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From one observer's perspective, on all moving objects time will run slower. But from the perspective of one of those objects, it's the observer who's slow. And the answer seems to be that both are correct!

Then there are (correct) statements like the ISS runs slower than the Earth. Based on above how can this be true? Why not the other way around?

xyz
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  • i THINK in the ISS station example the all-important factor is that the ISS is going "out and back" all the time, that is to say .. circularly. if the ISS was simply a spaceship passing by us, the "looks the same from either side" concept applies. I believe the apparent paradox you outline is explained that simply. – Fattie Dec 12 '15 at 18:15
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    Because the atomic clock we use/calibrate to is in Colorado? – Kyle Kanos Dec 12 '15 at 18:34
  • Note also that your last sentence of the first paragraph answers your questions, no? – Kyle Kanos Dec 12 '15 at 18:35
  • @KyleKanos no, if you put two twins one in earth, one on ISS, the person on earth will grow up faster. – xyz Dec 12 '15 at 18:35
  • @KyleKanos ISS is slower than earth, earth is faster than ISS. The first says the effect is symmetrical – xyz Dec 12 '15 at 18:36
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    Derp derp. Helps to have one conversation at a time. ISS runs slow due to gravitational time dilation, not SR time dilation. See also this post – Kyle Kanos Dec 12 '15 at 18:38
  • @KyleKanos: wrong I'm afraid. Gravitational time dilation would make the ISS clocks run fast not slow. – John Rennie Dec 12 '15 at 20:34
  • @JohnRennie: Fast, slow, whatever. The time difference is still due to gravitational time dilation & not the typical SR time dilation OP was applying. – Kyle Kanos Dec 12 '15 at 20:57
  • Because of lack of symmetry. – Viesr Dec 12 '15 at 21:12
  • @KyleKanos By gravitational time dilation, the ISS experiences less gravity than humans on surface hence time should run faster. The actual result is the opposite, time runs slow on ISS. SR is bigger than GR here. – xyz Dec 13 '15 at 12:47
  • Concerning ISS you are comparing one clock to one other clock.

    If however you have one frame of reference passing by another frame of reference, and it is assumed that in each of these frames of reference that all clocks are synchronized, you will use just one clock while examining at least two clocks in the other frame of reference as that frame passes by. This is what allows this strange phenomena to occur in which it always seems to be the "other" guy whose clocks are ticking slower than yours, a view which is shared from both frames of reference. See http://goo.gl/fz4R0I

     – Sean Dec 13 '15 at 13:22

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That's a good question, and it highlights the fact that special relativity describes far more than just motion at a constant speed in a straight line, and therefore the Lorentz transformations. Confusion about time dilation is almost invariably due to taking an overly simplistic view of special relativity.

The only way two observers can directly compare their clocks is if they are at the sample place in space. Two observers in linear motion can directly compare their clocks only once because by definition they can never meet again. That's why both can conclude the other's clock is running slow without fear of contradiction.

However accelerated observers can compare their clocks more than once - the obvious example is the infamous twin paradox (which isn't a paradox, but that's a rant for another day). When two observers can directly compare their clocks twice, or more, there can be no ambiguity about which clock has been running slow.

The ISS moves in a circle around the Earth. In principle I can put an observer hovering in space in the path of the ISS, so the ISS passes the observer once every orbit. That observer and the astronauts on the ISS can compare their clocks whenever they meet, and when they do all parties will agree that the clocks on the ISS have run slower than the clock held by the hovering observer. That's why we say the clocks on the ISS are running slow.

John Rennie
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