Loop Quantum Gravity (LQG) is a theory of quantum spacetime that attempts to describe the interconnection between general relativity and quantum mechanics. It's main postulate is the granularity of space on the quantum scale. Though, is there an experiment that can disprove it?
Some ideas of an experiment:

How can we test for the granularity of space and is there any feasible experiment that can be able to test this hypothesis of LQG in the near future?

Are there any consequences of LQG that have already been experimented with and exploited in that they can be potentially disproved with a similar subsequent experiment?

What are some theories of quantum gravity that explore the same or similar framework as LQG, and are there any experiments that can disprove those theories which will also impact LQG?
Best Answer
So, "phenomenological quantum gravity" is the particular field where we consider experimental tests of quantum gravity (with the hopes of winnowing the 3 dozen competing theories down to a handfull). To the best of my knowledge, Giovanni AmelinoCamelia pioneered the field (c.f., AmelinoCamelia's review article).
At any rate, when focusing on loop quantum gravity, there have been a few preprints. Most deal with the phenomology of loop quantum cosmology, but this one appears more general:
I think it's precisely what the OP is looking for...