  Inelastic neutron scattering is used to measure the spin excitation spectrum
of the Heisenberg $S=1/2$ ladder material (C$_7$H$_10$N)$_2$CuBr$_4$ in its
entirety, both in the gapped spin-liquid and the magnetic field induced
Tomonaga-Luttinger spin liquid regimes. A fundamental change of the spin
dynamics is observed between these two regimes. DMRG calculations
quantitatively reproduce and help understand the observed commensurate and
incommensurate excitations. The results validate long-standing quantum field
theoretical predictions, but also test the limits of that approach.
