Before we continue our exploration of quantum gravity, I want to remind you that, as Carlo Rovelli states in this quote, there don't seem to be any compelling observational or experimental reasons to seek a quantum theory of gravity. The motivations are theoretical and mainly stem from incompatibilities between our current theory of gravity, general relativity, and the quantum field theories that describe the other three fundamental physical forces. General relativity and quantum fields theories make contrary assumptions regarding the nature of space and time and about the relationships between observers and the systems they study. Efforts to create a viable quantum theory of gravity attempt to reconcile these differences.

As before, what I'm about to say will mostly be based on Lee Smolin's book "Three Roads to Quantum Gravity". Smolin's roads are ways of investigating the nature of space and time on the smallest scales and consist of consideration of the thermodynamics of black holes, the theory of loop quantum gravity, and string theories. All of the approaches indicate that spacetime is composed of tiny, indivisible units.