QFunity vs Hawking & Hertog | Deeper Resolution to Eternal Inflation

QFunity vs Hawking & Hertog

A Deeper Resolution to Eternal Inflation

1. The Hawking-Hertog Framework (2008)

Key Pillars of « A Smooth Exit from Eternal Inflation »

No-Boundary Proposal: Universe emerges from compact Euclidean geometry without initial singularity
Path integral over geometries & fields → Wave function Ψ[h,Φ]
Smooth exit: Selection of classical histories via late-time observers (anthropic weighting)
Goal: Explain emergence of one large, homogeneous, isotropic classical universe from quantum superposition

Reference: arXiv:0803.1663 (JHEP 04 (2008) 073)

HH offers an elegant semiclassical approach but remains limited to minisuperspace and anthropic selection.

2. QFunity: A More Fundamental Starting Point

The Emergent Pre-Temporal State (EPT)

EPT is the unique, acausal, pre-geometric, fractal substrate encoding all possibilities.

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

Ψ_EPT is the universal wave function before any geometry or time exists.

Link: EPT Page

EPT is ontologically deeper than HH path integral: no need to sum over geometries – they emerge from one substrate.

3. Emergence of Time: Beyond Wick Rotation

Symmetry Breaking as the Origin of Time

\[\boxed{i\hbar \frac{\partial}{\partial t} \equiv [\hat{B}^\epsilon, \hat{V}^\epsilon]}\]

\[\boxed{\lim_{\epsilon \to 0^+} [\hat{B}^\epsilon \hat{V}^\epsilon – \hat{V}^\epsilon \hat{B}^\epsilon] \Psi_{\text{EPT}} = \Lambda \cdot \frac{\Psi_{\text{EPT}}}{\sqrt{\|\Psi_{\text{EPT}}\|^2 + \epsilon^2}}}\]

Time is the dynamical consequence of non-commutativity – more intrinsic than Wick rotation.

QFunity’s mechanism is fully dynamical and unifies time, causality and scale dependence.

4. Emergence of Classical Spacetime

Scale-Dependent Metric

\[\boxed{g_{\mu\nu}(\epsilon) = g_{\mu\nu}^{\text{GR}} + \frac{\ell_P^2}{\epsilon^2} g_{\mu\nu}^{\text{LQG}} + \alpha’ g_{\mu\nu}^{\text{strings}}}\]

At observer scale ϵ ≫ ℓ_P → pure GR emerges naturally.

Classical 4D spacetime is an effective description at macroscopic ϵ – no need for post-selection.

5. The Measurement Problem & History Selection

Intrinsic Observer-Dependent Filtering

\[\boxed{P(\psi \to \phi) = \frac{|\langle \phi | \psi \rangle|^2}{\|\Psi\|^2 + \epsilon_O^2}}\]

Only histories observable at scale ϵ_O become classical – automatic physical selection, not anthropic.

Resolves the measurement problem more elegantly than late-time observer weighting.

6. Comparison Table: HH vs QFunity

Aspect	Hawking-Hertog (2008)	QFunity
Fundamental Substrate	Euclidean path integral over geometries	Single acausal EPT {B̂^ϵ, V̂^ϵ}
Emergence of Time	Wick rotation	Non-commutativity [B̂^ϵ, V̂^ϵ] → iℏ∂_t
Classical Spacetime	Selected history	Effective at large ϵ: g_μν(ϵ) ≈ g_GR
History Selection	Anthropic (late observers)	Automatic via observer scale ϵ_O
Multivers	Pocket universes with different constants	Fractal bubble-universes from local symmetry breaks
Measurement Problem	Remains open / anthropic	Resolved intrinsically

7. Conclusion: QFunity Makes HH Challenges Obsolete

QFunity does not merely solve the problems of eternal inflation and smooth exit – it renders them secondary by starting from a deeper ontological level:

One eternal EPT instead of infinite path integral
Intrinsic emergence of time, space, and classicality via symmetry breaking & scale ϵ
Physical resolution of the measurement problem without external anthropic principle

Why this history? Because our observer scale ϵ makes it the only one that becomes observable.

QFunity offers a more unified, elegant and falsifiable framework – a natural successor to Hawking-Hertog cosmology.

References & Links

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