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Assuming the mass of the universe was spread completely evenly throughout space why would gravitational attraction happen? All bodies in the universe would feel gravitational tug equally in all directions so why would they go anywhere?

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If one assumes the question in Newtonian dynamics (as distinct from gr) then the answer is that Newtonian gravity for an infinite uniform matter distribution in flat space is inconsistent. This can be shown from the equations of Newtonian gravity, in which the problem is that the integrals over all space do not converge, but a simple argument can also be found from Newton's shell theorem.

Let mass density be constant, $\rho$. Take any two points, $\mathrm A$ and $\mathrm O$, a distance $R=\mathrm {OA}$. According to Newton's shell theorem the gravitational force at $\mathrm A$ due to any spherical shell containing $\mathrm A$ and centred at $\mathrm O$ is zero. The gravitational acceleration due to matter inside a sphere of radius $R$ centred at $\mathrm O$ is $$ \frac {4\pi} 3 G \rho R $$

In other words the gravitational tug does not cancel out, but is towards $\mathrm O$, which is clearly inconsistent because $\mathrm O$ can be any point in the universe.

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  • $\begingroup$ I assume general relativity resolves the contradiction? $\endgroup$ – Derek Seabrooke Sep 14 '20 at 5:02

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