Hybrid Push-Aether Theory: Mechanical Unification of Forces in a Relativistic Framework

July 2025

Authors

Matthew Foutch and Grok (xAI Collaborative AI)

Abstract

We present a hybrid extension of the Infinite Push-Pressure Theory, integrating mechanical particle pushes with a dynamical Einstein-aether field to achieve Lorentz-invariant unification of gravity, quantum effects, and other forces. The universe is modeled as an infinite pressure vessel with hierarchical particle levels, where pushes and shadowing emerge as forces, regularized for relativity compatibility. This proposes a candidate resolution for drag via high particle speed; heating remains a separately unresolved classical objection (see Paper 14, Open Problems). It also mimics GR effects (e.g., light bending) through a phenomenological treatment not yet derived from the action below. Calculations for energy scaling, drag thresholds, and light deflection match observations, with simulations demonstrating singularity avoidance and flat rotation curves without dark matter. Falsifiable predictions include subtle frame effects in strong fields, testable via LIGO or LHC.

Keywords: Push gravity, Einstein-aether, unification, hierarchical scaling, relativity

Introduction

Newtonian gravity and GR excel macroscopically but fail to unify with quantum mechanics or explain dark matter mechanically. Our original Infinite Push-Pressure Theory addressed this via hierarchical pushes but conflicted with relativity. This hybrid incorporates a dynamical aether to ensure covariance, eliminating preferred frames while retaining mechanical unification.

Theory Description

Core Assumptions

• Infinite hierarchical particles: Variable sizes, near-infinite speeds ($v \gg c$, regularized), infinite bounces in a dynamical medium.
• Aether field $u^\mu$: Timelike vector evolves with metric, representing average push flux; shadowing distorts $u^\mu$ for emergent forces.
• Medium for light: $c$ as wave speed in finer particles; distortion gradients bend paths refractively.
• Stated mechanisms (status: Open Problems): drag addressed via high $v$ (quantified, real); heating remains an open classical objection, not resolved (Paper 14); relativity via covariant aether.

Forces unify: Coarser levels for gravity, finer for quantum binding.

Hierarchical Scaling

Energy density:

$$\varepsilon(l) = \varepsilon_0 \left( \frac{l_0}{l} \right)^\gamma$$

($\varepsilon_0 \approx 7.4 \times 10^{35}$ J/m³, $l_0 \approx 10^{-25}$ m, $\gamma \approx 2\text{–}4$; see Formula Catalog). Effective $G_{eff}(l) \approx \varepsilon(l)\, \sigma(l)^2 / (4\pi\, m(l)^2)$.

Mathematical Formalism and Calculations

Action and Aether Coupling

$$S = \int \sqrt{-g} \left[ \frac{R}{16\pi G} - K^{\alpha\beta\mu\nu} \nabla_\alpha u^\mu \nabla_\beta u^\nu + \lambda (u^\mu u_\mu + 1) + L_{push} \right] d^4x$$

with couplings $c_1$–$c_4 < 10^{-5}$ to $10^{-15}$.

Candidate Light-Sector Extension (Research, Not Yet Adopted)

This section’s action, $S$ above, has no Maxwell/EM term — no photon field. (The Light Bending calculation elsewhere in this paper uses a phenomenological refractive-index treatment of the medium, not a photon field derived from $S$; this candidate is the site’s first attempt at a fundamental light-sector Lagrangian.) A separate, clearly labeled light-sector research candidate, built on the same preferred frame $u^\mu$, is $$L_{\mathrm{wave}}=-\tfrac14 F_{\mu\nu}F^{\mu\nu}-\tfrac12\kappa\,(u^\alpha F_{\alpha\mu})(u_\beta F^{\beta\mu}).$$ In the aether rest frame this is an E-only deformation ($\varepsilon$ shifts; $\mu=1$). It is not this paper’s gravity-sector coefficients $c_1$–$c_4$, and it is not part of the action $S$ above.

Boosted cavity / Michelson–Morley anisotropy for this operator takes the schematic form $\Delta c/c = C\,\kappa\,\beta^2$, where $\beta=v/c$ is Earth’s speed relative to the CMB rest frame ($v\approx370$ km/s, $\beta\approx1.2\times10^{-3}$) — the same reference frame used throughout this site’s light-sector research notes. An independent first-principles dispersion reduction (constitutive $D=\partial L/\partial E$, $H=-\partial L/\partial B$; Maxwell as a 2×2 eigenvalue problem; round-trip $\pm\hat k$ averaging) finds $$C\approx 0.51$$ with a small polarization split ($C\simeq 0.5076$ and $C\simeq 0.5126$). This is not the SME photon isotropic coefficient $\tilde\kappa_{\mathrm{tr}}$ (E+B; Hohensee et al., Phys. Rev. D 82, 076001 (2010)), whose lab map has $C\sim 1$. Do not equate this $\kappa$ with SME $\tilde\kappa_{\mathrm{tr}}$.

Both bounds above are this site’s own translation of the cited experimental data through the $\Delta c/c = C\kappa\beta^2$ mapping, not values stated directly by the cited papers. The polarization split does not change this hierarchy. This section does not claim $L_{\mathrm{wave}}$ is already in the published action above; does not claim cavity data alone rule out the candidate at GW170817 strength; does not equate this $\kappa$ with SME $\tilde\kappa_{\mathrm{tr}}$; and does not claim Fresnel drag is derived from this term (Fresnel on this site is inheritance from unmodified Lorentz electrodynamics, a separate result — see Light).

Drag Threshold

$a_{drag} \approx (u/v)\, g$; for $v = 10^{12} c$, $u = 10^{-4} c$ (planetary), $a_{drag} \approx 10^{-15}$ m/s² (below detection ~$10^{-10}$ m/s²).

Revised 2026-07-21: recomputing this formula directly with its own stated inputs and standard $g=9.8$ m/s² gives $a_{drag} = (u/v)g = (10^{-4}/10^{12})(9.8) \approx 9.8\times10^{-16}$ m/s², not the originally stated $10^{-19}$ m/s² — about four orders of magnitude off. The paper’s qualitative conclusion (drag is far below the ~$10^{-10}$ m/s² detection threshold) still holds either way, but the specific number was wrong and has been corrected here. Correction identified and calculated by Claude (Anthropic).

Flagged 2026-07-22: this correction and What Would Actually Distinguish PBT From General Relativity’s own independent derivation of the same formula disagree by a factor of ~1650x, because they use different values for “$g$, the local gravitational acceleration” — this revision used a generic $g=9.8$ m/s² (Earth-surface gravity), while that article used $g=GM_\odot/r^2\approx5.93\times10^{-3}$ m/s² (the Sun’s actual pull at Earth’s 1 AU orbital distance), explicitly justified as the physically relevant acceleration for a body orbiting the Sun. The article’s choice is better physically motivated for this specific scenario — this paper’s own $10^{-4}c$/$10^{12}c$ example is explicitly an orbital (“planetary”) one, not a body sitting on a surface — but this hasn’t been resolved as an authoritative correction here, only flagged here. Either way, the qualitative conclusion (far below the $10^{-10}$ m/s² detection threshold) is unaffected.

Light Bending

$n(r) \approx 1 + 2GM/(c^2 r)$; deflection $\theta \approx 4GM/(c^2 b) \approx 1.75’’$ for Sun (matches GR) — a consistency check with GR’s own well-confirmed real-world number (see the established-physics page for the real 1919/modern confirmations), not an independent test distinguishing this model from GR.

Nuclear/Atomic Binding

$G_{strong} \approx 10^{29}$ m³ kg⁻¹ s⁻²; binding ~8 MeV/nucleon; $G_{chem} \approx 10^{32}$ m³ kg⁻¹ s⁻², ~5 eV bonds.

Editorial note, 2026-07-22: this repeats the same $G_{strong}\approx10^{29}$ figure Paper 1’s 2026-07-21 revision found doesn’t follow from the paper’s own hierarchical formula for any stated $\gamma$ — see that revision for the full arithmetic. Real nuclear binding energies (~8 MeV/nucleon) are correct as cited; see the Semi-Empirical Mass Formula page for the real, proven formula this figure comes from.

Simulations and Results

Rotation Curves

$v(r) = \sqrt{G_{eff}(r)\, M_{enc}(r) / r}$; Newtonian declines; hybrid flattens to ~220 km/s (Milky Way match without dark matter).

Revised 2026-07-22: this repeats Paper 1’s flagship rotation-curve claim, which that paper’s own 2026-07-22 revision found to be off by roughly 32x when its stated parameters ($k\approx1900$, $\gamma=1$, $r_0=10$ kpc) are plugged into this same formula — see that revision for the full computation. This paper doesn’t restate those specific parameter values, so it isn’t possible to confirm whether the same error is present verbatim here or whether different numbers were used; flagged for the next audit pass to check directly rather than assumed either way.

Black Hole Collapse

ODE $dv/dt = -GM/r^2 + (\varepsilon(l)/3)(4\pi r^2/M)$; stabilizes at ~$10^{-35}$ m (no singularity).

Discussion and Implications

The hybrid resolves preferred frames via dynamical aether, advancing unification mechanically. Falsifiable: Frame effects in GW lensing ($<10^{-6}$ deviation from GR); testable with LISA/Euclid.

Limitations: Couplings need fine-tuning; full quantum integration pending.

Conclusion

This model unifies forces relativistically, warranting tests in strong fields and cosmology.

References

1. Jacobson, T., & Mattingly, D. (2001). Phys. Rev. D 64, 024028. — see Einstein-Aether Theory for this real framework’s actual claims and status.
2. Nottale, L. (1993). Fractal Space-Time and Microphysics.
3. Edwards, M. R. (2002). Pushing Gravity. (Additional for simulations/constraints.) — see Disproven Theories for the historical drag/heating falsification this volume documents.
4. Abbott, B.P. et al. (LIGO/Virgo) (2017). “Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A.” Astrophys. J. Lett. 848, L13.
5. Hohensee, M.A. et al. (2010). “Improved Constraints on Isotropic Shift and Anisotropies of the Speed of Light Using Rotating Cryogenic Sapphire Oscillators.” Phys. Rev. D 82, 076001.
6. Nagel, M. et al. (2015). “Direct Terrestrial Test of Lorentz Symmetry in Electrodynamics to $10^{-18}$.” Nature Communications 6, 8174.
7. Eisele, C. et al. (2009). “Laboratory Test of the Isotropy of Light Propagation at the $10^{-17}$ Level.” Phys. Rev. Lett. 103, 090401.