  We examine the phase shifts and inelasticities associated with the
$N^*(1440)$ Roper resonance and connect these infinite-volume observables to
the finite-volume spectrum of lattice QCD using Hamiltonian effective field
theory. We explore three hypotheses for the structure of the Roper resonance.
All three hypotheses are able to describe the scattering data well. In the
third hypothesis the Roper resonance couples the low-lying bare basis-state
component associated with the ground state nucleon with the virtual
meson-baryon contributions. Here the non-trivial superpositions of the
meson-baryon scattering states are complemented by bare basis-state components
explaining their observation in contemporary lattice QCD calculations. The
merit of this scenario lies in its ability to not only describe the observed
nucleon energy levels in large-volume lattice QCD simulations but also explain
why other low-lying states have been missed in today's lattice QCD results for
the nucleon spectrum.
