Thinking about the hypothetical dark matter, I came to the following (primitive) thought experiment. Consider a large sphere (say radius R) filled uniformily with matter and a small test mass located at radius R1. This test mass will experience a force to the centre of the sphere and the strenght of this force is proportional to the mass content of the sphere limited to R1 (the effect of the outer mass cancel outs, as is well known). Now, increase the radius R to a very large value. Again, the force should remain the same. In fact, one can make R arbitrarily large.(adsbygoogle = window.adsbygoogle || []).push({});

So, now consider aninfinitespace, filled uniformily with matter. The test mass will now not experience a force towards a specific direction, because of symmetry.

So, one gets the strange thing that there is a difference between R being arbitrary large and R being infinite. What does this mean ?

Rudi Van Nieuwenhove

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# A paradox ?

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