In introduction, I want to draw your attention to this quote from Carlo Rovelli, who is one of the principal developers of the theory of loop quantum gravity. He points out that there are no experimental or observational results that contradict the Standard Model, which is the synthesis of all of our accepted quantum field theories, or that suggest that the Standard Model is lacking in any way. The combination of the Standard Model and General Relativity describe all of the phenomena that have been observed to a remarkable degree of accuracy. Therefore, everything that I am going to discuss today and next time is purely speculative. There are, however, good theoretical reasons for constructing a quantum theory of gravity, as I will indicate later.

My talk will be primarily based on this book — "Three Roads to Quantum Gravity" by Lee Smolin. One thing that confused me when I first read the book is that Smolin's roads are not all quantum theories of gravity. They're ways of investigating spacetime on the smallest scales and all of them suggest that spacetime is discrete. The first road is consideration of the thermodynamics of black holes, independent of any previously developed fundamental theory. The second road is a theory called loop quantum gravity. And the last road is string theories.