Model EPT

The Unique Fractal EPT and Genesis of Bubble-Universes

From Symmetry Breaking to Time Arrows and Black Hole Interfaces

1. The Fundamental Substrate: The Rotative Fractal EPT

The Pre-Temporal Space (EPT) is not a chronological « before » but the absolute, unique, and eternal substrate. According to QFunity’s fractal principles and weak rotation:

Fractal Geometry: The EPT has a non-integer Hausdorff dimension \( d_H > 4 \) (see Extra Dimensions), where each « scale » contains self-similarity of the presentation state. Its state is described by a universal wave function \( \Psi_{EPT}(\{x_f\}) \), where \( \{x_f\} \) are fractal coordinates.
Weak Rotation Motion: This introduces a fundamental angular momentum operator \( \hat{L}_{EPT} \) in the fractal space. This slight « spin » of the background originates the observed chirality in the universe (matter/antimatter asymmetry, particle helicity). The base Hamiltonian includes a term \( H_{rot} = \omega \hat{L}_{EPT} \), with \( \omega \) extremely weak.
No Time, No Matter: In this state, the operators for time \( \hat{T} \) and matter \( \hat{M} \) have zero average values and are highly delocalized: \( \langle \Psi_{EPT} | \hat{T} | \Psi_{EPT} \rangle = 0 \), \( \langle \Psi_{EPT} | \hat{M} | \Psi_{EPT} \rangle = 0 \). Only a purely informational presentation field exists.

The fractal EPT metric and base Hamiltonian are:

\[ ds^2_{EPT} = \ell_P^2 \sum_{\alpha} \Lambda(\alpha)^{-\theta} \left[ d\chi_\alpha^2 + \epsilon(\alpha) \hat{S}_f \cdot d\phi_\alpha^2 \right] \]

\[ H_{EPT}^0 = \sum_\alpha \hbar \omega_\alpha \left( a_\alpha^\dagger a_\alpha + \frac{1}{2} \right) + \sum_{\alpha < \beta} J_{\alpha\beta} \hat{S}_f^{(\alpha)} \cdot \hat{S}_f^{(\beta)} \]

Explanation
Where \( \ell_P \): Planck length; \( \alpha \): fractal scale index; \( \Lambda(\alpha) \): dilation factor; \( \theta = d_H - 4 \): critical fractal exponent; \( \epsilon(\alpha) \sim 10^{-60} \): weak rotation parameter, constrained by CMB isotropy (Planck 2018).

Full details: Micro-EPT

2. Symmetry Breaking: Birth of « Bubble-Universes »

A. Mechanism

Symmetry breaking is an event (or continuous process) within the fractal EPT. A quantum fluctuation in the weak rotation, or a resonance between fractal scales, triggers a local phase transition. Mathematically, a potential term \( V(\phi) \) of the presentation field \( \phi \) (linked to the primordial gravitational field) develops a non-zero minimum. This is the Presentation Transition.

B. Emergence of Time and Matter

This breaking « freezes » a direction in the fractal field, defining a local time arrow \( \vec{\tau} \) and condensing a portion of presentation information into matter-energy according to \( E = k \cdot S_p \) (where \( S_p \) is presentation entropy, cf. Micro-EPT). Each region where this occurs forms a « bubble-universe ».

C. Unicity of EPT, Plurality of Bubbles

There is only one EPT, but it can contain multiple disjoint bubble-universes, each with its own symmetry breaking, time arrow \( \vec{\tau}_i \), and matter \( M_i \). Our universe is one such bubble.

\[ V_{\rm eff}(\Phi) = \frac{\lambda}{4} (\Phi^\dagger \Phi - v^2)^2 + \gamma (\hat{S}_f \cdot \nabla_f \Phi)^2 \]

\[ \vec{\tau} = \nabla_f \eta = \nabla_f \langle \Phi \rangle \]

\[ E = k_p S_p \quad \text{with} \quad k_p = \frac{\hbar}{t_P} \frac{1}{\sqrt{\Lambda}} \]

Explanation
The minimum is at \( |\Phi| = v \), where \( v \sim M_P \) (Planck mass). The time arrow operator is \( \hat{T} \propto \int d^d_H x \, \Phi^\dagger \partial_{t_f} \Phi \), with \( t_f \) a fictitious fractal evolution parameter. \( \Lambda \): effective cosmological constant.

Full details: Micro-EPT

3. Primordial Black Holes: Gateways to the Fractal EPT

A. Heart of a Black Hole = Connection to Fractal State

Primordial black holes form directly during breaking, where presentation density was extreme. A black hole, especially primordial, has no singularity. Its center is a region where symmetry breaking is locally inverted. Extreme gravity « de-condenses » matter and reconnects the bubble-universe spacetime to the underlying fractal EPT state. It is an interface.

B. Time Arrow at the Interface

At this interface, the bubble-universe time arrow \( \vec{\tau}_+ \) is encoded in the coupling structure. Passing « through » would require locally inverting the breaking operator \( \hat{B} \), energetically forbidden by QFunity’s generalized second thermodynamic law.

\[ r_c \sim \ell_P (M/m_P)^{1/3} \]

\[ H_{\rm cœur}(t) = H_{EPT}^0 + g_{EPT}(t) \int_{r_c} d^3x \, \Phi^\dagger \Phi_{\rm bulle} \]

Explanation
For a black hole of mass \( M \), the heart is modeled as a quantum EPT sphere of radius \( r_c \). Primordial black holes (PBH) as breaking relics are natural dark matter candidates.

Full details: Black Hole EPT | Dark Matter | Primordial Fields Gravity