The atomic theory as first theorised by Democritus has been successfully applied to matter and to energy (quanta).
Space-time is still generally seen as a continuum. What arguments are there (if any) in support of there being a particulate structure of space-time?
If you believe that quantum theory (Hilbert space + Hamiltonian) describes our world, then we need to believe that the quantum theory for a space with a finite volume has a finite dimensional Hilbert space. This （plus locality) implies an atomic structure of space:
Space = a collection of many many qubits.
Vacuum = the ground state of the qubits.
Elementary particles = collective excitations of the qubits.
