Penrose proposes that a quantum state remains in superposition until the difference of space-time curvature attains a significant level.
[1] Despite the difficulties of specifying this in a rigorous way, he proposes that the basis states into which the collapse takes place are mathematically described by the stationary solutions of the Schrödinger–Newton equation.
A microscopic system, like an electron, can exist in more than one location significantly longer (thousands of years), until its space-time curvature separation reaches collapse threshold.
Over time, an unstable system tends to settle back to its simplest, lowest-energy state: in this case, one object in one location producing one gravitational field.
He has proposed an experiment to test this theory, called FELIX (free-orbit experiment with laser interferometry X-rays), in which an X-ray laser in space is directed toward a tiny mirror and fissioned by a beam splitter from tens of thousands of miles away, with which the photons are directed toward other mirrors and reflected back.
If Penrose's hypothesis is correct, the mirror's superposition will collapse to one location in about a second, allowing half the photons to reach the detector.
[2] However, because this experiment would be difficult to arrange, a table-top version that uses optical cavities to trap the photons long enough for achieving the desired delay has been proposed instead.