If there was a quantum theory of gravity, what would it describe, and why would it be useful?

Answer 1

It would be useful for describing the very earliest stages of the universe,when both quantum and gravitation effects were of similar magnitude. It would clarify processes near the event horizon of black holes. It might be useful for explaining certain particle properties, such a their mass, that are currently phenomenological parameters (ie, must be measured) in the "Standard Model". But most importantly, it would bring us closer, or indeed represent, the ever elusive "Theory of Everything" that explains, well, everything. As for *practical* applications, perhaps nothing, or perhaps a new amazing form of matter can be made using the knowledge. We'll have to wait to see what the theory has in store for such things after it's discovered before you can answer such a question.

Answer 2

A gent by the name of DeBroglie speculates that all mass has a characteristic wavelength. Therefore all mass, no matter how big or small, is subject to the Heisenberg Uncertainty Principle, which is a major tenet of quantum theory. And all mass, no matter how big or small, can be described as packets of energy with a discrete wavelength.

If someone were to find how to explain gravity in terms of a DeBroglie wave, that would unify the four forces: gravity, EM, and the strong and weak atomic forces. The non-gravity forces are already covered by quantum mechanics.