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In the GR Einstein's interpretation was in terms of a deformation of the geometry of the space ending in a curvature of spacetime.

I've thought that mass could do this by interacting with other mass and causes gravitational waves which makes the space curved. But a prof told me that this isn't the case. For example the gravitational waves caused between the earth and the sun is just a very tiny effect which causes spiraling earth to the sun which is of little effect.

So mass is establishing the geometry of the space and the time. But the question remains how is mass doing that (curving spacetime)?

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  • $\begingroup$ That is a defining characteristic of "mass" in GR. That is what it does. If you are asking how do you derive the GR field equations, then I don't think there is any answer. $\endgroup$
    – ProfRob
    Commented Mar 10, 2016 at 20:53

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In general relativity, the curvature of spacetime is an interpretation of the model for gravity: Starting with the assumptions of gravity being equivalent to acceleration, and the speed of light being constant, a mathematical framework that describes gravity is developed. The mathematical conclusion of this model is that the distances between points is dependent on the distribution of mass and energy. A simple way of describing this is to say that spacetime is curved.

In GR, the apparent force of gravity is explained by the curvature of spacetime. It is reasonable to ask if there is a more fundamental theory that can explain the curvature. String theory provides one possibility. In string theory it is possible to deduce the existence of a particle that would be a graviton, and the from that the field equations that describe gravity. In other words, string theory can predict exactly the same mathematical formulae that arise from curved spacetime in GR. However, on very small scales, string theory makes a series of corrections to the field theory, suggesting that the curvature of spacetime is actually an approximation, which is valid on the large scale, to a string theory of gravity.

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  • $\begingroup$ Do you think that virtual particles in the quantum vacuum can interact with gravitons to curve spacetime? $\endgroup$
    – Marijn
    Commented Mar 11, 2016 at 13:50
  • $\begingroup$ The equations are the model. "curvature of spacetime" is an interpretation of the equations. $\endgroup$
    – James K
    Commented Mar 11, 2016 at 16:44
  • $\begingroup$ Newton had declared the orbits of the planets due to an action at distance. But Einstein didn't really like 'spooky action at a distance'. But is his theory of GR really isn't such a thing $\endgroup$
    – Marijn
    Commented Mar 13, 2016 at 9:10
  • $\begingroup$ Yes, GR is a classical theory, in that it doesn't incorporate quantum mechanics. There is "action at a distance" in GR, the presence of a mass causes the curvature of (distant) spacetime. There is no instantaneous action at a distance (and nor is there in QM either). There is no complete and consistent quantum theory of gravity, but string theory is one of the contenders. $\endgroup$
    – James K
    Commented Mar 13, 2016 at 16:40
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    $\begingroup$ There is no answer beyond Rob's comment: "That is a defining characteristic of 'mass' in GR". GR is a model formed by various equations. The interpretation of these equations is that spacetime is curved. GR doesn't provide a mechanism for the curvature of space, only a description. A mechanism may not exist, or it may come from some quantum theory of gravity, such as strings. $\endgroup$
    – James K
    Commented Mar 14, 2016 at 21:34

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