Density Field Dynamics Resolves the Penrose Superposition Paradox

Abstract (Theoretical Physics; Preprint)

Penrose has argued that a quantum superposition of mass distributions leads to a structural inconsistency: in general relativity, each branch would source a distinct spacetime geometry, whereas quantum mechanics allows only a single state until collapse. We show that Density Field Dynamics (DFD), a scalar-field completion of Einstein’s 1911–12 variable-c program, avoids this paradox entirely. In DFD there is no manifold branching: superposed mass distributions source a single classical (c-number) refractive field ψ, which governs both light (n = e^ψ) and matter (a = c²/2 ∇ψ). In the weak-field linear regime (μ → 1), ψ is the convex sum of the branch fields; in the full quasilinear regime, monotonicity of the crossover function μ ensures existence and uniqueness of a single solution. Thus DFD is structurally compatible with quantum superposition, unlike GR, and the decisive discriminator remains laboratory testability: the co-located cavity–atom redshift comparison at two altitudes, where GR predicts zero slope and DFD predicts a geometry-locked slope of O(ΔΦ/c²) ~ 10^−14 per 100 m.