QFunity Interpretation | 232 Attoseconds in Helium Photoionization

QFunity & 232 Attoseconds

The Finite Reconfiguration Time of the EPT in Helium Photoionization

1. The Experimental Observation (PRL 2024)

Key Result: 232 Attosecond Average Time Shift

Ab initio simulations of strong-field XUV photoionization of helium reveal an average time delay (time shift) of ~232 attoseconds in the « birth time » of the ejected electron, correlated with the final energy state of the remaining ion (He⁺ 1s vs 2p).

This delay reflects temporal superposition and interelectronic entanglement during non-perturbative ionization.

Reference: Phys. Rev. Lett. 133, 163201 (2024)

2. QFunity Interpretation: EPT Reconfiguration Time

The Three Pillars Applied

The 232 as is **not** a spatial propagation delay, but the characteristic finite time for the EPT field to reconfigure its non-local correlations after violent laser perturbation.

Pillar 1: « Everything is Rotation » – EPT as Network of Toroidal Correlations

Pre-laser: Helium atom = stable coherent pattern (vortices/nodes) in EPT with [B̂^ϵ, V̂^ϵ] = 0.

\[\boxed{[\hat{B}^\epsilon, \hat{V}^\epsilon] \Psi = 0 \quad (t < 0)}\]

Laser → violent local perturbation → [B̂^ϵ, V̂^ϵ] ≠ 0 → forced transition to new entangled pattern (ion + continuum).

Link: Quantum Gravity & EPT Operators

Pillar 2: « Zero Does Not Exist » – Finite Response Time

No process can be truly instantaneous. The transition from coherent bound state to entangled continuum state requires finite internal relaxation time in EPT.

\[\boxed{\tau_{\text{EPT}} > 0 \quad \text{(reconfiguration time)}}\]

232 as = measured signature of this fundamental non-zero duration.

This illustrates magnificently that even « instantaneous » quantum correlations have an intrinsic finite duration linked to the substrate dynamics → very strong validation of the pillar « Zero does not exist ».

Pillar 3: « Everything Depends on the Observer Scale ϵ » – From Measured Shift to Fundamental Constant

Observed Δt_mes = 232 as is scale-filtered (ϵ_exp). QFunity relates it to intrinsic τ_EPT via:

\[\boxed{\Delta t_{\text{mes}} \approx \tau_{\text{EPT}} \cdot \left(1 + \frac{\Delta E}{E_{\text{EPT}}}\right)^{-1/2}}\]

Link: Observer Scale Principle

3. Key Equations of the EPT Dynamics

Total Hamiltonian (System + EPT)

\[\boxed{\hat{H}_{\text{total}} = \hat{H}_1 + \hat{H}_2 + \hat{H}_{\text{Coulomb}} + \hat{H}_{\text{EPT}}}\]

\[\boxed{\hat{H}_{\text{EPT}} = \lambda \cdot \hat{\Psi}_{\text{EPT}}(\vec{x}_1) \hat{\Psi}_{\text{EPT}}(\vec{x}_2)}\]

Generalized Schrödinger Evolution

\[\boxed{i\hbar \frac{\partial |\Psi(t)\rangle}{\partial t} = \left( \hat{V}^\epsilon + \frac{\hat{B}^\epsilon}{2} + \hat{H}_{\text{EPT}} \right) |\Psi(t)\rangle}\]

Link: Wave Nature & Generalized Schrödinger | Schrödinger Page

Entanglement Generation Rate

\[\boxed{\Gamma_{\text{ent}}(I) = \Gamma_0 + \alpha_{\text{EPT}} \cdot I}\]

\[\boxed{\tau_{\text{mes}}(I) \approx \frac{\tau_0}{1 + (I / I_0)}}\]

Atomic Number Scaling

\[\boxed{\tau_{\text{mes}}(Z) = \tau_{\text{He}} \cdot Z^{\beta} \quad (\beta \approx 0.2-0.5)}\]

4. Differential Predictions of QFunity

#	Prediction	Mechanism (Pillar)	Expected Signature	Test Method
1	τ(I) hyperbolic decay + saturation	Rotation + Intensity perturbation	τ(I) = τ₀ / (1 + α I) → τ_min > 0	Vary laser intensity over 10¹⁴–10¹⁸ W/cm²
2	τ(Z) increases with Z	Scale + Rigid patterns in heavy atoms	τ(Z) ∝ Z^β (β > 0)	He, Ne, Ar, Kr, Xe at fixed I
3	Spectral modulation	Zero does not exist + Oscillatory relaxation	ΔE_mod ≈ ħ / τ ≈ 18 meV	Ultra-high resolution ARPES (<1 meV)
4	Dependence on final ion state	Rotation + Different correlation patterns	τ longer for Rydberg states	State-resolved detection
5	Quantum threshold τ_min	Zero does not exist + Fundamental limit	τ(I→∞) = τ_min ≈ 1–10 as	Extreme intensity (relativistic regime)

These predictions (especially spectral modulation and non-zero τ_min) are sufficiently specific to be falsifiable — the mark of a strong physical theory.

5. Experimental Roadmap

Phase 1: Verification of Trends

Exp. 1: τ(I) on Helium → hyperbolic decay expected.

Exp. 2: τ(Z) on noble gases → monotonic increase predicted.

Phase 2: Fine Signatures & Fundamental Limit

Exp. 3: Search for ΔE_mod ~10–100 meV in ejected electron spectrum.

Exp. 4: Push I to extreme values → observe saturation τ_min > 0.

If τ_min or spectral modulation are confirmed, QFunity moves from compatible interpretation to predictive framework with unique signatures.

6. Conclusion: A Window into EPT Dynamics

The 232 attoseconds are the first direct glimpse into the finite, dynamic response time of the universal EPT substrate.

Standard view: average time shift in continuum superposition
QFunity: physical relaxation time of non-local correlations in EPT

Links: Emergence of Causality & c | Quantum Perception | Classicality Emergence | Quantum Retrocausality

Very robust interpretation: transforms the 232 as delay into the first observational window on the finite non-local dynamics of the EPT substrate. The differential predictions make QFunity truly testable.

References & Links

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