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This may be an elementary question, but if gravity causes a curvature in spacetime, then why isn't everything distorted when looking down on earth, or up at the moon? Shouldn't there be a pincushion effect when viewing an object that is bending spacetime?

I understand that being here on the surface of the earth, everything relative appears normal, but far away, shouldn't it all look warped?

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The bending is very subtle until you approach the gravitational field of a black hole. 1 / c^2 is a tiny number –  Pieter Geerkens Sep 6 '13 at 21:33
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The distortion caused by the moon and the earth is too small. But it has been observed for larger bodies, see deflection of light by the Sun, and gravitational lensing.

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That's amazing. It makes me wonder what kind of spacial curvature there was before the big bang, when there was thought to have only been a singularity. –  user29303 Sep 6 '13 at 23:46
    
@user29303: General relativity predicts singularities at the Big Bang. One approach is to introduce quantum effects that may avoid the initial singularity, as in arxiv.org/abs/0812.0177. Another possibility is to see what really happens in general relativity, how bad are those singularities. It turns out that they are not that bad, that they can be described in terms of finite quantities (arxiv.org/abs/1112.4508, arxiv.org/abs/1203.1819, arxiv.org/abs/1203.3382). In both cases, the solutions can be extended past the Big Bang. –  Cristi Stoica Sep 7 '13 at 8:24
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