Radial Accommodation in the Ehrenfest Problem A Conditional Layered-Ring Model with an Effective Covariant Phase-Stiffness Realization

Abstract

The Ehrenfest problem is traditionally formulated by considering an ideally Born- rigid disk accelerated from rest into uniform rotation. Tangential material elements are associated with local Lorentz contraction in an inertial laboratory frame, while radial elements are instantaneously perpendicular to the tangential motion and therefore do not undergo direct longitudinal Lorentz contraction. The further conclusion that the material radius must remain unchanged is, however, an additional mechanical assumption rather than a direct consequence of the Lorentz transformation. A conditional layered- ring construction is presented. Each concentric material ring is allowed to change its laboratory radius while preserving the sum of its local comoving circumferential lengths. Under this closure condition, the stationary radial map is r(ρ) = ρ / sqrt(1 + ω²ρ² / c²), where ρ is the initial material radius and ω is the angular velocity of the final stationary configuration. The construction preserves C_lab = 2πr on laboratory simultaneity slices while satisfying C_proper = γ C_lab = 2πρ. The kinematic construction is supplemented by an effective stationary radial- support model. Reducing a covariant spatial phase- gradient sector on a uniformly wound thin ring produces the proper circumference energy U_wind(C) = (K̅_s / 2) C [ (2πN / C)² - q₀² ]². Its minimum fixes the summed local comoving circumference to C₀ = 2π|N| / q₀, and near that minimum the reduced theory yields κ_eff = 4K̅_s q₀⁴ / C₀. In the strong- locking limit, the stationary thin ring satisfies C_proper = C₀, and the radial map follows exactly. A phenomenological fixed- ω radial Lagrangian gives a finite- stiffness radius correction and a local radial stability condition within that reduced model. The paper compares stationary nonrotating and uniformly rotating configurations. It does not model the transient spin- up process, a time- dependent torque law, or a Hamiltonian evolution between the two states. It also does not establish that all physical matter possesses the proposed phase sector or derive a complete continuous interacting disk. Finally, the geometric second moment of the mapped rest- mass distribution is derived; it must not be identified with the full relativistic dynamical moment of inertia. As a separate observational extension, a dimensionless orbital- transfer template is applied to the published osculating orbit of the Galactic- centre star S2. For unit transfer amplitude, the fi

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