Why Don't Quantum Mechanics and General Relativity Overlap?

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unchained1978
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I've been studying GR for 2 semesters now and am about to dive into quantum mechanics and so I thought it appropriate to ask this question. Why is it that Quantum theory and GR don't interlap at quantum scales? More generally, why doesn't QED fit into GR? fundamental concepts as well as specific examples are welcome.
 
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