  We combine hydrodynamic and field theoretic methods to develop a general
theory of phonons as Goldstone bosons in crystals, glasses and liquids based on
non-affine displacements and the consequent Goldstones phase relaxation. We
relate the conservation, or lack thereof, of specific higher-form currents with
properties of the underlying deformation field -- non-affinity -- which
dictates how molecules move under an applied stress or deformation. In
particular, the single-valuedness of the deformation field is associated with
conservation of higher-form charges that count the number of topological
defects. Our formalism predicts, from first principles, the presence of
propagating shear waves above a critical wave-vector in liquids, thus giving
the first formal derivation of the phenomenon in terms of fundamental
symmetries. The same picture provides also a theoretical explanation of the
corresponding "positive sound dispersion" phenomenon for longitudinal sound.
Importantly, accordingly to our theory, the main collective relaxation
timescale of a liquid or a glass (known as the $\alpha$ relaxation for the
latter) is given by the phase relaxation time, which is not necessarily related
to the Maxwell time. Finally, we build a non-equilibrium effective action using
the in-in formalism defined on the Schwinger-Keldysh contour, that further
supports the emerging picture. In summary, our work suggests that the
fundamental difference between solids, fluids and glasses has to be identified
with the associated generalized higher-from global symmetries and their
topological structure, and that the Burgers vector for the displacement fields
serves as a suitable topological order parameter distinguishing the solid
(ordered) phase and the amorphous ones (fluids, glasses).
