In this video I tell you about the five currently most promising approaches to a theory of quantum gravity that physicists are presently pursuing. These are: string theory, loop quantum gravity, asymptotically safe gravity, causal dynamical triangulation, and emergent gravity.
I also explain why quantizing gravity per se is not actually the problem. The real problem is that the naive, perturbative, quantization is not UV-complete. I also briefly tell you why I think that solving this problem is so important.
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