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Relative motion and accumulated time dilation

  1. May 11, 2012 #1
    I have a few questions about time dilation and how it accumulates.

    1a. Say you have a situation where you have two clocks that move away from each other with symmetrical acceleration and relative motion. From what I understand, each clock would appear to have slowed down relative to the other, and this is not a paradox because each is in their own reference frame. Then the two clocks move back towards each other with symmetrical acceleration and relative motion. How would they compare to each other once they were back in the same reference frame?

    1b. Same question as above, but assume there is instant acceleration.

    1c. What if instead of moving back towards each other, they were teleported back together?


    2. Though time dilation at earthly speeds is negligible in our every day lives, it still occurs. How is it that it does not accumulate over time and lead to small differences in our watches and such? Or, does it, but it is so small as to be unnoticeable? This applies to both gravitational and velocity-based time dilation, but I'm mostly interested in velocity for the sake of this question.

    Thanks!
     
  2. jcsd
  3. May 11, 2012 #2
    1a.
    Not an expert on General Relativity, but since this situation is perfectly symmetric, they'll have the same time. General Relativity is required if you want to see how one observes the other over the course of the experiment.

    1b.
    Same.

    1c.
    Invalid, one cannot teleport and time travel would necessarily follow from being able to teleport, which raises some paradoxes. This also raises some issues with Relativity of Simultaneity.

    2.
    Yes, it does lead to tiny differences, but they are so phenomenally tiny that they're unnoticeable.

    Also, the differences are small enough that they're within the improbability range of Quantum Mechanics, so you've got some problems there. And before anyone gets mad at me for trying to combine Quantum Mechanics and General Relativity, note that I'm combining Quantum Mechanics with Special Relativity, which has been done and is very well done.
     
  4. May 11, 2012 #3

    A.T.

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    If the paths are symmetrical in an inertial frame, the accumulated times will be same.

    Same

    Depends on the teleporter specifications.

    Yes.
     
  5. May 11, 2012 #4
    Does this mean that they will both dilate, but by the same amount (relative to a third stationary clock, say), or that neither will dilate? Will they dilate on the way away from each other, and then contract on the way back towards each other?

    Thanks for your responses!
     
  6. May 11, 2012 #5
    I think it means that both will dilate, but by the same amount, and they'll both dilate both ways. Then again, a perfect explanation requires GR, which I'm no expert at.
     
  7. May 11, 2012 #6

    Mentz114

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    coktail, the reading on a clock between two events can be calculated from the proper time of the clocks worldline between the events. And, most importantly, this time is the same in any frame. It is absolutely invariant. Time dilation is a coordinate effect and is not directly observable, whereas the proper time is ( you can look at the reading on any clock) and is invariant.

    No it does not. It is not helpful to bring GR into this. Differential ageing is completely explained by the proper time as I've stated above.
     
  8. May 11, 2012 #7
    True, but what if we want to figure out what one of the watches observes? This is a change of reference frames ... which is only valid with *gasps* GR, I thought? Or probably my brain isn't working at its best at the moment.
     
  9. May 11, 2012 #8

    Dale

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  10. May 11, 2012 #9
    I was under the impression that time dilation was observable, but only from an external reference frame. For example, for clocks observe (if they have eyes or an observer sitting on top of them) each other dilating, but to each clock its own time remains unchanged.
     
  11. May 11, 2012 #10

    Mentz114

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    A change of coordinates does not require GR. A Lorentz transformation in SR is just a change of coordinates from one frame to another.

    The accumulated time on any clock between events is easy to calculate using the line element of Minowski spacetime

    c22 = c2dt2 - dx2 - dy2 - dz2
     
  12. May 11, 2012 #11
    Under no acceleration, yes.

    Thanks, DaleSpam, I heard accelerating reference frames are treatable under SR, but not necessarily in the same way. Probably got my information from a not so great source.
     
  13. May 11, 2012 #12
    Ah, so with acceleration clock A would see clock B slow down, while clock B would see clock A speed up? What if the acceleration is symmetrical?
     
  14. May 11, 2012 #13

    Mentz114

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    I think if you watch a moving clock the Doppler effect takes over. You would see a receding clock ticking more slowly, and an approaching clock ticking faster.

    Yes, an observer will see no change in his clock.

    Please look at this page and the especially the section 'What it Looks Like'

    http://en.wikipedia.org/wiki/Twin_paradox
     
  15. May 11, 2012 #14

    ghwellsjr

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    Although we don't notice any difference in the watches we carry around, time dilation, both gravitational and velocity-based, is noticed by the precise atomic clocks that are the international standards and for the GPS clocks in orbit around the earth. They all run at different rates depending mainly on their elevation. So, for purposes of knowing what time it is, we can't rely on our own precise atomic clocks, if we had them, but instead on a co-ordinated time source like GPS.
     
  16. May 11, 2012 #15
    My impression was that since the speed of light is constant, the only thing the Doppler effect would cause is a red/blue shift...
     
  17. May 11, 2012 #16
    Also, in the Twin Paradox, I don't understand why a change in acceleration as the spaceship twin turns around sets off the asymmetry, but the initial acceleration of the spaceship doest not. Sorry for the side tangent.
     
  18. May 11, 2012 #17

    ghwellsjr

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    Even without gravity effects, if clock B is moving at a constant speed but remains a constant distance from clock A so that it is accelerating in a circle around clock A (think orbit), then clock A will observe clock B to be running at a slower rate and clock B will observe clock A to be running at a faster rate. But this is clearly a non-symmetrical acceleration because only clock A is accelerating.

    If you are going to talk about a symmetrical acceleration such that the clocks start out together and follow the same acceleration/velocity profile except in opposite directions and they eventually reunite, then each one will view the other ones clock in the same way and they will end up with the same time on them.
     
  19. May 11, 2012 #18
    Thank you, George.
    Given this, would clock and A and B detect discrepancies between their times as they travel, but they would resolved themselves by the time they reunited, or would they stay "in sync" the entire time?
     
  20. May 11, 2012 #19

    Mentz114

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    Any oscillatory process is subject to the Doppler effect, including clocks ticking.
     
  21. May 11, 2012 #20
    But the relativistic Doppler effect just affects the perceived frequency of the light (e.g. red/blue shift), not the time dilation itself, correct?
     
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