Perturbation theory in bohmian mechanics

Detlef Dürr, Stefan Teufel

Detlef Dürr, Sheldon Goldstein, Nino Zanghı̀

Arthur Fine, Sheldon Goldstein, James T. Cushing

Roy Herbert

Bohmian Perturbations as Admissible Continuity Branches Roy D. Herbert ORCID: 0009-0001-2132-2194 This work develops a continuity-first reconstruction of the Bohmian perturbation sector through the combined structures of covariant continuity, stability, recoverability, admissibility, and transport closure. The manuscript does not attempt to derive all of quantum mechanics from primitive continuity alone. Rather, it investigates a more specific question: whether the familiar Bohmian guidance structure emerges naturally as an admissible coherent branch of a continuity-preserving perturbative hierarchy. Beginning from covariant continuity, local exchange, perturbative stability, stress-energy closure, wave emergence, vorticity conservation, phase transport, and quantised circulation, the analysis recovers the standard amplitude-phase representation and the corresponding Bohmian guidance sector. The quantum-potential contribution is retained as part of the coherent branch action. As such, the work does not derive the Bohm curvature term directly from primitive continuity. Instead, it demonstrates how the standard Bohmian sector is recovered as the ideal admissible limit of a broader transport hierarchy and then extends that sector through a recoverability-dependent admissibility correction. A central contribution of the manuscript is the introduction of an admissibility functional that combines continuity closure, recoverability, persistence, and global phase consistency into a single branch-survival measure. In the ideal admissible limit the familiar Bohmian sector is recovered. Away from that limit, admissibility gradients generate corrections to the curvature-pressure sector, producing experimentally testable departures from the ideal branch. The manuscript develops explicit falsification criteria and proposes the relativistic Dirac-fluid regime of ultra-clean graphene as an empirical testbed. A phenomenological admissibility hierarchy is constructed using measurable transport quantities including viscosity, momentum relaxation, phase coherence, boundary exchange, and reconstruction loss. Order-of-magnitude estimates indicate that admissibility corrections may naturally occur within experimentally accessible transport scales. The work forms part of the broader Chronoflux continuity programme and draws upon earlier developments in covariant transport, recoverability, admissibility, and continuity closure. The present contribution should therefore be understood as a continuity-based reformulation of the Bohmian sector together with a falsifiable extension beyond the ideal coherent limit. Keywords: Bohmian mechanics, pilot-wave theory, quantum foundations, Madelung hydrodynamics, continuity equation, covariant continuity, admissibility, recoverability, persistence, transport theory, graphene, Dirac fluid, quantum hydrodynamics, phase transport, variational methods, perturbation theory, continuity closure, Chronoflux, mathematical physics.

Bohmian mechanics [1, 2] is a mechanical theory about the motion of particles. In contrast to quantum mechanics, Bohmian mechanics is a complete physical theory which leaves no interpretational freedom; in particular, it is free of paradoxes like Schrödinger’s cat. This completeness is achieved by introducing a definite configuration of particles for all times which is governed by the Bohmian velocity law. The predictions of Bohmian mechanics agree with those of quantum mechanics whenever the latter are unambiguous. Besides that, it turns out that in some situations the Bohmian velocity law is a convenient tool for the numerical integration of the Schrödinger equation. There is a lot of literature which explains the physical side of Bohmian mechanics, see e.g. Ref. [2]. The role of this chapter is to explain the advantages in using Bohmian mechanics for numerics.

E. Deotto, G. C. Ghirardi