Ultimate Components of Matter in QFunity

Ultimate Components of Matter

Particles as vibrations of the Emergent Pre-Temporal substrate

Matter’s Ultimate Components in QFunity

QFunity redefines the ultimate components of matter as stable vibrations of the Emergent Pre-Temporal (EPT) state, emerging from a fractal, rotational substrate. This page details the process using QFunity’s equations, offering a unified view of particles, duality, and interactions.

1. The Emergent Pre-Temporal (EPT) Substrate

The EPT is the primordial state, characterized by acausality, non-locality, and fractal rotation:

\[ \left[ \hat{\mathbb{B}}_\epsilon, \hat{\mathbb{V}}_\epsilon \right] \Psi_{\text{EPT}} = 0 \]

Properties:

At \(\epsilon \to \ell_P\), \(\hat{\mathbb{B}}_\epsilon = \epsilon^2 (\nabla \times \boldsymbol{\omega})\) and \(\hat{\mathbb{V}}_\epsilon = -\frac{\hbar^2}{2\epsilon^2} \nabla^2 + \frac{\rho_{\text{vac}}(\epsilon)}{\epsilon^2}\) form a « full void » of fluctuations, with \(\rho_{\text{vac}}(\epsilon) = \rho_0 \epsilon^{-4} e^{-\epsilon/\ell_P}\).

2. Emergence of Particles via Symmetry Breaking

Particles emerge from EPT fluctuations:

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

Mechanism:

1. \(\mathcal{E}_{\text{EPT}} > \mathcal{E}_{\text{crit}}\) triggers a torsion-potential « bubble. » 2. Symmetry breaks, enabling causality. 3. \(\epsilon^2\) stabilizes the wave packet \(\Psi_{\text{particule}}\).

3. Wave-Particle Duality and Scale Dependence

Particle nature depends on \(\epsilon_O\):

\[ \langle \hat{O} \rangle_{\epsilon_O} = \frac{\langle \Psi | \hat{O} | \Psi \rangle}{\langle \Psi | \Psi \rangle + \epsilon_O^2} \]

Scale Effects:

At \(\epsilon_O \sim \ell_P\), \(\Psi\) is an extended wave; at \(\epsilon_O \gg \ell_P\), it appears discrete (e.g., electron mass).

4. Classification of Particles

Particle types arise from EPT vibration topologies:

Fermions:

\(\Psi_{\text{fermion}}\) is antisymmetric, with \(\hat{\mathbb{B}}_\epsilon \Psi = \frac{\hbar}{2} \Psi\) enforcing Pauli exclusion.

Bosons:

\(\Psi_{\text{boson}}\) is symmetric, with \(\hat{\mathbb{B}}_\epsilon \Psi = 0\) allowing superposition.

Hadrons:

\(\Psi_{\text{hadron}} = \Psi_1 \otimes \Psi_2\), composites of quarks.

\[ g_{\mu\nu}^{\text{particule}}(\epsilon) = \frac{\ell_P^2}{\epsilon^2} g_{\mu\nu}^{\text{EPT}} + \alpha’ g_{\mu\nu}^{\text{interactions}} \]

Mass and charge are rotational properties.

5. Key Equations for Particles

\[ \left( \hat{\mathbb{V}}_\epsilon + \hat{\mathbb{B}}_\epsilon^2 \right) \Psi_{\text{particule}} = E_{\text{particule}} \cdot \frac{\Psi_{\text{particule}}}{\|\Psi_{\text{particule}}\|^2 + \epsilon^2} \]

Defines stable vibration modes.

Conclusion

In QFunity, particles are EPT vibrations, with duality as a scale effect. This unifies quantum mechanics and gravity via rotational dynamics.

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