  Both acoustics and electromagnetism represent measurable fields in terms of
dynamical potential fields. Electromagnetic force-fields form a spacetime
bivector that is represented by a dynamical energy-momentum 4-vector potential
field. Acoustic pressure and velocity fields form an energy-momentum density
4-vector field that is represented by a dynamical action scalar potential
field. Surprisingly, standard field theory analyses of spin angular momentum
based on these traditional potential representations contradict recent
experiments, which motivates a careful reassessment of both theories. We
analyze extensions of both theories that use the full geometric structure of
spacetime to respect essential symmetries enforced by vacuum wave propagation.
The resulting extensions are geometrically complete and phase-invariant (i.e.,
dual-symmetric) formulations that span all five grades of spacetime, with
dynamical potentials and measurable fields spanning complementary grades that
are related by a spacetime vector derivative (i.e., the quantum Dirac
operator). These complete representations correct the equations of motion,
energy-momentum tensors, forces experienced by probes, Lagrangian densities,
and allowed gauge freedoms, while making manifest the deep structural
connections to relativistic quantum field theories. Finally, we discuss the
implications of these corrections to experimental tests.
