Consider an infinite homogeneous static universe with a constant mass density $$\rho$$. If we were to calculate the force on a test particle located at a certain point accoring to Newtons law of gravity. It would be logical to conclude from a symmetry argument that the force on the particle should be zero. But is this true? For as we know, the force on that particle depends on how we are adding up the contributions of mass in the universe. So one way to calculate the force will give a 0 net force on the particle, and another way of doing it will give a net force in a certain direction. In fact, depending on how we do the sum, we can come to the conclusion that the particle can be subject to any force, even an infinite force.(adsbygoogle = window.adsbygoogle || []).push({});

So how is this problem resolved? From a mathematical standpoint it should have a solution.

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# I Homogeneous static universe

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