Twin paradox in a circle

  1. phinds

    phinds 8,320
    Gold Member

    There have been a couple of posts over the last few months that posit a relativistic-speed path in a circle around the earth and I want to make sure I correctly understand the ramifications. It's the twin paradox in a circle. SO ... here's a scenario that I think will solidify it for me:

    This is a thought experiment, not something that would be practical, but it is remotely within the realm of physical possibility.

    Rocket achieves earth orbit and then with a massive waste of fuel accelerates in the circular orbit to very low relativistic speeds (say .001c), and then decelerates in the orbit and returns to earth.

    The person on the craft would be slightly younger than the one on earth, yes? I don't care if it's fractions of a second or what, just the absolute fact.

    That is, the end result is exactly the same as if the craft had accelerated away from earth and then it had turned around and came back (which is in essence what it IS doing).
     
  2. jcsd
  3. Thats entirely correct as I understand it.

    My understanding is time dilation is directly related to curvature, curvature is intrinsically linked to gravity and geometry: acceleration can be used to "create" curvature and therefore time dilation.

    Any corrections to my understanding are welcome.
     
  4. Well, first, I think your question is more appropriate for the SR-GR forum than for the Cosmology forum.

    Second, you can answer this by yourself by doing some simple calculations.
     
  5. phinds

    phinds 8,320
    Gold Member

    I suspect that if I could do the calculation, I would not have needed to ask the question.
     
  6. I've read lots of your posts, and from those I believe that you're quite capable of doing the calculations that will answer your question.

    EDIT: Though you might have to look something up. Everybody has to do this from time to time.
     
  7. phinds

    phinds 8,320
    Gold Member

    Oh, I might be able to do the math, but first I'd have to know what math to DO, and I don't.
     
  8. Drakkith

    Staff: Mentor

    Phinds, that would only be correct if the velocity is high enough to offset the reduced effect of Earth's gravity on time dilation. GPS satellites are slower than Earth based clocks by 7 microseconds per day due to time dilation caused by their velocity, however they are FASTER by 45 microseconds per day due to being further away from Earth. Combined the two effects cause satellite clocks to be faster by 38 microseconds per day. AKA they age faster by 38 microseconds per day than those of us on Earth do.
     
  9. Drakkith

    Staff: Mentor

  10. DaveC426913

    DaveC426913 16,081
    Gold Member

    OK so move the experiment to a location around a nominal mass asteroid. Or an imaginary point in space.
     
  11. Drakkith

    Staff: Mentor

    Exactly!
     
  12. Whether wrt the Earth or an asteroid or an imaginary point in space, I'm pretty sure, without doing the calculations because, yeah, I'm lazy, that a traveller moving at .001c away from and then back to the Earth or an asteroid or an imaginary point in space will have aged less than a person on either the Earth or an asteroid or occupying an imaginary point in space, respectively.

    My point to Phinds was that by doing a few actual calculations, then he can answer lots of these sorts of questions for himself, more or less intuitively.

    As to the deeper question of what, physically, causes differential aging. Who knows? Superficially, it suggests that what we refer to as empty space isn't empty. And, as Cosmo Novice suggested, acceleration/deceleration seems to be affecting (producing changes in) the periods/frequencies of oscillators that are accelerating/decelerating.
     
  13. DaveC426913

    DaveC426913 16,081
    Gold Member

    I think he addressed this adequately by pointing out that he does not know which equations he would apply and how, even if he is able to do the calculations once he has them.
     
  14. George Jones

    George Jones 6,363
    Staff Emeritus
    Science Advisor
    Gold Member

    The analysis of circular motion does contain some surprises.
     
  15. phinds

    phinds 8,320
    Gold Member

    THanks for reminding me of that. I WAS aware of it, but didn't think about it in this instance. I often don't connect the dots between various facts that I am aware of. Probably comes from (1) only doing this stuff casually, (2) not remembering all of them all of the time, and (3) ... uh ... I forget.
     
  16. phinds

    phinds 8,320
    Gold Member

  17. I guarantee you that he has the ability to find the proper equations and do the calculations on his own. He was just being a bit lazy, and I called him on it. That's all.

    While I admire your defending him, I don't see any problem with requiring him to do a bit of homework.

    If you want some examples of extreme laziness, then just look at some of my posts. :smile:

    Anyway, bottom line, we all, including now Phinds I think, know the answer to his question. The really deep, intriguing question concerns, at least for me, the physical nature of relativistic differential aging.

    EDIT: And, thanks to George Jones for presenting a nice complication.
     
    Last edited: Nov 16, 2011
  18. Me either.

    I think you nailed it. I'm pretty sure that I've forgotten a lot (most?) of the physics I learned many years ago, but I can't be sure. :smile:

    Anyway, keep asking questions. I think we both find this stuff fascinating, and are thankful for the science advisors and mentors who donate their time to help us better understand what physics can tell us about our world.

    And, I apologize if I in any way offended you. My replies weren't meant to do that. As I mentioned, I've read many of your posts, and from those I think you are a thoughtful and intelligent person.
     
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