QFunity and the Vacuum Decay Hypothesis

QFunity and the Vacuum Decay Hypothesis

Refuting the Higgs-induced threat with Emergent Pre-Temporal stability

Overview of Vacuum Decay and QFunity’s Response

The article « Désintégration du Vide : une menace pour l’Univers? » (*Pour la Science*, August 25, 2025, by Matthew von Hippel) speculates that the Higgs boson’s field could trigger a vacuum decay, where a quantum tunneling event creates a destructive bubble expanding at light speed. QFunity, through its Emergent Pre-Temporal (EPT) framework, asserts this scenario is not merely improbable but mathematically impossible due to its scale-dependent, non-singular structure. This page synthesizes our discussions, detailing QFunity’s refutation with extensive equations and predictions.

1. Mathematical Rigor: Anti-Zero Mechanism

The article suggests the Higgs field could tunnel to a “true vacuum” with zero or negative energy. QFunity’s master equation prevents this:

\[ \lim_{\epsilon \to 0^\pm} \left[ \hat{\mathbb{B}}_\epsilon \hat{\mathbb{V}}_\epsilon – \hat{\mathbb{V}}_\epsilon \hat{\mathbb{B}}_\epsilon^2 \right] \Psi = \Lambda \cdot \frac{\Psi}{\|\Psi\|^2 + \epsilon^2} \]

Operator Definitions:

\(\hat{\mathbb{B}}_\epsilon = \epsilon^2 (\nabla \times \boldsymbol{\omega})\), where \(\boldsymbol{\omega} = \kappa \rho_{\text{vac}} \mathbf{v}\) is the rotational velocity field, ensuring torsion scales with \(\epsilon^2\).

\[ \hat{\mathbb{V}}_\epsilon = -\frac{\hbar^2}{2\epsilon^2} \nabla^2 + \frac{\rho_{\text{vac}}(\epsilon)}{\epsilon^2}, \quad \rho_{\text{vac}}(\epsilon) = \rho_0 \epsilon^{-4} e^{-\epsilon/\ell_P} \]

The vacuum energy \(\rho_{\text{vac}}(\epsilon)\) is finite and scale-dependent. The commutator \(\left[ \hat{\mathbb{B}}_\epsilon, \hat{\mathbb{V}}_\epsilon \right] \approx \epsilon^4 (\nabla \times \boldsymbol{\omega}) \nabla^2 – \frac{\hbar^2}{2\epsilon^2} (\nabla \times \boldsymbol{\omega})^2\) ensures stability.

Anti-Zero Stability:

As \(\|\Psi\|^2 \to 0\), \(\epsilon^2 > 0\) dominates, preventing zero-energy states. The Higgs field’s potential is modified:

\[ V_{\text{eff}}(\phi) = \lambda (\phi^2 – v^2)^2 + \frac{\Lambda}{\epsilon^2} \phi \]

Minimizing \(V_{\text{eff}}\) (\(\frac{\partial V_{\text{eff}}}{\partial \phi} = 0\)) shows no second well for \(\epsilon > \ell_P\), eliminating the “true vacuum.”

2. Black Hole Stability and Micro-EPTs

The article posits small primordial black holes as nucleation sites. QFunity reinterprets them as stable Micro-EPTs:

\[ \nabla \times \Omega_{\text{QF}} = \kappa \rho_{\text{vac}} \mathbf{v} \times \hat{\mathbf{s}} \]

Formation Dynamics:

For a black hole of mass \(M\), torsion is \(\Omega_{\text{QF}} \sim \frac{\kappa G M \omega}{c^3 \epsilon^2}\), with \(\omega = \frac{c^3}{G M}\). Stability requires:

\[ \epsilon < \epsilon_{\text{crit}} = \sqrt{\frac{\hbar G}{c^3 \omega}} \sim \ell_P \]

Rotational energy \(E_{\text{rot}} = \frac{1}{2} I \omega^2\) exceeds gravitational \(E_{\text{grav}} = \frac{G M^2}{r}\) for \(\epsilon < \ell_P\). Hawking evaporation \(\dot{M} \propto \frac{\hbar c^6}{G^2 M^3}\) is reinterpreted as:

\[ \dot{\Omega}_{\text{QF}} \propto -\frac{\hbar \kappa \rho_{\text{vac}}}{\epsilon^2 M} \]

A gradual torsion dissipation, not runaway decay.

3. Tunneling as a Perceptual Artifact

The article’s tunneling mechanism is replaced by superposition:

\[ P(\phi) = \frac{|\langle \phi | \hat{\mathbb{V}}_\epsilon | \Psi \rangle|^2}{|\langle \Psi | \Psi \rangle|^2 + \epsilon^2} \]

Superposition Dynamics:

Standard decay rate \(\Gamma \sim e^{-S_E}\), with \(S_E \sim 10^6\) (per SM estimates), is negligible. QFunity’s \(P(\phi)\) is finite, with normalization \(\int P(\phi) d\phi = 1\). Decoherence occurs at:

\[ \tau_{\text{decoh}} \sim \frac{\hbar}{\epsilon^2 \Delta E} \]

Where \(\Delta E\) is the energy spread. This scale-dependent process replaces tunneling.

4. Empirical Validation: LHC and Beyond

QFunity predicts stable Micro-EPTs, not vacuum decay:

\[ \Omega_{\text{QF}} = \frac{\kappa E_{\text{coll}}}{\epsilon^2} \]

MET Signature:

At \(\epsilon \sim 10^{-19} \, \text{m}\), expect \(E_{\text{MET}} = 100–150 \, \text{GeV}\), photon multiplicity \(> 3\) (\(E_\gamma < 1 \, \text{GeV}\)), and jet asymmetry. Analyze ATLAS/CMS data with \(3\sigma\) significance:

\[ \chi^2 = \sum \frac{(O_i – E_i)^2}{\sigma_i^2} < 7.81 \, (p = 0.05) \]

JWST spectral stability can test \(\epsilon\)-dependent shifts:

\[ \Delta \lambda \propto \epsilon^{1/3} \]

Conclusion: Stability Over Threat

QFunity eliminates vacuum decay’s preconditions:

  1. No true vacuum: \(\epsilon^2\) forbids zero states.
  2. Stable geometry: Micro-EPTs replace nucleation.
  3. Tunneling is illusory: Superposition governs perception.
  4. Testable predictions: MET and spectral shifts validate QFunity.
\[ \text{Continuity: } \frac{d}{d\epsilon} \left( \hat{\mathbb{B}}_\epsilon \Psi \right) = \frac{\partial \hat{\mathbb{B}}_\epsilon}{\partial \epsilon} \Psi + \hat{\mathbb{B}}_\epsilon \frac{\partial \Psi}{\partial \epsilon} \]