On the Causal Incompleteness of Entropic Information: A Theory of Rooted Causal Blocks
JOSE MARIA LANCHO RODRIGUEZ
Quantum information is usually characterized by a state available at a given time and by entropic or channel-theoretic quantities derived from it. We develop a broader operational framework in which entropic content is one coordinate of physical information ratherthan its exhaustive causal description. The primitive structure is an accessibility restriction CX together with an admissible intervention class F. Relative to it we distinguish entropic content S; total and quantum generative capacities GI and GE ; globally produced and regionally accessible causal ecacy gall and gX ; causal shielding fX ; and the local, distributed, recoverable and blocked records of a specied physical history. We retain and unify the mathematically stable results of the preceding programme: S does not determine G in a Rindler family; accessible causal ecacy has an asymmetry-resource structure and can be locked in correlations; horizons can suppress quantum generative structure while preserving entropic or classical content; and local QFT yields complete exterior shielding for genuinely localized, gauge-neutral interventions under the stated assumptions. Rooted causal blocks are introduced as history-labelled points in bres of the restriction map over a local carrier state. The Causal-Fibre Shielding and Recovery Theorem links local equivalence, complete shielding, distributed historical record and future recovery: equal local carrier states imply RX =gX =0, while global distinction implies positive external historical record, quantitatively lower-bounded by binary distinguishability, and any later common map that restores local distinction certies a recoverable fraction of that record. This makes precise the original photon hypothesis: local photon identity need not imply historical-causal identity. We further prove a Bekenstein causal non-exhaustiveness result: for a bounded carrier with xed local Hamiltonian and radius, equal local states have equal entropy, energy expectation and Bekenstein bound, yet may belong to distinct rooted blocks with dierent distributed record and causal futures. This does not violate the Bekenstein entropy bound; it rejects only its interpretation as a complete taxonomy of causal information. The horizon programme is restored through the generative causal residue and causal quality index q, treated as history diagnostics rather than established geometric hair. A structured Causal-Block Completion Hypothesis then introduces a possible universal sector C. In a minimal local scalar realization, Kallen-Lehmann positivity, response-noise consistency, coherent history writing and fth-force constraints turn completion into a positive-measure feasibility problem with a dual no-go certicate. Finally, we dene a microscopic historical causal tension as the extra eld energy required to make a rooted history compatible with present constraints. Its time integral supplies a candidate action scale. A Historical Tension Principle and Historical Backreaction are retained as stronger hypotheses: in a consistent two-boundary completion, the globally realized physical history could depend jointly on past and future boundary data. No alteration of the past is derived by the forward-time theorems. The resulting programme is a falsiable hierarchy from established information identities to a constrained candidate new eld and a separate two-boundary conjecture.
•Sep 5, 2026•0 citations