The Limit of the Propositional Lens: Why Physics Cannot Solve Its Own Frontier Problems

We identify the structural limit of the propositional lens through which modern physics describes reality. Physical theories formulated exclusively in terms of local field equations on a differentiable manifold—what we call propositional field physics—cannot determine their own vacuum state, and hence their own background metric, from within their own algebra. The obstruction is formal, not technical: it arises from the non-uniqueness of unitarily inequivalent vacuum representations in curved spacetimes (Fulling–Davies–Unruh), combined with the tension between locality of the field equations and diffeomorphism equivariance of any selection rule. We formalize this tension in the language of equivariant fibre bundles. We draw an explicit analogy with Gödel’s first incompleteness theorem, identifying the physical analogue of the undecidable sentence. State selection requires an external operational structure: a self-adjoint recognition generator Kˆ acting on a composite Hilbert space HA ⊗ HT , whose open Lindblad dynamics implements the missing selection at the level of individual quantum trajectories (quantum-jump unravelling). We make the ensemble/trajectory distinction mathematically precise and show that the physical metric is the trace of a particular operational history, not of the ensemble. Spacetime geometry and rest mass emerge as measurement invariants of this operational cycle. The frontier problems of physics—singularities, the measurement problem, information loss—are not failures of the world but symptoms of the lens. This is the English version of the work El límite de la lente proposicional: Por qué la física no puede resolver sus propios problemas de frontera, also available in Spanish: https://doi.org/10.5281/zenodo.22820030