Quantum mechanics from some viewpoints seems to suggest reality is discontinuous. While much of the debate is purely about what empirical reality is like, only parts of the problems in quantum theory might be called ‘metaphysical’, which scientists in the field try to ignore as they can’t always be resolved by an experiment.
Some features of the world at a quantum level suggest ‘discreteness’ is a very deep property of quantum objects and interactions, however there are also other properties between interacting quantum entities (such as non-locality) which seem to suggest reality is more like a unified whole. Like many problems which raise the metaphysical problem of the ‘one and the many’, resolving this is a sort of logical dialectic where both perspectives are integrated into a wider and more inclusive view which allows the phenomena to make more sense.