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What makes Quantum mechanics and the General Theory of Relativity incompatible? : r/askscience

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I am reading The Elegant Universe by Brian Green. Right at the beginning Brian says that Quantum mechanics and General Theory of Relativity aren't compatible with each other, ie, they both can't coexist under the same set of laws. But he never explains and details what's making it so. Can someone enlighten me where they clash? It's a pretty technical issue that has to do with renormalization, in that quantum general relativity is nonrenormalizable, as opposed to the standard model which is renormalizable. We could talk about renormalization for days and we wouldn't even begin to scrape the surface. I'll try the best I can here to reduce the issue to its lowest terms, at the cost perhaps of being imprecise. Classically (meaning, not quantum mechanically) a field theory is specified by which fields you have, which type of interactions are there between the fields, and what the strength of the interactions is. For example, in GR the field is the gravitational field (plus other fields for

It's a pretty technical issue that has to do with renormalization, in that quantum general relativity is nonrenormalizable, as opposed to the standard model which is renormalizable. We could talk about renormalization for days and we wouldn't even begin to scrape the surface. I'll try the best I can here to reduce the issue to its lowest terms, at the cost perhaps of being imprecise. Classically (meaning, not quantum mechanically) a field theory is specified by which fields you have, which type of interactions are there between the fields, and what the strength of the interactions is. For…

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