniversary.

Can you explain the meaning of your phrase above specifically in terms of these numbers? If the Earth twin's "now" when he celebrates the 25th anniversary is simultaneous with the traveling twin celebrating the 20th anniversary, would the event of the traveling twin celebrating the 20th anniversary is somehow "the past of the moving twin, relative to another observer who is at rest with the moving twin?" If so, why? When the traveling twin celebrates the 20th anniversary, the inertial observer moving along with him has also measured 20 years to have elapsed since the twin's departure from Earth.

 

[JesseM]

Ok, I get it from the perspective of the moving twin, that his lines of simultaneity change orientation. But what happens from the stationary twin's perspective? I still don't understand it. How come his lines of simultaneity do not change orientation, since we can consider him to move away during the first leg of the trip, and therefore having events that are past (or that preceded others) in his present, and after that he has future events of the moving twin that can be considered to be his present. I still don't understand it. This disbalance confuses me.

Do you understand that acceleration is absolute in relativity? There is no doubt about which twin accelerated to change direction and which didn't--the one that did can measure G-forces during the acceleration. Also, the laws of physics don't obey the same equations in non-inertial coordinate systems as they do in inertial frames, so that's a more general way to distinguish them.

 

[analyst5]

Do you understand that acceleration is absolute in relativity? There is no doubt about which twin accelerated to change direction and which didn't--the one that did can measure G-forces during the acceleration. Also, the laws of physics don't obey the same equations in non-inertial coordinate systems as they do in inertial frames, so that's a more general way to distinguish them.

I do, but what's bothering me is in fact the difference between simultaneity in two perspectives. The first one is the observer which is at rest with the moving twin and the events that the considers to be happening now over a period of time. The second is the home twin. From the perspective of the home twin, the events on the worldtube of the moving twin that he considers present are past, or happened before, the events that the observers which is at rest with the moving twin consider to be present. Then after the turnaround, on the inbound trip, the events that the stationary twin considers to be present are really the future, or happened after the events that the co-moving observer considers to be the present. This is what confuses me. The description of two perspectives and why the twin, for instance doesn't consider the past of the moving twin to be his present all the time, but in fact, it's first past, then after the turnaround, the future.

 

[Dale]

Hi analyst5, I have read all of your posts in this thread and I have no idea what you are asking.

From the perspective of the home twin, the events on the worldtube of the moving twin that he considers present are past, or happened before, the events that the observers which is at rest with the moving twin consider to be present.

For instance, this sentence makes no sense that I can tell. I cannot decipher what you mean.

Let's take the following situation for definiteness. We will use unprimed coordinates for the stay at home twin's frame, O, single primed coordinates for the outgoing inertial frame, O', and double primed coordinates for the ingoing inertial frame, O'', and we will fix the origin of all three frames at the event of the twin's separation. We will use $\tau_H$ to refer to proper time along the stay at home twin's worldline and $\tau_T$ to refer to proper time along the traveller's worldline. In O the traveller travels at .6 c in the x direction for 5 y and then instantaneously turns around traveling at .6 c in the -x direction for 5 y, meaning that he travels to a point x = 3 ly.

Can you explain with numbers using this scenario precisely what it is that bothers you?

 

[JesseM]

From the perspective of the home twin, the events on the worldtube of the moving twin that he considers present are past, or happened before, the events that the observers which is at rest with the moving twin consider to be present.

I still don't understand what this means. Did you see I had posted two posts in a row, and that the one before the one you just responded to asked for clarification on this phrasing, in the context of a simple numerical example?

 

[ghwellsjr]

I do, but what's bothering me is in fact the difference between simultaneity in two perspectives. The first one is the observer which is at rest with the moving twin and the events that the considers to be happening now over a period of time.

This would be the non-inertial rest frame of the black moving twin, the last diagram in the above link according to the radar method.

The second is the blue home twin.

This would be the inertial rest frame of the home twin, the first diagram in the above link.

I have redrawn the two diagrams into one drawing and added in additional radar signals. The moving black twin's non-inertial rest frame is on the left and the blue home twin's inertial rest frame is on the right:

Note that each twin establishes the distance to the other twin by sending a radar signal to the other twin, noting the time it was sent and waiting for the return signal, noting the time it was received, along with the time that he sees on the other twin's clock. He then takes the difference between the sent and received times and divides that by two and assumes (according to Einstein's second postulate) that the signal traveled at c to get to the other twin and that the echo traveled back at the same speed so this allows him to establish a distance to the other twin as simply the time multiplied by c. He also assumes that the time according to his own clock at which this distance applies is the average of the sent and received times.

You can look at either diagram and see how they support the radar signals for either twin but each twin draws his own diagram such that he is at rest. For example, the blue home twin sends a signal at his time of 2008 years (follow the thin blue line up and to the right) and receives the echo at his time of 2011 (follow the thin black line up and to the left) along with his observation that the other black moving twin's clock displayed 2009 at the point of reflection. So he takes the difference of the 2008 and 2011 which is 3 and divides that by 2 to get a distance of 1.5 light-years and since the average of 2008 and 2011 is 2009.5, he puts that black moving twin at 1.5 light-years away at his time of 2009.5 and marks the black moving twin's time at 2009.

In the same way, the black moving twin does a similar thing gets the same answers, except that his outgoing signal is a thin black line and the reflected signal is a thin blue line. But if you repeat the process for later years, you will see that they get different answers.

From the perspective of the home twin, the events on the worldtube of the moving twin that he considers present are past, or happened before, the events that the observers which is at rest with the moving twin consider to be present. Then after the turnaround, on the inbound trip, the events that the stationary twin considers to be present are really the future, or happened after the events that the co-moving observer considers to be the present. This is what confuses me. The description of two perspectives and why the twin, for instance doesn't consider the past of the moving twin to be his present all the time, but in fact, it's first past, then after the turnaround, the future.

I think you are a little mixed up here. The blue home twin always establishes that the black moving twin's clock is behind his own for the entire trip. In fact, the moving twin's clock is ticking at 80% of his own so that during the ten-year interval on the blue home twin's clock, he establishes by radar measurements, that the black moving twin's clock has ticked eight years and that's exactly what has happened when they get back together.

On the other hand, the black moving twin establishes that the blue home twin's clock is behind his for only three years. In fact, for the first two years and a half, their experiences are symmetrical, they both have established that the other ones clock has progressed through only two years but at that point the black moving twin establishes that the blue home twin quits moving away and his clock speeds up so that in just another half year, the blue home twin's clock matches his own at the year 2010. During the next two and a half years, the black moving twin establishes that the blue home twin's clock continues to tick away at twice the rate of his own so that it has reached the year 2015 while he has only progressed half way through 2012. At that point, the black moving twin establishes that the blue home twin starts moving towards him and his clock slows down to the 80% rate once again so that when they reunite, the time on the blue home twin's clock is 2017 compared to his own at 2015.

Does this make sense to you? Remember, they both are establishing the distance to the other one as a function of their own clock by making radar measurements. They both do the same thing but they get different answers.

 

[PeterDonis]

what happens from the stationary twin's perspective? I still don't understand it. How come his lines of simultaneity do not change orientation

Because he never changes his state of motion. Using the definition of "lines of simultaneity" that you are using, the only way they will change orientation is if your state of motion changes--i.e., if you experience proper acceleration. The stationary twin never experiences proper acceleration, so his lines of simultaneity never change orientation.

since we can consider him to move away during the first leg of the trip, and therefore having events that are past (or that preceded others) in his present, and after that he has future events of the moving twin that can be considered to be his present.

This is irrelevant, because motion is frame-dependent, but proper acceleration is not. So you can't look at motion to determine what the lines of simultaneity do; you have to look at proper acceleration, as above.

 

[pervect]

I do, but what's bothering me is in fact the difference between simultaneity in two perspectives.

Why does this matter to you? I could go on about simultaneity being conventional, etc etc, but I think everyone has already done that, and you still have some sort of mental reservation. But I don't think you know what it is. So it's rather hard to address the issue :-). So take it as a given that simultaneity is not the same for the two perspectives, exactly why is this an issue?