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What relative effects be for an object with near light speed velocity in compactified dimensions?

Does gravity increase the same as for an object with near light speed velocity in usual spacial dimensions?

What does it happen if size of compactified dimensions is much less than uncertainty principle scale (for corresponding impulse of the object with near light speed velocity)?

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  • $\begingroup$ By compactified dimension you mean you add a point at infinity? Normally space extends as far as you like, but doesn't get to infinity. Compactified space does. I wouldn't think this kind of space is representative of flat physical 3 space. For example, all continuous functions on a compact space are bounded. So you can't have a rocket traveling in a straight line at constant acceleration forever, with an unbounded velocity. It would be more suitable to a rocket on a circular track, where every time it goes around it has the same velocity at the same point. $\endgroup$ – mmesser314 May 15 '16 at 1:37
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    $\begingroup$ Compactified dimension are additional small-sized rounded dimensions in string and superstring theories. It means: x = x + 2*pi*R. $\endgroup$ – Dmitry May 15 '16 at 1:42
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A very peculiar fact is that in a compact space THERE IS a preferred inertial system. Indeed even if locally there is no way to single out a preferred inertial system, globally you can do it. Is the topology that tells you that an observer doing a loop around a torus is topologically different from an observer moving around simply connected loops.

So for instance, the twin paradox is solved in this space too, and the observer traveling around a not simply connected loop is younger than his twin. For references see: Twin Paradox in a Torus

For the second question, I guess that that dimension would be negligible from the point of view of extended dimensions. Nevertheless many quantum gravity theories seems to suggest that spacetime is an emergent phenomenon so I'm not sure that insisting with the classical spacetime picture at energies near the Planck scale is still meaningful.

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