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I read, long ago, a book, whose title I can't remember but I think the author was Carl Sagan. In the book was saying that gravity follows the inverse square law because of our Universe was 3 dimensions of space. (I'm obviously not taking into account string theory which states that are extra dimensions). By this logic, if the Universe had 4 spatial dimensions the law would be 1/r^3 and if there were 5 dimensions, it would be 1/r^4.

So my question is: is this true? And if it is, could you elaborate and state exactly how do we know this is true? I think this might be related to GR theory, but I'm not very sure. Thank you in advance.

Qmechanic
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    See https://en.wikipedia.org/wiki/Inverse-square_law#Field_theory_interpretation. – HDE 226868 Dec 18 '15 at 01:45
  • general Stokes theorem applied to a flow through a n-sphere around a dot. It is a mathematical model suitable for the case. Nobody knows what would happen in the physical world if it has more than 3 spacial dimensions , before a measures campaign :) –  Dec 18 '15 at 02:25

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