Angular Momentum in QFunity

Context and Motivation (January 2026)

Inspired by a discussion on X about a universe rotating every 500 billion years to resolve the Hubble tension, this exploration delves into angular momentum within the QFunity framework. The goal is to unify cosmic rotation, spin-field interactions, and the « Zero Principle » into a testable Theory of Everything (ToE). See the initial post: All day Astronomy Post.

Core Concept: Spin-Field Coupling via Φ

QFunity posits a scalar field \( \Phi \) that couples to matter and spin, driven by the « Zero Principle » from QFunity Zero, where no physical quantity reaches zero due to quantum regularization. This leads to an anharmonic potential and long-period oscillations.

Anharmonic Potential \( V(\Phi) \)

The potential is regularized to avoid a perfect minimum: \[ V_{\text{eff}}(\Phi) \approx V_{\text{min}} + \frac{m_\Phi^2 \epsilon^2}{2} \left[ \sqrt{1 + \left(\frac{\Phi – \Phi_0}{\epsilon}\right)^2} – 1 \right] \] where \( \epsilon \sim \hbar/2 \) flattens the potential.

Coupling Mechanism

The coupling to spin is defined as: \[ \mathcal{L}_{\text{matter}} = \frac{\Phi}{M_*} \left[ \frac{\beta_g}{2g} G_{\mu\nu} G^{\mu\nu} – \sum_{q=d,s,b} \gamma_q m_q \bar{q}q \right] + \frac{\partial_\mu \Phi}{M_*} \bar{\psi} \gamma^\mu \gamma^5 \psi \] where the axial term induces a spin-dependent interaction: \[ H_{\text{int}} \approx -\frac{1}{M_*} \vec{S} \cdot \vec{\nabla} \Phi \] with \( \lambda \equiv 1/M_* < 10^{-10} \, \text{GeV}^{-1} \) from EDM constraints (arXiv: 2303.01596).

Angular Momentum of the Universe

In a FLRW universe, total angular momentum is zero by symmetry. QFunity introduces a complex \( \Phi = \phi e^{i\theta} \), yielding: \[ L_{\Phi}^k = \varepsilon^{ijk} \int d^3x \, \phi^2 (\partial_t \theta) (x_i \partial_j \theta) \] For homogeneity (\( \partial_j \theta = 0 \)), \( L_{\Phi} = 0 \), but CMB fluctuations (\( \langle (\delta \rho / \rho)^2 \rangle^{1/2} \sim 10^{-5} \)) may contribute a small, random effect.

Context from X Discussion

The X post (ID: 2007933066862547252) suggests a 500-billion-year rotation resolves the Hubble tension. QFunity adapts this via \( \Phi \)’s oscillations: \[ H_0(\epsilon) \approx H_{0,\Lambda\text{CDM}} \left[ 1 + \beta \left( \frac{\epsilon_0}{\epsilon} \right)^{3 – D_f} \right] \] with \( D_f \approx 2.718 \) and \( \beta \sim 0.065 \).

Fuzzy Dark Matter (FDM) Signature

For a 10-year « respiration » period, \( m_{\text{fdm}} \sim 10^{-19} \, \text{eV} \) and \( \lambda_{\text{wave}} \sim 0.06 \, \text{pc} \): \[ m_{\text{fdm}} \approx \frac{\hbar}{v \lambda} \approx \frac{1.05 \times 10^{-34} \, \text{J·s}}{(2.2 \times 10^5 \, \text{m/s}) \cdot (1.8 \times 10^{15} \, \text{m})} \approx 2.6 \times 10^{-55} \, \text{kg} \] Predictions include:

• Lensing: No substructures < 0.1 pc (DOI: 10.1093/mnras/staa3631).
• Dynamics: Homogeneous density < 0.1 pc.
• Interferometry: \( \nu \sim 3.6 \times 10^{-5} \, \text{Hz} \) (period ~8 hours).

Solar System Constants Network (SSCN)

A network of 4-5 optical atomic clocks (e.g., \( ^{87}\text{Sr} \)) across the solar system: \[ \frac{\delta(\nu_{Sr})}{\nu_{Sr}} = K_{Sr}^{\alpha} \frac{\delta\alpha}{\alpha} + K_{Sr}^{m_q} \frac{\delta m_q}{m_q} \] Tests for a 10-year modulation, rejecting systematic effects.

THE COSMIC BREATH AND SPIN OF QFUNITY

Angular momentum and \( \Phi \)’s oscillations unify the Hubble tension, spin coupling, and cosmic structure within QFunity. The « Zero Principle » provides a novel regularization, predicting testable signatures from FDM to clock networks.