Abstract

We present a mathematically well-posed, ghost-free scalar–tensor–electromagnetic theory in which a coherence scalar Φ, a U(1) gauge field Aµ, and a Fisher-information term for the density ρ are coupled by two dimension-four interactions ξΦR and ηΦF². From a covariant action we derive the Euler–Lagrange equations, the improved stress tensor, a unified conserved current via Noether symmetries, and the linearized system. In the operating regime 1 + κξΦ₀ > 0, ε₀ ≡ 1 − 4ηΦ₀ > 0, λ ≥ 0, m²Φ ≥ 0, and γ ≥ 0, the principal symbol is real and diagonalizable, and the first-order form admits a positive symmetrizer, establishing strong hyperbolicity and well-posed Cauchy evolution; the quadratic Hamiltonian is positive definite. The weak-coupling limit continuously recovers Einstein–Maxwell. The theory yields falsifiable predictions: a Yukawa correction to PPN γ, an optical phase/velocity shift Δn ≈ 2ηΔΦ, and a stabilizing quartic dispersion αk⁴ with α = γ/4.

Overview

This work formalizes the unification of energy, information, and coherence through a covariant field framework. It demonstrates causal, ghost-free evolution and yields falsifiable predictions testable in optical and gravitational domains.

Key Findings

• Unified conserved current merging energetic and informational flux.
• Strongly hyperbolic, well-posed Cauchy evolution.
• Experimental predictions: Yukawa corrections, optical phase shifts, quartic dispersion.

Abstract

We establish full Cauchy well-posedness and Hamiltonian positivity for a scalar–tensor–electromagnetic field system unifying geometry, gauge, and informational dynamics. The action couples a coherence scalar Φ, a U(1) gauge field Aμ, and a Fisher-information density ρ through the dimension-four interactions ξΦR and ηΦF² with a stabilizing −(γ/4ρ)(∇ρ)² term. In the regime 1 + κξΦ₀ > 0, ε₀ ≡ 1 − 4ηΦ₀ > 0, λ ≥ 0, m²Φ ≥ 0, γ ≥ 0, the linearized equations admit a real, diagonalizable principal symbol and a positive-definite symmetrizer. The first-order form is symmetric-hyperbolic, constraints propagate, and the quadratic Hamiltonian is positive definite, guaranteeing causal, ghost-free evolution. The Einstein–Maxwell limit is recovered continuously as (ξ, η, γ) → 0. The framework yields concrete observables: a Yukawa correction to PPN γ, an optical phase shift Δn ≈ 2ηΔΦ, and a quartic dispersive tail αk⁴ with α = γ/4.

Overview

This work closes the mathematical gap between unification proposals and rigorous Cauchy analysis. It demonstrates that a scalar–tensor–electromagnetic coupling can preserve hyperbolicity, positivity, and causality simultaneously, placing coherence-based gravity extensions on a strict analytic footing.

Key Findings

• Strong hyperbolicity: A real, diagonalizable principal symbol and positive symmetrizer ensure well-posed evolution.
• Positive Hamiltonian: Energy density remains strictly positive in all physical sectors.
• Constraint propagation: Gauge and ADM constraints remain closed under evolution.
• Empirical signatures: Yukawa deviation of PPN γ, optical Δn ≈ 2ηΔΦ, stabilizing αk⁴ dispersion.
• Continuity with Einstein–Maxwell: Smooth limit guarantees physical recoverability.