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The amplitude of quadrupole radiation is proportional to the source's value of $d^3 x/dt^3$. This applies to both electromagnetic radiation and gravitational radiation (for which quadrupole radiation is the lowest possible multipolarity).


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As far as we can tell (up to energy scales we've measured so far), spacetime is a nice and smooth manifold. It might happen that the smoothness is approximate and spacetime is discrete at a much more microscopic scale, or it could turn out that spacetime is smooth all the way through. Short answer: We don't know. About the notion of energy quantization: ...



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