azeddine ennabati

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Azeddine Ennabati
Independent researcher in theoretical and mathematical physics (Morocco)

My research focuses on developing a unified energetic framework that bridges relativity, quantum mechanics, and cosmology through the Theory of Relative Cosmic Equilibrium (RCE).
The RCE framework reformulates mass, gravity, and the fundamental forces as expressions of dynamic energy balance, providing a coherent link between microscopic quantum phenomena and macroscopic spacetime structure.

Recent submission:
Ennabati, A. (2025). Correcting the Navier–Stokes Millennium Problem through ΔE Field Reformulation in the Theory of Relative Cosmic Equilibrium (RCE).
Submitted to Communications in Mathematical Physics (Springer), Manuscript ID: CIMP-D-25-01482.

Research Interests: unified field theories | quantum gravity | energetic formulations of physics | Navier–Stokes problem | cosmology | mathematical physics.

Keywords: RCE Theory, ΔE Field, Energetic Equilibrium, Unification of Forces.
Phone: +212708050607
Address: Lot Elhassania n 35, Ouedzem 25350 Moroccan

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The Theory of Relative Cosmic Equilibrium (RCE): A Complete Unification of the Four Fundamental Forces

We introduce the Theory of Relative Cosmic Equilibrium (RCE), a unified framework in which all fu... more We introduce the Theory of Relative Cosmic Equilibrium (RCE), a unified framework in which all fundamental interactions arise as emergent manifestations of the energetic differential field ∆E(x, t). In this paradigm, gravity, electromagnetism, and nuclear forces correspond to distinct relaxation channels of the same underlying field, resolving the long-standing quantum-gravity tension and eliminating curvaturebased singularities. We construct the full RCE Lagrangian, derive two-loop renormalizationgroup equations, and compute the one-and two-loop effective potential V eff (ϕ), demonstrating perturbative stability up to the Planck scale. Using the predicted particle spectrum, we evaluate the oblique parameters (S, T, U) and show compatibility with LEP, SLD, and LHC data. Gravitational dynamics arise from the effective metric g eff µν = Z-1 (∆E)η µν , reproducing the Newtonian limit, gravitational lensing, and gravitational-wave propagation. RCE replaces geometric curvature with energetic imbalance while retaining all observable gravitational effects. The framework yields testable predictions-including singularity-free collapse, frequencydependent gravitational-wave dispersion, and quadrupole-driven lensing-making RCE a viable six-parameter alternative to conventional unification schemes.

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Correcting the Navier-Stokes Millennium Problem through ∆E Field Reformulation in the Theory of Relative Cosmic Equilibrium (RCE)

Correcting the Navier-Stokes Millennium Problem through ∆E Field Reformulation in the Theory of Relative Cosmic Equilibrium (RCE), 2025

We argue that the classical Navier-Stokes millennium problem, posed in terms of the velocity fiel... more We argue that the classical Navier-Stokes millennium problem, posed in terms of the velocity field v and pressure p, is conceptually misformulated. Within the framework of Relative Cosmic Equilibrium (RCE), the true fundamental quantity is the relational energy difference ∆E, from which motion, pressure, and flow arise as secondary effects. We demonstrate that the proper variables of the theory lead to two stable forms: (i) an exact energy-balance equation (RCE-2) equivalent to Navier-Stokes but physically meaningful, and (ii) a diffusive limit (RCE-1) that obeys a maximum principle ensuring boundedness and smoothness. Through numerical experiments with spectral forcing, we confirm that ∆E naturally generates complex yet finite structures without any singularities or blow-up. We conclude that the supposed difficulty of the Navier-Stokes problem stems from measuring the effect (velocity) instead of the cause (energy difference), and that reframing the equations in terms of ∆E resolves the paradox and restores physical coherence.

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Relative Cosmic Equilibrium: A Unified Framework for Mass, Gravity, and the Fundamental Forces

Ennabati Azeddine, 2025

The Theory of Relative Cosmic Equilibrium (RCE) proposes a unified quantum framework that reinter... more The Theory of Relative Cosmic Equilibrium (RCE) proposes a unified quantum framework that reinterprets all physical phenomena as manifestations of structured energetic imbalances within a single scalar field ∆E(x, t). Instead of treating mass, time, forces, or spacetime as fundamental entities, the theory describes the universe as a dynamic, self-organizing spectral system seeking equilibrium, where gravity, matter, and fields emerge from local departures from balance. The theory provides a unified field equation with topological structure capable of generating all four fundamental interactions-gravity, electromagnetism, strong, and weak nuclear forces-from a single spectral principle. It predicts deflection angles consistent with observation (e.g., 1.7505 ′′ near the Sun), and testable quantum deviations in atomic clocks subjected to engineered ∆E gradients. Furthermore, RCE redefines foundational concepts: mass as confined energy imbalance, time as a rate of relaxation toward equilibrium, gravity as a spectral gradient, and electric charge as a topological twist. These insights offer not just unification, but a new ontological foundation for physics-mathematically coherent, empirically testable, and conceptually transparent.

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Quantifying Existence: Energy, Relational Measurement, and the ∆E Field in the Theory of Relative Cosmic Equilibrium (RCE) A Complementary Study to the Unified Field Framework of Relative Cosmic Equilibrium

This paper presents a continuation and deepening of the Theory of Relative Cosmic Equilibrium (RC... more This paper presents a continuation and deepening of the Theory of Relative Cosmic Equilibrium (RCE), focusing on the relational nature of energy and measurement. While the first RCE paper unified the four fundamental forces under the dynamic field ∆E, this second paper redefines energy itself as a measure of deviation from absolute equilibrium. It introduces the relational quantity Q(x, t) = |∆E(x, t)|, which serves as the fundamental measurable essence of reality. Through analytical reasoning and empirical calibration (GPS, NIST, SLACS lenses), the study establishes that all observable quantities-gravity, time, and light-emerge as different relational expressions of the same energetic equilibrium field. This redefinition not only reconciles relativity and quantum mechanics but also extends physics toward a relational understanding of existence itself.

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A Unitary–Determinantal Proof of the Riemann Hypothesis

A Unitary–Determinantal Proof of the Riemann Hypothesis, 2025

We present a proof of the Riemann Hypothesis within a unitary–determinantal framework for L-funct... more We present a proof of the Riemann Hypothesis within a unitary–determinantal framework for L-functions. For the completed Riemann function ξ(s), we construct an analytic family of unitary operators U_ren(s), obtained as a renormalized direct sum of local CMV blocks together with an Archimedean block matched to A(s) = (1/2) s(s−1) π^(−s/2) Γ(s/2).

Under hypotheses (A1)–(A3), we establish on the critical line Re(s) = 1/2 a boundary log–derivative identity:
d/ds log ξ(s) = − d/ds log det₂(I − U_ren(s)).

Admissibility on strips and a Privalov-type closure promote this boundary identity to the full critical strip, yielding the determinantal representation
ξ(s) = C · det₂(I − U_ren(s))^(−1).

In a Clark model we design a quantitative head–tail mechanism: if τ₀(σ) + C*(σ)√κ(σ;M) < 1 for some M and σ ≠ 1/2, then the spectral measure has no atom at 1, which excludes zeros off the critical line. This completes the proof that all nontrivial zeros of ξ(s) lie on Re(s) = 1/2.

The approach is modular and extends, mutatis mutandis, to other L-functions.

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