Semiclassical Recovery, Decoherence, Obstructions, and Status

A quantum-cosmology state supports semiclassical spacetime when a WKB branch defines a stable relational time, perturbations obey approximately unitary QFT evolution, environmental records suppress interference, backreaction remains small, and a positive physical measure normalizes branch probabilities. Decoherence explains effective branch autonomy; it does not derive the Born rule, select a unique boundary state, or prove singularity resolution.

Required background. Bounce and Singularity-Resolution Claims, Quantum Geometrodynamics Beyond Minisuperspace, and Initial-State and Trans-Planckian Interfaces supply the model inputs.

Helpful background. Decoherence and the Quantum-to-Classical Claim, Canonical and Loop Programs: Evidence, Obstructions, and Current Status, and Cosmological Backreaction Benchmarks supply controls.

Branch decoherence

For two WKB backgrounds entangled with perturbative environments,

$$|\Psi\rangle=c_+|+\rangle|E_+\rangle +c_-|-\rangle|E_-\rangle.$$

Tracing the environment gives off-diagonal factor

$$D=\langle E_-|E_+\rangle.$$

For approximately independent modes, $D=\prod_kD_k$, so many weak records can make $|D|\ll1$. Each branch may then support an effective Schrödinger evolution. This does not make $|c_\pm|^2$ probabilities without a physical inner product and interpretive rule.

Application: a recovery test

Compute $D$ while varying the environmental cutoff, then verify on each branch:

$$\frac{\Delta a}{\langle a\rangle}\ll1,\qquad \frac{\rho_{\mathrm{pert}}}{\rho_{\mathrm{bg}}}\ll1, \qquad \partial_t\langle H_{\mathrm{constraint}}\rangle\simeq0.$$

Normalize with the same physical measure used to define conditional probabilities. Reverse the tracing or include recoherence-capable modes; branch autonomy should be stated for the tested observables and times.

Status through August 2026

Wheeler–DeWitt and WKB methods derive semiclassical QFT under controlled branch assumptions. No-boundary and tunneling programs possess explicit saddles but retain contour, perturbation, and measure disputes; recent Lorentzian analyses continue to find problematic perturbation sectors in many setups Matsui 2024. Standard LQC models give precise relational bounces, while covariance, quantization ambiguity, inhomogeneous stability, and full-LQG derivation remain active; current contrary models can retain singularities Bojowald, Diaz, and Duque 2025.

Adversarial conclusion test

Change clock, inner product, contour, factor ordering, environment split, fiducial cell, and perturbation cutoff. Demand agreement of relational observables within errors. Add BKL and gradient modes and test curvature and geodesic criteria. If only interference is suppressed, report decoherence—not classical selection or resolution.

Strongest conclusion

Quantum cosmology contains controlled model calculations of relational evolution, state preparation, decoherence, and bounces. No current program jointly supplies a unique physical measure, generic inhomogeneous singularity resolution, derivation from a complete full theory, and distinctive empirical prediction. The partial achievements remain real when stated at their actual level.

The chapter overview contains the structure diagram and validity and failure diagram. They are embedded there once so that their shared chapter-level context is not repeated on every article.

For the chapter-wide comparison of assumptions, counterevidence, falsifiers, and claim ceilings, see the claim-domain table.

References

• Bojowald, M., M. Diaz, and E. I. Duque. “Singularities in Loop Quantum Cosmology.” July 2025. arXiv:2507.08116.
• Halliwell, J. J., and S. W. Hawking. “Origin of Structure in the Universe.” Physical Review D 31 (1985): 1777–1791. DOI.
• Matsui, H. “No Smooth Spacetime: Exploring Primordial Perturbations in Lorentzian Quantum Cosmology.” April 2024. arXiv:2404.18609.