What are the informational requirements for the curvature of space? If gravitational waves convey energy, then they also convey information, which means that the curvature of space contains information generally, which means that the information ingested in a black hole must be expressed in part in the curvature of space due to the increase in gravity. But the curvature of space does not create discrete bits of information around a large body consisting of many discrete particles. Electromagnetism is clearly quantised, but gravitational curvature appears smoothly singular regardless of the composition of the curving mass.
A single pulse wave is a soliton. Gravity for a single particle or a group of indistinguishably interacting particles behaves as if it forms a soliton in space around the particles, which may be disrupted by acceleration into propagating gravity waves.
If you think of gravitons as solitons you can see why they don’t provide much information. Solitons don’t interfere with one another destructively, so they don’t create an observable interference pattern, they just appear as a larger individual.
In the soliton model, each particle has a single gravitational wave, like a soliton bow wave, but in three dimensions. The size of the gravitational soliton is relative to the momentum and mass of its particles, as opposed to the velocity and area of the boat that creates a soliton in water. These waves combine when particles interact, (as in quantum entanglement), so that they appear to be one wave for any group of bound particles, scaled again to the total mass/momentum in the same way that a bow wave for many little boats bound together is the same as the bow wave of one big boat. Each discrete particle has only one graviton, but the gravitons do not interact like ordinary waves. Gravity may be quantised, but the quanta combine so perfectly with one another that there is no interactive distinction between them, and so no meaningful way to distinguish one wave from another except in terms of large bodies bleeding wave energy as they interact periodically, as with orbiting masses.
If gravity is a standing soliton wave around each particle in space. Each wave constructively interferes with nearby waves so that there is no quantum difference between the gravitation of interacting particles. The combined wave appears then as a curvature in space and time. It even has the shape of a wave increasing linearly from the centre of mass to the surface and then decreasing at the square of the radius from the surface into space. You could look at the graviton as a bow wave in space moving through time as a three dimensional analogy for a bow wave moving through water, but I don’t like using time as a function.
Time is a measure of distance. Distance is a measure of momentum. Momentum and mass are functions of information, but there is no information on position. There are no privileged observers, so space is made up of the relative momentum of particles, and nothing is located in a specific place in space, only in relative places with respect to each particle with which they could interact. Without at least one photon of communication, space is meaningless. The problem is not that quantum mechanics is incomplete. It is a complete view of the information multiverse. The problem is that there is no information in distance and time. Distance and time are in a state of continuous flux. You don’t fall because gravity pulls but because the distance between you and earth is decreasing. Distance and time both dilate continuously, so information about them can only be hypothecated probabilistically in terms of sets of identical particles and identical interactions. This is both the genius and the limitation of statistical mechanics.