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Presume that I have made a space elevator with two cars. As one car descends it causes the other to ascend. Presume now that I've placed this elevator on a planet with a very strong gravitational field, and that I have a suitably precise clock and I am far from the planet, observing both cars.

As the descending car gets closer to the surface, it experiences more time dilation than the ascending car. Does someone in the ascending car notice that they are accelerating more slowly than expected? Would I notice the same thing?

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  • $\begingroup$ If the ascending and decending cars are linked to each other, and the descent of one causes the ascent of the other, neither can be freely falling. $\endgroup$ Commented Apr 12, 2021 at 19:51
  • $\begingroup$ I see. I was thinking something along the lines of an old timey elevator, where the descent of one car at least helped in the ascent of another. Perhaps a slightly different way of asking this question is: what happens to the cable between them? As the cable has to be fed around a loop of some kind parts of it would experience different time dilations than others, but in theory the entire thing would have to be fed through the loop at the "same" time $\endgroup$ Commented Apr 12, 2021 at 20:14
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    $\begingroup$ In your own reference frame time will always appear to run normally to you no matter how dilated it appears from a different frame. $\endgroup$ Commented Apr 12, 2021 at 20:39
  • $\begingroup$ @JerrySchirmer I don't see where the OP mentions free-fall (edit?). In any case, in true free-fall neither would experience gravitational time dilation (see equivalence principle). $\endgroup$
    – m4r35n357
    Commented Apr 13, 2021 at 8:47
  • $\begingroup$ @AdrianHoward I think that's the crux of my misunderstanding. To each part of the cable, time is running normally. However, from the perspective of the top of the cable, the bottom has more time dilation. If relativity were ignored, then the amount of cable moving through a given area (call it the "volume flow rate" or something) at a given place would be constant, otherwise the cable would bunch up or snap. How does that change in a relativistic context? $\endgroup$ Commented Apr 13, 2021 at 12:47

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