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B The Twins "Paradox" Redux?

  1. Nov 16, 2016 #1
    Twins leave earth in opposite directions, accelerate at the same rate until their relative v = ~c, hold this v for 20 years (or however long), then decelerate at the same rate to v=0, and accelerate at the same rate back towards earth until their relative v again =~c, hold for same amount of time, then decelerate at the same rate until they reunite where they started. For the entire journey, wouldn't each have seen the other as aging much more slowly? Are they the same age now? How much time has passed on earth?
     
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  3. Nov 16, 2016 #2

    Ibix

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    They'd be the same age. A triplet at home would be older. Look up Orodruin's Insight on the geometric resolution of the twin paradox.

    Edit: one of the learning points of the twin paradox is that time dilation isn't anywhere near the whole story.
     
  4. Nov 16, 2016 #3
    Thanks, that's what I thought. So even though each twin "saw" the other as aging more slowly for the entire trip, they are the same age when they reunite. It's like their triplet's/earth's frame or reference retroactively reverses their in-trip observations.
     
  5. Nov 16, 2016 #4

    Orodruin

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    To boil it down: The time dilation formula is based on the assumption of the simultaneity in a particular frame. This notion of simultaneity will differ from frame to frame and will therefore change as an observer accelerates.

    Note that time dilation does not describe what an observer actually sees, but what it can deduce happened. In order to find out how it would actually look you would need to take the finite travel time of light into account.
     
  6. Nov 16, 2016 #5

    Ibix

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    No. Their observations are always consistent with the notion that the travellers will be the same age when they return. The Earth frame does nothing. It's just a choice of coordinates.
     
  7. Nov 16, 2016 #6

    Orodruin

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    Oh, and the easiest way to find this text is by following the "My Insights" link in my signature.
     
  8. Nov 16, 2016 #7
    If it were possible for each twin to observe the other for the entire trip then they couldn't see each other as ageing slower for the entire duration. That would be like Twin A watching Twin B's clock running slower for the whole trip and then suddenly at the end of the journey the clock jumps forward to the same time as Twin A

    I'm not too sure what twin A would observe if he could watch Twin B's clock for the entire journey but what ever he sees it must symmetrical (e.g. if he sees twin B's clock running slower then at some point he must see it running equally faster.) as the two clocks have to read the same time again at the end of their journeys.
     
  9. Nov 16, 2016 #8

    Bandersnatch

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  10. Nov 16, 2016 #9
    Thanks, Orodruin. I get that acceleration impacts t dilation, which is why I kept it symmetrical. I also get that neither can really observe in "real" time the other's clocks (biological or mechanical). But, for the purposes of this thought experiment, can I not assume some sort of instantaneous (say entanglement based) method of observation? In any case, what both deduced was occurring, via SR, clearly was not, or was retroactively undone?
     
  11. Nov 16, 2016 #10

    PeroK

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    If you are serious about learning SR, you need to knuckle down and study the relativity of simultaneity and the so-called leading clocks lag rule, which lies at the heart of these problems.

    Coming up with a pseudo explanation like this is not the real understanding.
     
  12. Nov 16, 2016 #11

    Orodruin

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    This is exactly what you will find if you compute what the observers will actually see, as mentioned in my previous post. This is not what time dilation is about. Time dilation is about what time coordinates are assigned to different events in a particular frame and its comparison to the proper time.

    This is based on the notion of simultaneity in the particular frame and changes when you change reference frame by accelerating.
     
  13. Nov 16, 2016 #12
    And yet this (each seeing the other's clocks running slower for the entire trip) is exactly what SR predicts they would each observe, which is why it's called a paradox, I guess.
     
  14. Nov 16, 2016 #13

    PeroK

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    If you are serious about learning SR, you need to knuckle down and study the relativity of simultaneity and the so-called leading clocks lag rule, which lies at the heart of these problems.

    Coming up with a pseudo explanation like this is not the real understanding.
     
  15. Nov 16, 2016 #14

    Orodruin

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    No

    Even if you could it would depend on which frame you want it to be instantaneous in. If it is instantaneous in one frame it will not be in another (it will be an FTL communication that could a priori go back in time). This is at the very core of relativity and is called the relativity of simultaneity: what is "at the same time" in one frame is not "at the same time" in another.

    Failing to understand the relativity of simultaneity is likely responsible for more than 90 % of the misconceptions beginners have of relativity. Understanding it is crucial if you want to have any chance of understanding SR at a deeper level than popular science.
     
  16. Nov 16, 2016 #15

    PeroK

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    It's what you think SR predicts, because you only know about time dilation. SR is more than just time dilation.
     
  17. Nov 16, 2016 #16

    jbriggs444

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    Acceleration does not affect time dilation. Acceleration results in a change of synchronization convention.
     
  18. Nov 16, 2016 #17
    so acceleration is not the same as a gravity (feels the same though), been wondering
     
  19. Nov 16, 2016 #18
    I'm not sure I have the grey matter or mathematical chops to understand SR well. It'd be nice not to totally embarrass myself writing SF, though. And, so far, this site's been helpful in that regard.

    PS

    Aren't entanglement's changes simultaneous across any distance? And so FTL?
     
  20. Nov 16, 2016 #19

    jbriggs444

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    No. You continue to misunderstand.

    Gravity is the same as an acceleration. That's the equivalence principle. But gravitational acceleration is NOT associated with time dilation. Gravitational potential is. The distinction is that potential is a combination of an acceleration and a distance.

    Accelerations in special relativity can be interpreted as an incremental change of reference frame and an associated incremental change of clock synchronization. The amount of clock change scales with distance. A mere acceleration is not enough. You need an acceleration and a remote clock some distance away.
     
  21. Nov 16, 2016 #20
    It's not a real paradox, it's an apparent paradox. This is why you often see it referred to as the Twin Trip or some such, as it really doesn't deserve the name Twin Paradox. A less complex apparent paradox is the symmetry of time dilation, which really ought to be resolved before tackling the twin paradox as glossing over it means you'll forever find the twin paradox baffling.

    But to address the issue you raise, imagine each twin with a flashing strobe light. Let's call these strobe lights clocks, as they send out the flashes at regular intervals, say once per minute. When each is at rest relative to the other, the rate at which the flashes are seen by one twin is equal to the rate at which they are sent by the other. But if there is relative motion between the twins, that will not be the case. When moving apart each will see the other's flashes as slow, but when they approach each other, each will see the other's as fast. Now this speeding up and slowing down of clock rates is due only partially to time dilation, the other part being due to light travel time. So each will see the other's clock as running fast or slow depending on whether they are approaching or receding, but if you subtract off the part of the effect due to light travel time, then each will observe that the other's clock is running slow, regardless of whether they are approaching or receding.

    So what you see is different from what you observe.

    Anyway, if you go through the details you will find that after the twins reunite to compare notes, the number of flashes that each sent will equal the number of flashes that the other received. But they may not agree on the time that elapsed between the flashes, and when the total time between flashes is added up, they may get different sums.

    Now, if the journeys are symmetrical in the way you propose, the sums will match. But a triplet that stayed home will get a larger sum.

    There's a hokey old cartoon that can you find by searching YouTube for "Paul Hewitt Twin Trip". The physics is solid.
     
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