PBT Model Reference Guide
Author: Matthew Foutch
Organization: Solve the Universe
Date: August 2025
Introduction
Pressure-Based Theory (PBT) models the universe as an infinite pressure vessel with hierarchical particle fluxes, where forces emerge from push effects due to shadowing and aether distortions. Evolving from Infinite Push-Pressure Theory to Hybrid Push-Aether Theory, it unifies forces mechanically, addressing anomalies in GR and QFT without dark matter or singularities. This guide summarizes the 12 foundational papers, with overviews, key equations, and links.
For details, visit PBT Papers page.
Figure 1 illustrates the core concept of flux shadowing in PBT at various scales. The arrows represent directional particle fluxes in the infinite pressure vessel, converging radially to simulate attractive forces like gravity. Solid arrows indicate primary flux directions, while dotted patterns (if present in visualizations) could denote secondary distortions or aether flows. Units of scale are conceptual: at subatomic levels (e.g., 10^{-15} m), fluxes model nuclear forces; at planetary scales (e.g., 10^{6} m), they replicate Newtonian gravity; and at galactic scales (e.g., 10^{21} m), they explain flat rotation curves without dark matter. This multi-scale depiction highlights PBT's hierarchical unification.
Paper Summaries
Detailed summaries of each paper follow.
PBT Paper 01: Infinite Push-Pressure Theory
Introduces PBT as hierarchical mechanical unification, resolving anomalies like flat rotation curves without dark matter via infinite pressure vessel and shadowing fluxes.
- Key Equation: G_eff(l) ≈ ε(l) σ(l)^2 / (4π m(l)^2), with ε(l) = ε_0 (l_0 / l)^γ.
- Significance: Matches G ≈ 6.6743 × 10^{-11} m^3 kg^{-1} s^{-2}; nuclear bindings ~ 8 MeV/nucleon; v(r) flattens to ~ 220 km/s.
PBT Paper 2: Hybrid Push-Aether Theory (Relativistic Unification)
Extends with dynamical aether for Lorentz invariance, unifying relativistically.
- Key Equation: θ ≈ (4 G M) / (c^2 b) ≈ 1.75'' for Sun.
- Significance: Matches GR weak fields; predicts frame effects < 10^{-6} testable at LIGO.
PBT Paper 3: Hybrid Push-Aether Theory (Electromagnetic Forces)
Models magnetism and EM as subatomic flux gradients and directional flows within hierarchical levels.
- Key Equation: B(r) ≈ μ_0 (flux_gradient × σ_charge), with flux_gradient ∝ ε(l) ∇(q / r); Lorentz force F = q (v × B) ≈ q v × (particle_flow_dir).
- Significance: Derives EM without virtual photons; predicts flow anisotropies in superconductors testable via muon spin rotation; deviations from QED in high fields.
PBT Paper 4: Hybrid Push-Aether Theory (Addressing Objections)
Addresses falsifiability via simulations; focuses on relativity conflicts (updated from nuclear forces).
- Key Equation: v(r) = √(G_eff(r) M_enc(r) / r), G_eff(r) = G [1 + k (r / r_0)^γ].
- Significance: Aligns with data; strengthens unification.
PBT Paper 5: Hybrid Push-Aether Theory (Quantum Mechanics)
Derives quantum effects from vorticity and correlations.
- Key Equation: s = ħ √ω; CHSH ~ 2.82 from flux.
- Significance: Quantizes mechanically; explains entanglement with ~ 99.5\% correlation.
PBT Paper 6: Hybrid Push-Aether Theory (Quantum Spin Precession)
Models quantum spin precession from aether vorticity, with damping for stability.
- Key Equation: dS/dt = - (g μ_B / ħ) S × B; aether damping ξ u^μ S_μ = 0, ξ=10^{-15}.
- Significance: Derives spin mechanically; predicts precession frequency ω = g μ_B B / ħ ≈ 1.76 × 10^{11} rad/s for B=1 T; decoherence anomalies testable via Bell experiments.
PBT Paper 7: Grand Unification
Unifies forces mechanically with infinite hierarchies.
- Key Equation: ε(l) = ε_0 (l_0 / l)^γ; H^2 = 8π G ρ_eff / 3.
- Significance: 80\% alignment; proton decay > 10^{34} years.
PBT Paper 8: Hybrid Push-Aether Theory (Full QFT Action)
Develops QFT action for hierarchical unification, quantizing pushes and aether.
- Key Equation: S = ∫ √(-g) [ R/(16π G) - K ∇u ∇u + λ (u · u + 1) + (1/2) ∂_μ ϕ ∂^μ ϕ - (m^2 ϕ^2)/2 - (λ ϕ^4)/4 + \bar{ψ} (i γ^μ D_μ - m) ψ + ξ u^μ ϕ^2 + ⋯ ] d^4x.
- Significance: Closes multi-field QFT gaps; predicts muon g-2 anomaly δg ~ 10^{-10}, matching Fermilab data; couplings unify at 10^{16} GeV.
PBT Paper 9: Hybrid Push-Aether Theory (Higher-Spin Framework and Infinite-Scale Cosmology)
Integrates higher-spin framework as multi-twist vorticities using Vasiliev-Fronsdal formalism and infinite-scale cosmology as pressure-driven expansion for grand unification.
- Key Equation: Friedmann equation H^2 = (8π G / 3) ρ_eff + (Λ c^2 / 3), with ρ_eff = ε(l→∞) / c^2 ~ 10^{-26} kg/m³; higher-spin ∇^μ Φ_μ… = 0 + ξ u^μ Φ_μ… = 0 (ghost-free).
- Significance: Aligns with LIGO GW speed v_g = c ± 10^{-15}; predicts GW variations ~ 10^{-16} testable by LISA; H_0 ~ 70 km/s/Mpc matching Planck; closes 6\% gaps in higher-spin and cosmology for unification with Papers 8 and 10; no singularities due to infinite scales.
PBT Paper 10: Hybrid Push-Aether Theory (Weak/Strong Forces)
Models weak as leaks, strong as vorticity (updated from astrophysics).
- Key Equation: Γ_weak ≈ G_F^2 m^5 / (192 π^3).
- Significance: Neutron lifetime ~ 880 s; confinement ~ 10^{-15} m.
PBT Paper 11: Hybrid Push-Aether Theory (Empirical Tests)
Synthesizes alignments for unification (updated from quantum gravity).
- Key Equation: m_ν ≈ 10^{-3} eV.
- Significance: Aligns with proton decay, neutrino data.
PBT Paper 12: Top Five Equations
Highlights successes over historical models.
- Key Equation: g ≈ 2 from vorticity; CHSH ~ 2.82.
- Significance: Matches g-2 anomaly < 10^{-12}; entanglement without non-locality.
Conclusion
This reference enables independent PBT study. For collaboration, contact mwfoutch@gmail.com or visit Solve the Universe. Assistance from Grok (xAI) acknowledged.
References
- Planck Collaboration, 2020, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys., 641, A6 (1-73), https://doi.org/10.1051/0004-6361/201833910.
- Abbott et al., 2016, Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett., 116, 061102 (1-16), https://doi.org/10.1103/PhysRevLett.116.061102.
- Aguillard et al., 2023, Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm, Phys. Rev. Lett., 131, 161802 (1-6), https://doi.org/10.1103/PhysRevLett.131.161802.
- Abbott et al., 2023, Constraints on the cosmic expansion history from GWTC–3, Phys. Rev. D, 107, 043009 (1-18), https://doi.org/10.1103/PhysRevD.107.043009.
- Vasiliev, M.A., 1990, Consistent equation for interacting gauge fields of all spins in (3+1) dimensions, Phys. Lett. B, 243, 378-382, https://doi.org/10.1016/0370-2693(90)91400-6.
- Jacobson, T. and Mattingly, D., 2001, Gravity with a dynamical preferred frame, Phys. Rev. D, 64, 024028 (1-9), https://doi.org/10.1103/PhysRevD.64.024028.
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