From Quantum to Cosmos: The Hawking Information Paradox -- Full Quantum

Description (English) We present a full quantum formulation in which gravity and matter inhabit a common Hilbert space, and dynamics is governed by an operator version of Einstein’s equation. Composite operators are defined via a covariant Planck-scale averaging over the invariant two-measure:σₚ := ℓₚ·tₚ = ħ·G / c⁴.The central operator constraint holds in the weak (distributional) sense, preserving diffeomorphism covariance and conservation: ( Ĝ_{μν} − (8πG/c⁴) T̂_{μν} )^{(σₚ)} |Ψ⟩ = 0. Time evolution can be formulated in ADM Schrödinger or Tomonaga–Schwinger form. The mass operator is m̂ = Ĥ / c², so iħ ∂ₜ|Ψ⟩ = Ĥ|Ψ⟩ = c² m̂ |Ψ⟩.No constants beyond {ħ, c, G, k_B} are introduced. The framework predicts small, structured non-thermality of Hawking radiation at O(ε²) withε = max{ τ·κ/c, L/r₊ } (surface gravity κ, correlation time τ, coarse-graining scale L, horizon radius r₊), Implying a smooth, unitary Page curve without islands. Beschreibung (Deutsch): Wir stellen eine vollquantische Formulierung vor, in der Gravitation und Materie einen gemeinsamen Hilbertraum teilen und die Dynamik durch eine operatorielle Einstein-Gleichung bestimmt ist. Zusammengesetzte Operatoren werden über eine planck-kovariante Glättung auf der invarianten Zweimaß: σₚ := ℓₚ·tₚ = ħ·G / c⁴ definiert. Die zentrale Operatorbedingung gilt im schwachen (distributionellen) Sinn und bewahrt Diffeomorphismus-Kovarianz sowie Erhaltungssätze:( Ĝ_{μν} − (8πG/c⁴) T̂_{μν} )^{(σₚ)} |Ψ⟩ = 0. Die Zeitevolution kann in ADM-Schrödinger- oder Tomonaga–Schwinger-Form gegeben werden. Der Massenoperator ist m̂ = Ĥ / c², somit iħ ∂ₜ|Ψ⟩ = Ĥ|Ψ⟩ = c² m̂ |Ψ⟩. Es werden keine Konstanten über {ħ, c, G, k_B} hinaus eingeführt. Das Rahmenwerk sagt eine kleine, strukturierte Nicht-Thermalität der Hawking-Strahlung bei O(ε²) voraus, mitε = max{ τ·κ/c, L/r₊ } (Oberflächengravitation κ, Korrelationszeit τ, Glättungsskala L, Horizont-Radius r₊) und führt zu einer glatten, unitären Page-Kurve ohne „Islands“. Related Works: 10.5281/zenodo.16933270 Zander, A. (2025). From Quantum to Cosmos: The Natural Law of Quantum Fields General Relativity 10.5281/zenodo.15578802 Zander, A. (2025). From Quantum to Cosmos: About Space and Time, Mass and Inertia (Also includes every Paper in an extra Zip in English): 10.5281/zenodo.16925937 Zander, A. (2025). From Quantum Structure to Galactic Rotation: Eliminating Dark Matter with Planck-Covariant Gravity.10.5281/zenodo.16925299 Zander, A. (2025). From Quantum to Cosmos: ZE-Qubit10.5281/zenodo.16925145 Zander, A. (2025). From Quantum to Cosmos - Schrödinger-Zander and Einstein-Zander Equation10.5281/zenodo.16924975 Zander, A. (2025). From Quantum to Cosmos – No Singularities: Planck-Covariant Averaging as Natural Cutoff10.5281/zenodo.16922391 Zander, A. (2025). From Quantum to Cosmos - Planck Two-Measure: Vacuum Catastrophe Fixed, Muon g-2 Consistent10.5281/zenodo.16921499 Zander, A. (2025). From Quantum to Cosmos: Solving the Λ Problem via (ℓₚ·tₚ)/(Rₒᵦₛ·t₀) ⇒ α_σ ≈ 4.60×10⁻¹²³ ⇒ Λ = α_σ/ℓₚ² ≈ 10⁻¹²³10.5281/zenodo.16929728 Zander, A. (2025). From Quantum to Cosmos: The Hawking Information Paradox -- Full Quantum10.5281/zenodo.16929833 Zander, A. (2025). From Quantum to Cosmos: Defusing the Hubble Tension with Planck-Covariant Spacetime Fine-Structure 10.5281/zenodo.16929899 Zander, A. (2025). From Quantum to Cosmos: Planck-Covariant Flavor: Fermion Mass Hierarchies Without New Sectors10.5281/zenodo.16929940 Zander, A. (2025). From Quantum to Cosmos: A Planck-Covariant, Unitary Solution to the Measurement Problem10.5281/zenodo.16910481 Zander, A. (2025). From Quantum to Cosmos: The Hawking Information Paradox Solved (3+1D, No Islands)10.5281/zenodo.16930310 Zander, A. (2025). From Quantum to Cosmos: A Requiem for LCDM - full Scientific + Extra Paper for readers without specialized background Contact & SupportAdrian Zander (Independent Researcher)[email protected]: 0009-0005-2388-5440 Support Scientific Continuation:IBAN: DE73 6149 0150 0132 6850 00BIC: GENODES1AAVReference: Zander Research