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Quick twin paradox question

  1. Jan 28, 2014 #1
    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.
     
  2. jcsd
  3. Jan 28, 2014 #2

    mfb

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    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.
     
  4. Jan 28, 2014 #3
    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?
     
  5. Jan 28, 2014 #4

    Ibix

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    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.
     
  6. Jan 28, 2014 #5

    JesseM

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    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.
     
    Last edited: Jan 28, 2014
  7. Jan 28, 2014 #6
    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.
     
  8. Jan 28, 2014 #7

    PeterDonis

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    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.
     
  9. Jan 28, 2014 #8

    Ibix

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    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...
     
  10. Jan 28, 2014 #9

    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.
     
  11. Jan 29, 2014 #10
    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?
     
  12. Jan 29, 2014 #11

    PeterDonis

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    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.

    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.
     
  13. Jan 29, 2014 #12
    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.
     
  14. Jan 29, 2014 #13

    ghwellsjr

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    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.
     
  15. Jan 29, 2014 #14
    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'
     
  16. Jan 29, 2014 #15

    ghwellsjr

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    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.
     
  17. Jan 29, 2014 #16

    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.
     
  18. Jan 29, 2014 #17

    ghwellsjr

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    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.
     
  19. Jan 29, 2014 #18
    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.
     
  20. Jan 29, 2014 #19
    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.
     
    Last edited: Jan 29, 2014
  21. Jan 29, 2014 #20

    ghwellsjr

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    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.
     
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