The speaker says general relativity, the best theory of gravity, and quantum mechanics, the theory of how things behave at the smallest scales, are currently two completely separate theories. General relativity deals with the very big and makes concrete predictions, whereas quantum mechanics deals with the very small, where things are governed by probabilities, even for the location of a specific particle. What is missing is a unified theory combining the two. The speaker says this is not for lack of trying, and that people have tried for decades.
The speaker says a unified theory would help with the black hole question because in theories of quantum gravity, matter, space, and time cannot be infinitely compressed. The universe would then have a finite pixel scale, giving the ring singularity a very small but finite edge and giving spacetime curvature that is extreme but finite. The hope is that in such a theory, one is no longer in an infinite curvature state, so closed time loops do not form, mass inflation does not happen, and everything becomes deterministic again, though probabilistic as in quantum mechanics for small particles. The speaker stresses that this theory does not yet exist.
The speaker notes that a theory of quantum gravity has long felt like a pipe dream and will not arrive overnight. It took about 230 years to get from Newtonian gravity to Einstein's general relativity, so the speaker suggests it may take another 100 years before a theory explaining what happens to time inside a black hole is finally available. The speaker closes by saying perhaps only time will tell.