Ever since the emergence of quantum theory in the 1920s, theoretical physicists have been attempting to reconcile the contradictions between Einstein’s general relativity, the classical theory of gravitation in curved spacetime, and quantum mechanics, which describes the behaviour of fundamental particles, atoms, and the very small. In the century people have puzzled over this problem, experiments and observations on scales ranging from laboratory bench tops to the entire universe have tested general relativity to ever greater precision, while quantum mechanics has been tested by massive particle accelerators, electronics devices, super-cold experiments, chemistry, and even communication between spacecraft and the ground. In all of this time, no experiment has produced results that differ from predictions of the theories.
This has only deepened the mystery, since there are known to be places and epochs in the universe, such as in the vicinity of black holes and in the very early universe, where both theories are equally important in understanding phenomena, and the theories just don’t fit together mathematically. The holy grail has been finding a theory of quantum gravity which resolves the contradictions, but every theorist who has tried to find such a theory has failed, quickly running into ridiculous predictions at variance with the simplest observations and/or common sense.
Experimentalists have offered no guidance. Every attempt to find phenomena that might indicate quantum corrections to classical general relativity have come up empty, gravity is dozens of orders of magnitude too weak to affect experiments in quantum mechanics, and some theorists believe that any apparatus which could detect such phenomena would inevitably immediately collapse into a black hole, which would prevent the intrepid researchers from publishing their results.
What if gravity isn’t quantised? Maybe both general relativity and quantum mechanics are effective theories, based upon the 19th century mathematics of the continuum, each valid in its own domain, but only approximations to a deeper level which may be very different, perhaps, as Stephen Wolfram suggests and is actively investigating, some kind of discrete structure (perhaps Star Trek was on to something with “subspace”) that is performing a kind of simple computation.
Here is Freeman Dyson in 2013 discussing whether any detector which can be constructed within our universe could possibly detect a graviton, providing direct evidence for quantum gravity.