Unified Field Equation derived from natural Λ: (ℓₚ·tₚ)/(Rₒᵦₛ·t₀) ⇒ α_σ ≈ 4.60×10⁻¹²³ ⇒ Λ = α_σ/ℓₚ² ≈ 10⁻¹²³ ⇒ ρ_vac^(σ) ≈ α_σ·ħ·c / ℓₚ⁴

Update This work develops a unified field framework based on the Planck two-measureσₚ = ℓₚ·tₚ = ħ·G / c⁴,interpreted as the fundamental quantum of spacetime.Without introducing new fields or adjustable parameters, this scale simultaneously regulates vacuum fluctuations and point singularities.A single dimensionless numberα_σ = σₚ / (R·t)links microscopic and cosmological domains, leading to: – a dynamic cosmological term Λ_eff(t) ≈ α_σ / ℓₚ² that explains cosmic acceleration without dark energy,– the removal of curvature singularities via Planck-covariant source smearing,– and a parameter-free interpolation law that reproduces galactic rotation curves and the radial acceleration relation without dark matter. A key technical element is the covariantly windowed path integral, which replaces both IR and UV divergences with a finite causal domain (R, t) and a Planck minimal cell σₚ.This yields the universal scalingρ_vac^(σ) ≈ α_σ·ħ·c / ℓₚ⁴and provides a first-principles derivation of the observed cosmological constant. The result is a scale-covariant, observer-compatible structure that unifies geometry, vacuum energy, and galactic dynamics using only the constants {ħ, c, G, k_B}. Description We present a non–ad-hoc unification of Quantum Field Theory, Special Relativity, and General Relativity as natural laws, derived directly from the constants {ℏ, c, G, kB}. The core object is the Planck two–measure:σₚ = ℓₚ·tₚ = ℏG/c⁴,a quantized spacetime cell. From this follows a direct, testable prediction for the cosmological fine-structure number:ασ = σₚ / (R_obs·t₀) ≈ 4.60 × 10⁻¹²³,Λ = ασ / ℓₚ² ≈ 10⁻¹²³. Thus, Λ is not “dark energy” but the natural fine-structure of spacetime itself.At galactic scales, the same σₚ-field explains rotation curves and the RAR/BTFR relation without dark matter halos. ≈95% of the cosmic energy budget attributed to “dark” components in ΛCDM is explained naturally by the σₚ-field:– “Dark energy” = global fine-structure Λ = 1/(cRt),– “Dark matter” = emergent low-g response. -> Quantum Gravity The framework keeps curvature invariants finite, eliminates singularities, and reveals that inertia, curvature, and oscillation are one law:mc² = hf. All results follow directly from natural constants and measured (R, t), with no exotic fields or hidden sectors. Kids’ Talk: The Universe as a Carpet Imagine the world as a giant carpet made of tiny tiles.Each tile is a σₚ-cell — the smallest building block of spacetime. Things with mass press on the carpet and make it vibrate: Pressing ⇒ Curvature (GR). Vibrating ⇒ Ticking/Oscillation f = mc²/h (QFT). The vibration runs across the carpet at a fixed tempo: c, the speed of light. Very, very far away you can see a faint texture of the carpet itself:Λ = 1/(c·R·t).This is not a “mysterious dark energy,” but simply the natural fine-texture of the spacetime carpet. And flat galaxy rotation curves?That is how the carpet yields elastically under weak pressure —no invisible matter is needed. Kids’ Talk: The Universe as a Brain Imagine the universe as a giant brain. Neurons = Mass/Energy. Synapses = spacetime cells σₚ = ℏG/c⁴. Fine-structure = the network architecture ασ ≈ 10⁻¹²³. Signals = Information flow at ℓₚ/tₚ = c. Things with mass are neurons pressing on the spacetime brain, making it curve (GR).At the same time, they vibrate and tick (QFT: f = mc²/h).The signal runs across the network at a fixed tempo (c, the speed of light). And the faint texture we see from far away? That is Λ = 1/(c·R·t), the fine texture of the brain itself — not a mysterious dark energy.Flat galaxy rotation curves? That is how the brain’s network yields elastically under weak pressure — no invisible matter is needed. Deutsche Beschreibung Quantengravitation als planck-kovariantes FrameworkDiese Arbeit entwickelt ein minimales, nicht-ad-hoc Framework für die Quantengravitation, das direkt auf den Naturkonstanten {ħ, c, G, kB} basiert.Im Zentrum steht das invariante Planck-Zweimaß: σₚ = ℓₚ · tₚ = ħG / c⁴, das das fundamentale Raumzeitquantum definiert. Diese Struktur reguliert Krümmungen, verhindert Singularitäten und verbindet Quantenmechanik und Allgemeine Relativität konsistent über alle Skalen hinweg. Zentrale Ergebnisse: Lösung des kosmologischen Konstantenproblems durch die Raumzeit-Feinstruktur αₛ = σₚ / (R·t) ≈ 4.6 × 10⁻¹²³. Flache Rotationskurven von Galaxien ohne Dunkle Materie durch σₚ-kovariantes Mittel. Konsistente Operator-Brücke: E = mc² = hf, wobei Masse, Energie und Frequenz in einem einzigen Formalismus verknüpft sind. Ein einheitliches Gleichungssystem (Einstein–Zander und Schrödinger–Zander), gültig von Mikro- bis Makroskalen. Kurzum: Quantengravitation erscheint nicht als spekulative Erweiterung, sondern als natürliche Konsequenz der Planck-Struktur — eine Welt, ein Framework, keine künstliche Trennung von Mikro- und Makrophysik. 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