Quantum Gravity Dynamics: Dark Matter and Dark energy from Quantum Gravity in Dirac Spinor Fields deriving General Relativity
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2026
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| _version_ | 1866901977971032064 |
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| author | Matshaba, Romeo |
| author_facet | Matshaba, Romeo |
| contents | <p>We present Quantum Gravity Dynamics (QGD), deriving classical gravity from quantum wavefunction structure in flat Minkowski spacetime.</p> <p>Core formalism: Bridge equation |ψ|²=C/|p| connects quantum amplitude to classical momentum. All stress-energy (mass ρ, pressure P, angular momentum J, EM field F, Λ) enters unified denominator Δ = E + mc² + ∫ρc²dV - ∫PdV - J²/(2mr²) + V_EM + ρ_Λ.</p> <p>Complete wavefunction: ψ = (GMm/ℏc)[ψ₀,ψ₁,ψ₂,ψ₃] with graviton scalars σ_μ = p_μc/Δ.</p> <p>Master equation: g_μν = T^α_μ T^β_ν [M_αβ ∘ (η_αβ - Σ_a ε_a σ^(a)_α σ^(a)_β - κℓ_Q² ∂σ²)]</p> <p>Universal forms:<br>- Schwarzschild: σ_r = √(2GM/c²r)<br>- Kerr: σ_φ = a·sin(θ)√(2Mr/Σ)<br>- RN: -GQ²/c⁴r² term<br>- SdS: +Λr²/3 term<br>- FLRW: H²r² cosmology<br>- Wormholes: +b(r)/r</p> <p>Dark matter prediction: Factorial κ-factors κ_j=√[(2j-1)!/2^(2j-2)] = [1.00, 1.225, 2.74, 8.87, 37.7, 197,...] explain rotation curves. R²=0.908 across 4,248 measurements, zero free parameters per galaxy.</p> <p>Energy localization: ρ_grav(x) = ½(∂σ)² manifestly positive, resolves GR pseudotensor problem.</p> <p>Key results: (1) Newton's F=GMm/r² from phase e^(2ipr/ℏ), determines k=GMm/ℏc. and higher order terms (2) All EFE solutions from master equation. (3) Quantum corrections prevent singularities. (4) Dark matter = gravitational self-energy Q_μ. (5) Positive energy trivial. (6) Two body problem analytical solution (6) three body problem calculable in QGD (7) higher order quantum effects of Hawking temperature (8) dark energy naturally emerges from Quantum gravity</p> <p>Testable: rotation κ-scaling, CMB peaks (κ₄=8.87), wide binary 15% deviation, GW self-interaction.</p> <p>Keywords: quantum gravity, emergent spacetime, dark matter, rotation curves, MOND, Dirac spinor, gravitational energy, master equation, factorial enhancement</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18704492 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Quantum Gravity Dynamics: Dark Matter and Dark energy from Quantum Gravity in Dirac Spinor Fields deriving General Relativity Matshaba, Romeo dark matter quantum gravity general relativity alternatives flat spacetime gravity dark energy Energy problem in General Relativity exact solution two body problem computable three body problem <p>We present Quantum Gravity Dynamics (QGD), deriving classical gravity from quantum wavefunction structure in flat Minkowski spacetime.</p> <p>Core formalism: Bridge equation |ψ|²=C/|p| connects quantum amplitude to classical momentum. All stress-energy (mass ρ, pressure P, angular momentum J, EM field F, Λ) enters unified denominator Δ = E + mc² + ∫ρc²dV - ∫PdV - J²/(2mr²) + V_EM + ρ_Λ.</p> <p>Complete wavefunction: ψ = (GMm/ℏc)[ψ₀,ψ₁,ψ₂,ψ₃] with graviton scalars σ_μ = p_μc/Δ.</p> <p>Master equation: g_μν = T^α_μ T^β_ν [M_αβ ∘ (η_αβ - Σ_a ε_a σ^(a)_α σ^(a)_β - κℓ_Q² ∂σ²)]</p> <p>Universal forms:<br>- Schwarzschild: σ_r = √(2GM/c²r)<br>- Kerr: σ_φ = a·sin(θ)√(2Mr/Σ)<br>- RN: -GQ²/c⁴r² term<br>- SdS: +Λr²/3 term<br>- FLRW: H²r² cosmology<br>- Wormholes: +b(r)/r</p> <p>Dark matter prediction: Factorial κ-factors κ_j=√[(2j-1)!/2^(2j-2)] = [1.00, 1.225, 2.74, 8.87, 37.7, 197,...] explain rotation curves. R²=0.908 across 4,248 measurements, zero free parameters per galaxy.</p> <p>Energy localization: ρ_grav(x) = ½(∂σ)² manifestly positive, resolves GR pseudotensor problem.</p> <p>Key results: (1) Newton's F=GMm/r² from phase e^(2ipr/ℏ), determines k=GMm/ℏc. and higher order terms (2) All EFE solutions from master equation. (3) Quantum corrections prevent singularities. (4) Dark matter = gravitational self-energy Q_μ. (5) Positive energy trivial. (6) Two body problem analytical solution (6) three body problem calculable in QGD (7) higher order quantum effects of Hawking temperature (8) dark energy naturally emerges from Quantum gravity</p> <p>Testable: rotation κ-scaling, CMB peaks (κ₄=8.87), wide binary 15% deviation, GW self-interaction.</p> <p>Keywords: quantum gravity, emergent spacetime, dark matter, rotation curves, MOND, Dirac spinor, gravitational energy, master equation, factorial enhancement</p> |
| title | Quantum Gravity Dynamics: Dark Matter and Dark energy from Quantum Gravity in Dirac Spinor Fields deriving General Relativity |
| topic | dark matter quantum gravity general relativity alternatives flat spacetime gravity dark energy Energy problem in General Relativity exact solution two body problem computable three body problem |
| url | https://doi.org/10.5281/zenodo.18704492 |