Spacetime geometry of acoustics and electromagnetism

Abstract

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.

27 pages, 4 tables, for the Advances in Operator Theory with Applications to Mathematical Physics Conference, November 2022

References in corpus (28)

• Transverse and longitudinal angular momenta of light
• Extraordinary momentum and spin in evanescent waves
• The angular momentum controversy: What's it all about and does it matter?
• Dual electromagnetism: Helicity, spin, momentum, and angular momentum
• Constraining Early Dark Energy with Large-Scale Structure
• Gravity, Gauge Theories and Geometric Algebra
• Photon wave functions, wave-packet quantization of light, and coherence theory
• Electromagnetic duality symmetry and helicity conservation for the macroscopic Maxwell's equations (previously "Experimental demonstration of electromagnetic duality symmetry breaking")
• Magnetoelectric Effects in Local Light-Matter Interactions
• Conservation of the spin and orbital angular momenta in electromagnetism
• The role of the Riemann-Silberstein vector in classical and quantum theories of electromagnetism
• Quantum Spin of Elastic Wave
• Spin and orbital angular momenta of acoustic beams
• Observation of acoustic spin
• Weak Values are Interference Phenomena
• Axion-Dilaton Destabilization and the Hubble Tension
• Photon trajectories, anomalous velocities, and weak measurements: A classical interpretation
• Acoustic Radiation Force and Torque on Small Particles as Measures of the Canonical Momentum and Spin Densities
• Transverse spin and surface waves in acoustic metamaterials
• Force and torque on an electric dipole by spinning light fields
• The optical torque: Electromagnetic spin and orbital angular momenta conservation laws and their significance
• The magnetic and electric transverse spin density of spatially confined light
• Spacetime algebra as a powerful tool for electromagnetism
• Acoustic versus electromagnetic field theory: scalar, vector, spinor representations and the emergence of acoustic spin
• Resolution of a conflict between Laser and Elementary Particle Physics
• Klein-Gordon representation of acoustic waves and topological origin of surface acoustic modes
• Acoustic vortex beams in synthetic magnetic fields
• Detecting axions via induced electron spin precession