arXiv subjects

Lucas Burns

Publications and source records attributed to Lucas Burns.

4 recordsLinked to original sources

arXiv2025

Delayed Choice Lorentz Transformations on a Qubit

A continuously monitored quantum bit (qubit) exhibits competition between unitary Hamiltonian dynamics and non-unitary measurement-collapse dynamics, which for diffusive measurements form an enlarged transformation group equivalent to the Lorentz group of spacetime. We leverage this equivalence to develop a four-dimensional generalization of the three-dimensional Bloch ball to visualize the state of a monitored qubit as the four-momentum of an effective classical charge affected by a stochastic electromagnetic force field. Unitary qubit dynamics generated by Hermitian Hamiltonians correspond to elliptic spatial rotations of this effective charge while non-unitary qubit dynamics generated by non-Hermitian Hamiltonians or stochastic measurement collapse correspond to hyperbolic Lorentz boosts. Notably, to faithfully emulate the stochastic qubit dynamics arising from continuous qubit measurement, the stochastic electromagnetic fields must depend on the velocity of the charge they are acting on. Moreover, continuous qubit measurements admit a dynamical delayed choice effect where a future experimental choice can appear to retroactively determine the type of past measurement backaction, so the corresponding point charge dynamics can also exhibit delayed choice Lorentz transformations in which a future experimental choice determines whether stochastic force fields are electric or magnetic in character long after they interact with the particle.

quant-ph↗

arXiv2024

Spacetime geometry of acoustics and electromagnetism

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.

math-ph↗

arXiv2020

Acoustic versus electromagnetic field theory: scalar, vector, spinor representations and the emergence of acoustic spin

We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a ${\it scalar}$ potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement ${\it vector}$ potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether currents. The results are consistent with recent theoretical analyses and experiments. Furthermore, by an analogy with dual-symmetric electromagnetic field theory that combines electric- and magnetic-potential representations, we put forward an acoustic ${\it spinor}$ representation combining the scalar and vector representations. This approach also includes naturally coupling to sources. The strong analogies between electromagnetism and acoustics suggest further productive inquiry, particularly regarding the nature of the apparent spacetime symmetries inherent to acoustic fields.

physics.class-ph↗

arXiv2019

Maxwell's equations are universal for locally conserved quantities

A fundamental result of classical electromagnetism is that Maxwell's equations imply that electric charge is locally conserved. Here we show the converse: Local charge conservation implies the local existence of fields satisfying Maxwell's equations. This holds true for any conserved quantity satisfying a continuity equation. It is obtained by means of a strong form of the Poincaré lemma presented here that states: Divergence-free multivector fields locally possess curl-free antiderivatives on flat manifolds. The above converse is an application of this lemma in the case of divergence-free vector fields in spacetime. We also provide conditions under which the result generalizes to curved manifolds.

physics.class-ph↗