Test 44 — Decoherence versus Hubble Time Cosmic Record Test — A Framework for a Theory of Everything

Test 44 — Decoherence versus Hubble Time Cosmic Record Test

Quantum alternatives only become classical, recordable history if decoherence — the loss of quantum coherence to an environment — happens fast enough relative to cosmic expansion and the relevant interaction rates. Does that hold at the epochs this framework treats as "new recordable distinctions," and does citing decoherence quietly smuggle in a solution to the harder problem of why one single outcome is actualized?

Agrees consistent with standard cosmology

Read this before anything else on this page: decoherence theory is mainstream, well-tested physics (Zurek 2003; Joos et al. 2003; Schlosshauer 2007) and its application to cosmology (Polarski & Starobinsky 1996; Kiefer & Polarski 2009; Guth & Pi 1985 for the closely related squeezing argument) is standard, not something unique to this framework. What decoherence explains is why an interference pattern between alternatives becomes practically unobservable and why a pointer-basis variable (density contrast, photon polarization, ionization state) becomes a stable, redundantly-recorded classical field. What decoherence does not explain is why any one outcome out of the decohered branches is the one that is actualized — that is the separate, unsolved measurement problem / preferred-outcome question. This page verifies the rate comparison (decoherence fast relative to Hubble time) at the two epochs this framework's other tests actually lean on, and explicitly routes the single-outcome question to the Actualization terminal anchor rather than pretending decoherence answers it.

What we're checking

Observable: How fast a quantum pattern loses its "quantumness" versus how fast the universe expands — the ratio Γ/H at the moment the cosmic microwave background is imprinted.
Standard cosmology: Compton coupling to the photon–baryon fluid runs about 100× faster than expansion right through recombination — Γ/H ≈ 1.3×10² (in the range ≈114–146 across z = 1000–1200).
Granularity (consistency reading): A record locks in exactly when decoherence beats expansion — the criterion Γ/H ≫ 1. Applying the same rule to the same citable physics lands on the same Γ/H ≈ 10².
Measured: Decoherence is textbook, laboratory-tested physics; the recombination redshift z⋆ = 1089.92 ± 0.25 is fixed by the CMB itself.
The epoch: ≈380,000 years after the Big Bang — this is when the check is evaluated, not the quantity being compared.
Verdict: Agrees — same ratio, both roads.

Turn the clock back to 380,000 years after the beginning. The universe is a fog of light and matter, and something is about to happen that can never be undone: the pattern we now read across the whole sky — the cosmic microwave background — gets written into permanent history. For a pattern to become a record, its quantum fuzziness has to drain away faster than space can stretch it apart. So we ask one sharp question at that instant: which is winning, the decoherence or the expansion?

Standard physics answers first. The scattering that couples light to matter at recombination runs about a hundred times faster than the universe is expanding — Γ/H ≈ 1.3×10². The record wins decisively. Now the reconstruction on this site walks up to the same moment along a completely different path: its rule is simply that classical history exists wherever a distinction becomes cheap enough to lock in, which is exactly the condition Γ/H ≫ 1. Feed it the same well-measured physics and it lands on the same number — roughly 100 to 1, right where the sky's pattern freezes. Two roads, one answer, at the one moment that made the CMB permanent.

Be precise about what that agreement is and isn't. This is a consistency reading, not a fresh number pulled out of the geometry: the record-cost picture uses the same Γ = H criterion and the same citable results, and it agrees because it is telling the same physical story — that is the honest strength of the match. And there is one thing this test deliberately does not settle: decoherence explains why the rival quantum possibilities stop interfering with each other, but not why this particular outcome is the one that got written down. That deeper "why this branch" question is scoped out and carried elsewhere — it takes nothing away from the clean, ~100× agreement on when the record locks in.

1. Verdict

The number, both ways

Number we’re testing: How fast a quantum pattern loses its quantumness versus how fast the universe expands — the ratio Γ/H at the moment the CMB record is imprinted
Standard cosmology: Compton coupling to the photon-baryon fluid runs about 100× faster than expansion right through recombination — Γ_T/H ≈ 1.3×10² (range ≈114–146 across z = 1000–1200); inflationary squeezing-driven decoherence exceeds H by factors ~e^{2N}
This framework (granularity): A record locks in exactly when decoherence beats expansion — the criterion Γ/H ≫ 1; applying the same rule to the same citable physics lands on the same Γ/H ≈ 10²
Measured: Decoherence is textbook, laboratory-tested physics; the recombination redshift z* = 1089.92 ± 0.25 is fixed by the CMB itself (inputs: H₀ = 67.36 ± 0.54 km/s/Mpc, Ω_b h² = 0.02237 ± 0.00015, σ_T = 6.6524587×10⁻²⁵ cm²)
Agreement: Same ratio, both roads — roughly 100 to 1 (Γ_T/H ≈ 1.3×10²) right where the sky's pattern freezes; the criterion Γ/H ≫ 1 is met by two orders of magnitude (consistency check — shared inputs)

Check the source → the calculation shown on this page (Data Used · Calculation Summary)

Agrees, with a secondary DEAD-END note. The framework does not derive a new decoherence mechanism of its own; it inherits the standard cosmological and quantum-optics decoherence machinery. What is verified here is the compressed, honest record that this framework is entitled to claim: at both epochs checked below (Thomson-scattering-coupled photon-baryon plasma before recombination, and superhorizon curvature perturbations during/after inflation) decoherence rates or squeezing-driven classicalization are enormously faster than the Hubble rate, so the "cosmic record" language used throughout this test suite (CMB anisotropies, density-perturbation seeds) is justified as tracking a genuinely classical, redundantly-recorded field. The unresolved which single history actually happened question is routed honestly to Actualization, not claimed as solved.

2. Tested Claim

The precise granularity claim under test: this framework treats several early-universe transitions — the freeze-out of the primordial curvature perturbation into a classical seed field (Tests 5, 7, 34), and the photon-baryon plasma's transition into the classical last-scattering surface recorded in the CMB (Tests 28, 29, 31) — as points where a quantum degree of freedom becomes a stable, recordable classical distinction. That labeling is only justified if decoherence of the relevant quantum alternatives is fast compared to (a) the Hubble expansion rate at that epoch and (b) any competing interaction timescale, so that interference between alternatives is suppressed and a pointer-basis variable is left as a stable record before the universe expands substantially further.

3. Data Used

Planck 2018 cosmological parameters (Planck Collaboration VI, 2020, A&A 641, A6, arXiv:1807.06209), base-ΛCDM, TT,TE,EE+lowE+lensing:
- \(H_0 = 67.36 \pm 0.54\) km/s/Mpc
- \(\Omega_b h^2 = 0.02237 \pm 0.00015\)
- \(\Omega_m = 0.3153 \pm 0.0073\)
- redshift of recombination \(z_\ast = 1089.92 \pm 0.25\) (Table 2, TT,TE,EE+lowE+lensing)
Thomson scattering cross-section (CODATA 2018/PDG): \(\sigma_T = 6.6524587\times 10^{-25}\,\text{cm}^2\).
Cosmological decoherence of curvature perturbations: Polarski, D. & Starobinsky, A.A. (1996), "Semiclassicality and decoherence of cosmological perturbations," Class. Quantum Grav. 13, 377, arXiv:gr-qc/9504030; Kiefer, C. & Polarski, D. (2009), "Why do cosmological perturbations look classical to us?," Adv. Sci. Lett. 2, 164, arXiv:0810.0087 — both establish that squeezing during inflation drives the effective decoherence/classicalization rate of superhorizon curvature-perturbation modes to values that exceed the Hubble rate by factors that grow exponentially with the number of e-folds since horizon exit, i.e. decoherence is parametrically much faster than \(H\) for any mode that has been outside the horizon for more than a few e-folds.
General decoherence theory: Zurek, W.H. (2003), "Decoherence, einselection, and the quantum origins of the classical," Rev. Mod. Phys. 75, 715, arXiv:quant-ph/0105127; Schlosshauer, M. (2007), Decoherence and the Quantum-to-Classical Transition, Springer — canonical statements that decoherence explains suppression of interference and einselection of a pointer basis, but not which single outcome is realized (the "and-and to or" step, i.e. the actualization/measurement problem).

4. Calculation Summary

Check A — photon-baryon plasma before recombination (Thomson-scattering environmental coupling). Baryon number density today from \(\Omega_b h^2\):

\[ n_{b,0} = \frac{\Omega_b h^2 \,\rho_{\text{crit},0}/h^2}{m_p} \approx 2.51\times10^{-7}\ \text{cm}^{-3}, \]

using \(\rho_{\text{crit},0} = 1.878\times10^{-29}h^2\ \text{g/cm}^3\) and \(m_p = 1.673\times10^{-24}\ \text{g}\). Scaling to \(z_\ast = 1089.92\) (Planck 2018):

\[ n_{b}(z_\ast) = n_{b,0}(1+z_\ast)^3 \approx 3.26\times10^{2}\ \text{cm}^{-3}. \]

Taking the free-electron (ionization) fraction \(x_e \approx 1\) (i.e. evaluating just before recombination collapses \(x_e\), which is the physically relevant regime for the "still coupled" side of the transition), the Compton/Thomson interaction rate on photons is:

\[ \Gamma_T = n_e\,\sigma_T\,c = x_e\,n_b(z_\ast)\,\sigma_T\,c \approx 6.5\times10^{-12}\ \text{s}^{-1}. \]

The Hubble rate at \(z_\ast\) (matter-dominated approximation, \(\Omega_m=0.3153\), small radiation correction \(\Omega_r\approx9.24\times10^{-5}\)):

\[ H(z_\ast) = H_0\sqrt{\Omega_m(1+z_\ast)^3+\Omega_r(1+z_\ast)^4} \approx 5.07\times10^{-14}\ \text{s}^{-1}. \]

Result: \(\Gamma_T/H(z_\ast) \approx 1.3\times10^{2}\) at fixed \(x_e=1\). Scanning \(z=1000\)–\(1200\) at fixed \(x_e=1\) gives the same result to within a factor of order unity (\(\Gamma_T/H\) ranges \(\approx\)114–146 over that range) — Compton coupling to the photon-baryon fluid is two orders of magnitude faster than the expansion rate right through the recombination epoch. Physically, the actual decoupling of photons from the plasma (Test 29) is driven by \(x_e\) collapsing via Saha/Peebles recombination physics on top of this already-large rate ratio, not by \(\Gamma_T\) itself dropping below \(H\) while \(x_e\) stays near unity — the interaction channel that would decohere any "quantum superposition of scattering histories" is comfortably fast compared to expansion up to and through last scattering.

Check B — superhorizon curvature perturbations (inflationary squeezing/decoherence). The Polarski & Starobinsky (1996) / Kiefer & Polarski (2009) result (cited, not re-derived here) is that the squeezing parameter of a curvature-perturbation mode that exited the horizon \(N\) e-folds ago grows as \(\sim e^{2N}\), and the effective decoherence rate induced by the mode's coupling to shorter-wavelength modes/tensor perturbations scales with this squeezing. For the observationally relevant modes (horizon exit \(N\gtrsim 50\)–60 e-folds before the end of inflation, consistent with the pivot-scale requirement used in Tests 7–9), the squeezing factor \(e^{2N}\) is astronomically larger than unity (\(e^{100}\sim10^{43}\)), so the induced decoherence rate exceeds \(H\) during inflation by a correspondingly enormous margin. This is a qualitative-order-of-magnitude citation of an established result, not a fresh numerical derivation by this framework.

Cross-epoch consistency check (guardrail from the test-suite procedure): both checks are consistency checks on inherited standard-cosmology and standard-decoherence-theory rates; they do not modify \(z_\ast\), \(\Omega_b h^2\), the BBN abundances (Test 23), \(N_{\text{eff}}\) (Test 22), or the acoustic-peak geometry (Test 31). No cross-epoch damage is introduced by this test.

5. Granularity Interpretation

What becomes newly stable and recordable at each checked epoch: (a) at recombination, the photon polarization/temperature pattern imprinted by Thomson scattering off the still-coupled electron-baryon fluid becomes a redundantly-recorded classical field the instant the interaction rate stays far above \(H\) — many "copies" of the same scattering information are deposited across the last-scattering surface, which is exactly the redundancy condition decoherence theory (quantum Darwinism, Zurek 2003) requires for a classical record; (b) during inflation, a superhorizon curvature-perturbation mode's phase information becomes practically unobservable (squeezed into an effectively classical stochastic field) once its squeezing factor is large, which is what licenses treating the primordial power spectrum (Tests 7, 34) as a classical, stochastic initial condition rather than a live quantum superposition. In both cases, decoherence answers why the alternatives stop interfering and a pointer variable becomes stable — it does not answer why this particular realized curvature/temperature pattern, rather than some other decohered branch, is the one observed. That second question is the actualization/measurement problem and is routed, not solved, by this test.

6. Gate Routing

This test informs the classical-record emergence gate, with Primary result on Actualization / Encoding (the speculative dead-end layer, labeled here only for cross-reference, not asserted as established). It underwrites the record-language used by Test 5 (entropy and scale-factor continuity), Test 7 (inflationary scalar spectrum), Test 28–31 (matter–radiation equality through CMB acoustic peaks), and Test 42 (the recordability/distinguishability ledger): those tests are entitled to call their respective fossils "classical records" precisely because this test confirms the relevant decoherence/squeezing rates are fast compared to \(H\). The single-outcome/actualization residual is explicitly not closed by this test and is carried forward as an open dead-end question, consistent with Test 43's finite-observer-capacity framing.

7. Failure Mode

No failure in the rate calculation itself — both checks reproduce standard, citable results (\(\Gamma_T \gg H\) near recombination; squeezing-driven decoherence \(\gg H\) for super-horizon inflationary modes). The failure mode this test is specifically designed to catch, and that this page avoids, is the following substitution error flagged in the test-suite guardrails: treating "decoherence is fast" as equivalent to "the single-outcome/measurement problem is solved." It is not — decoherence explains loss of interference and einselection of a pointer basis (a many-branches, reduced-density-matrix statement); it does not by itself explain why one branch is the one that is experienced/actualized. This page states that distinction explicitly in §5 rather than quietly using "decoherence" and "actualization" as interchangeable words, which is the specific failure mode named in the test suite ("confuses decoherence with single outcome").

8. Next Action

Dead-end routing, not further derivation at this layer: the single-outcome/actualization residual identified in §5–7 is routed to the Actualization terminal anchor (speculative ontology layer) rather than claimed as solved by decoherence. Within standard physics, no further calculation is owed here — the rate comparisons in §4 are the complete minimum check the test-suite procedure requires, and both are consistent with the established decoherence and cosmological-perturbation literature cited in §3. Future data (higher-precision CMB polarization from LiteBIRD/CMB-S4, or direct tests of squeezing signatures such as non-Gaussianity, Test 9) could sharpen the inflationary-epoch estimate in Check B, but would not change the qualitative conclusion that decoherence rates vastly exceed \(H\) at both epochs checked.

Bottom line

This is a consistent with standard cosmology result built on standard decoherence theory: Thomson scattering keeps the photon-baryon plasma's interaction rate \(\approx\)100–150\(\times\) the Hubble rate right through recombination (this page's own recomputation from Planck 2018 parameters), and published cosmological-perturbation-decoherence results (Polarski & Starobinsky 1996; Kiefer & Polarski 2009) show squeezing-driven decoherence of superhorizon curvature modes vastly exceeds \(H\) during inflation. Both results justify the "classical cosmic record" language this framework's other tests rely on. What is not closed, and is explicitly routed to the Actualization terminal anchor rather than glossed over, is why one single decohered outcome is the one actually recorded — that is a genuine open problem shared with all of decoherence-theory-based cosmology, not a gap unique to this framework.

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