Time & Gravity · T.11 · How the photon bath selects pointer states and broadcasts a classical record · Step 12 of 13 · 14 min read
What Selects the World a Clock Sees?
On T.10 unitarity kept the full quantum state pure while an observer holding only a subsystem saw entropy rise and turn over. Why, then, does a laboratory clock always display one definite position rather than a superposition of pointers? Because electromagnetic scattering commutes with position: the ambient photon bath diagonalises the clock in the position basis and copies that eigenvalue across millions of scattered photons—while anything that does not couple to the bath leaves no optical record at all.
Human LineagePioneers of Step T.11 · Hugh Everett III (1957) · H. Dieter Zeh (1970) · Wojciech Zurek (1981, 2003, 2009) · Erich Joos & H. Dieter Zeh (1985) · Michel Brune, Serge Haroche, Jean-Michel Raimond & Davidovich (1996) · Klaus Hornberger, Lucia Hackermüller & Markus Arndt (2003–2004)Honor the humans ↓
Fixed boundaryNo theory of everything here: six evidence labels, one open question per page.
Nothing on this page is a theory of everything, and this site proposes none. Every claim carries one of six labels, each tied to a ledger row: MEASURED, DERIVED, BOUND, PROPOSED, OPEN, or SINGLE RESULT. Preprints never rise above PROPOSED. Each page ends with one open question that the next page takes up.
Plate T.11-V · Left: the 2 × 2 clock reduced density matrix ρ_S as environmental photons scatter off the split, suppressing off-diagonal coherences as γ^N while leaving the pointer diagonal untouched. Right: the Quantum Darwinism mutual-information plateau I(S : E_k) across k of N = 6 bath modes. Drawn by timegravity/make_plates.py from tools/timegravity_kernel.py.About this illustrationThis plate is a deterministic drawing, not an AI-generated image and not a photograph. The curve is the kernel's own trajectory; the shading exaggerates a clock-rate difference of about one part in 10^16 per metre so that it can be seen at all.
Instrument · Pointer-state decoherence and the Quantum Darwinism redundancy plateau
Left: the mutual information I(S : E_k) (in bits) between a superposed pointer qubit S and a captured fragment E_k of k out of N = 6 environment photon modes, plotted alongside the decaying off-diagonal coherence |ρ_{S,01}(k)| / |ρ_{S,01}(0)| = cos^k(θ). Right: the Joos–Zeh / Romero-Isart thermal photon dipole localization time τ_sc = 1 / (Λ_sc Δx²) at Δx = 10 µm from the 2.725 K cosmic microwave background to 300 K for a 10 µm dust grain, a 1 µm microsphere (10⁶ times slower by R⁶), and an electromagnetically uncoupled mass (ε = 1, Λ_EM = 0). The sliders set the photon scattering angle θ per mode and the ambient temperature T_e. The knockout sets θ = 0 (no pointer-commuting bath imprinting): off-diagonal coherence stays at 1, the redundancy plateau collapses to 0 bits, and the verifier rejects the run. Keyboard: Tab and arrows. With reduced motion on, nothing animates.
Predict before you revealBefore you move the slider: at strong photon scattering (θ = 1.35 rad across N = 6 environment modes), how many modes must an observer intercept to learn over 99% of the pointer's 1 bit of classical position information?
Redundant record I(S : E₂) at k = 2 of 6 modes0.9983 bits (R_δ = 3.0)
Joos–Zeh photon bath τ_loc (Δx = 10 µm): 2.725 K CMB vs 300 K1.63 s · 6.89e-19 s
Statevector vs Zurek closed form1.7e-14 nats · PASS
Einselection & Quantum Darwinism: the interaction Hamiltonian [Ĥ_int, Z_S] = 0 preserves pointer populations while scattering copies of Z_S into the photon bath.
I · Measured decoherence in cavities and molecular beams
Environmental decoherence is not a philosophical postulate; its rate has been measured step by step as individual photons and gas molecules carry away which-path information: in 1996 Brune, Haroche and collaborators prepared a mesoscopic superposition of coherent microwave fields in a superconducting cavity and watched its interference fringes decay as photons leaked out, and in 2003 and 2004 the Vienna fullerene interferometers measured quantitative visibility loss of C₇₀ molecules from single background-gas collisions and from thermal blackbody photons emitted by the heated molecules themselves. Every time a photon or gas atom resolves whether a mass took the left path or the right path, the two environment states become more orthogonal and the interference term between the paths shrinks by their inner product.
In Plain Words · Extra-Easy Explanation
Think of wet ink on a printing press. If a sheet of paper touches the plate without smudging it sideways, the raised letters stay sharp while sheet after sheet carries away an identical copy of the words. Anyone in the room only needs to catch one sheet of paper to know what is written on the press, without ever touching the metal plate itself.
For ordinary matter, the ambient electromagnetic field is that stream of paper. Because electric charges and dipoles scatter photons according to where they sit in space, position is the 'raised letter' that survives the contact. Superpositions of different positions are rapidly diagonalised, while the surviving position is copied into millions of scattered photons—what physicists call environment-induced superselection (einselection) and Quantum Darwinism.
Everyday Analogy & Controls Primer
Everyday analogy: a lighthouse beam sweeping through fog. A ship that reflects light scatters droplets of glare in every direction, so twenty watchers on different cliffs all agree on the ship's bearing after catching a tiny fraction of the scattered light. Something completely transparent to light leaves the fog undisturbed—not because it is in another universe, but because photons pass straight through it without taking an imprint.
How the controls work in plain words: the first slider sets θ, how strongly each scattered photon mode distinguishes left from right. As θ grows, the orange coherence curve cos^k(θ) drops toward zero while the blue mutual-information curve I(S : E_k) rises into a flat plateau near 1 bit. The second slider changes the ambient photon temperature from the 2.725 K cosmic microwave background to 300 K room temperature, scaling the dipole scattering rate as T⁹. The knockout sets θ = 0 (an electromagnetically transparent coupling): coherence stays at 1 and the classical plateau vanishes.
Plate T.11-D · Visual Intuition Bridge: ambient photons scatter off a localized dust mote (left), selecting the pointer basis and broadcasting redundant classical records across the bath (centre), verified against the 1+6-qubit statevector and Joos–Zeh R⁶T⁹ scaling (right).
Archival Tribute · The Hands Behind the Instruments
The Humans Behind Step T.11 · Pointer Bases, Photon Baths, and Cavity Cat States
Why does a macroscopic clock appear in one definite position rather than a superposition of positions? These theorists and experimentalists showed how the interaction Hamiltonian and the ambient electromagnetic bath select the pointer states and copy them across the environment.
1957 & 1981–2009 · Princeton, Austin & Los Alamos
Hugh Everett III · Wojciech Hubert Zurek
Princeton University, University of Texas at Austin & Los Alamos National Laboratory
In 1957 Hugh Everett III formulated relative-state quantum mechanics without an external collapse postulate, leaving open why observers record one preferred basis. In 1981 Wojciech Zurek showed that the apparatus–environment interaction Hamiltonian selects the pointer projectors satisfying [Ĥ_int, Π_i] = 0, and in 2009 formulated Quantum Darwinism: the classical record is the observable redundantly copied into many small fragments of the bath.
1970 & 1985 · Heidelberg
Erich Joos & H. Dieter Zeh
Institut für Theoretische Physik, Universität Heidelberg
Following H. Dieter Zeh's 1970 insight that macroscopic quantum systems cannot be isolated from their surroundings, Erich Joos and Zeh calculated in 1985 the localization rate Λ of a dust grain bathed in thermal radiation. Because long-wavelength dipole scattering scales as R⁶T⁹|(ε−1)/(ε+2)|², even the 2.7 K cosmic microwave background localizes a 10 µm grain in about one second.
1996 & 2003–2004 · Paris & Vienna
Michel Brune, Serge Haroche & Jean-Michel Raimond · Klaus Hornberger, Lucia Hackermüller & Markus Arndt
École Normale Supérieure (Paris) & University of Vienna
At the École Normale Supérieure in 1996, Michel Brune, Serge Haroche, Jean-Michel Raimond, and colleagues prepared a mesoscopic superposition of two microwave field phases in a superconducting cavity and watched single rubidium atoms trace its decoherence into a mixture. In 2003–2004 in Vienna, Klaus Hornberger, Lucia Hackermüller, and Markus Arndt measured the loss of C₇₀ matter-wave fringes under controlled gas collisions and thermal photon emission.
II · Pointer states, the redundancy plateau, and the R⁶ T⁹ photon bath
Zurek showed in 1981 and 1982 that when a quantum system S couples to an environment E through an interaction Hamiltonian Ĥ_int, the eigenstates of the observable Π̂ that commutes with Ĥ_int ([Ĥ_int, Π̂] = 0) are dynamically stable pointer states: each environment mode E_j rotates conditionally on the pointer eigenvalue without flipping it, suppressing off-diagonal superpositions by the product of mode overlaps γ^N = |⟨E^{(0)}|E^{(1)}⟩|^N. Because the Coulomb and dipole couplings of light to matter depend on position x̂, the interaction term Ĥ_int commutes with x̂ (whereas the free kinetic term p̂²/2m does not), singling out localized position states as the pointer basis of macroscopic clocks.
In 2009 Zurek showed that pure pointer-state dephasing also explains why independent observers agree on the same classical readout (Quantum Darwinism): for a symmetric pointer superposition coupled to N modes with overlap γ = |cos θ|, the mutual information between S and a fragment E_k of k modes is I(S : E_k) = h₂(γ^N) + h₂(γ^k) − h₂(γ^{N−k}), which rises rapidly to a classical redundancy plateau at S(ρ_S) ≈ ln 2 and satisfies the exact midpoint identity I(S : E_{N/2}) = S(ρ_S). On 1 + 6 qubits (statevector dimension 128) at θ = 1.35 rad, the verifier computes every reduced density matrix ρ_S, ρ_{E_k} and ρ_{S E_k} by explicit partial trace, rotates each into a dense matrix via DCT-II, diagonalises it with the track's pure-Python Jacobi solver, and matches the closed-form binary entropy curve within 1.7×10⁻¹⁴ nats across all k = 0 … 6: capturing just k = 2 modes already yields 0.9983 bits while off-diagonal coherence on S has fallen to 1.1×10⁻⁴.
Joos and Zeh derived in 1985 the long-wavelength dipole Rayleigh scattering rate of thermal photons off a dielectric sphere of radius R and permittivity ε: the localization parameter Λ_sc scales as R⁶ T_e⁹ Re[(ε − 1)/(ε + 2)]², so even the 2.725 K cosmic microwave background localizes a R = 10 µm dust grain across Δx = 10 µm on a one-second timescale (τ_CMB = 1.63 s for ε = 5.7, or 0.61 s in the conducting limit Λ_CMB = 1.64×10⁶ cm⁻² s⁻¹), whereas 300 K room-temperature photons localize the same split in 6.89×10⁻¹⁹ s. Because of the sixth power in radius R⁶, shrinking the sphere tenfold from a 10 µm dust grain to the 1 µm diamond microsphere of T.05 reduces Λ_sc by exactly 10⁶ (lengthening τ_CMB to 1.63×10⁶ s and τ_300K to 0.69 ps). And for an electromagnetically uncoupled test mass (ε = 1, zero electric charge and dipole moment), Re[(ε − 1)/(ε + 2)] = 0 and Λ_sc = 0 at every temperature: the photon bath neither decoheres it nor records its position.
§ II.1 · The derivation the verifier runs, in four stages
|Ψ_{SE}(θ)⟩ = (|0⟩_S ⊗ |0⟩^{⊗6} + |1⟩_S ⊗ (cos θ |0⟩ + sin θ |1⟩)^{⊗6}) / √2 in 2⁷ = 128 dimensions. Tracing out all 6 modes leaves off-diagonal coherence |ρ_{S,01}| / (1/2) = cos⁶(θ), checked against explicit partial trace to < 1e-15.
Stage 2 · Partial-trace Jacobi diagonalisation across k = 0 … 6
For every fragment size k ∈ {0 … 6}, the kernel forms ρ_{E_k} (2^k × 2^k) and ρ_{S E_k} (2^{k+1} × 2^{k+1}) by explicit partial trace, rotates each by an orthogonal DCT-II matrix into a dense symmetric matrix, and diagonalises with cyclic Jacobi to obtain I(S : E_k).
Jacobi mutual information matches h₂(γ^N) + h₂(γ^k) − h₂(γ^{N−k}) within 1.7e-14 nats across all k and θ, reaching 0.9983 bits at k = 2 (θ = 1.35 rad) and obeying I(S : E_3) = S(ρ_S) to 2.4e-15. Dipole photon scattering verifies Λ(10 µm)/Λ(1 µm) = 10⁶ and Λ(300 K)/Λ(T_CMB) = (300/T_CMB)⁹ to < 1e-15.
Stage 4 · Planted defect knockout
Setting θ = 0 removes pointer-commuting bath imprinting: off-diagonal coherence remains 1.0 and the k = 2 mutual information collapses to 0 bits, failing the plateau gate and rejecting the run.
III · Three distinct concepts: pointer records, decohered branches, and dark sectors
Once environmental scattering drives the overlap ⟨E^{(0)}|E^{(1)}⟩ = γ^N toward zero, what happens to the unselected branch is the subject of competing proposals: Everett's 1957 relative-state formulation keeps the global state unitary so both orthogonal branches persist in Hilbert space without being able to interfere locally, whereas objective-reduction models such as Diósi (1987) and Penrose (1996) modify Schrödinger's equation so gravitational self-energy collapses superpositions at a physical rate.As examined on T.06, underground X-ray searches such as VIP-2 bound the parameter-free Diósi–Penrose cutoff to r₀ > 0.54×10⁻¹⁰ m while leaving softer smearing scales open.
Whether decohered branches of ordinary matter persist physically after photon scattering makes their environment records orthogonal or are eliminated by an objective collapse mechanism is not settled by any experiment to date: einselection and Quantum Darwinism derive why each branch sees a stable classical pointer, not why one branch is experienced rather than another. Crucially, this page keeps a strict three-way fence: (1) electromagnetic pointer selection (DERIVED from MEASURED cavity and molecular decoherence), (2) unselected decohered branches in Hilbert space (whose ontological status is OPEN), and (3) matter in our same four-dimensional spacetime that has zero tree-level electromagnetic coupling (ε = 1, α_EM = 0). Decohered branches and electromagnetically uncoupled dark sectors are completely different physical concepts—and the next page asks how two clocks can meet through gravity alone when the electromagnetic bath is completely silent.
Grounding ledger rows cited on this page
Every row below resolves in the site's offline Crossref cache. The lint derives what each set of rows can carry; a person decided the label on each claim above. Rows pass a review date and the build fails until someone rereads the source.
Scite column: [observed: Scite ML citation classification, accessed 2026-11-09, 2026-11-10] via Scite's public tallies endpoint. The counts are a classifier's output over indexed citation statements, an evidence-synthesis habit borrowed from medicine; they never replace reading the source, and a row with more contrasting than supporting statements is flagged for a human re-read in the label checklist.
AI contribution to the cited results: none. No AI system contributed to any measurement or derivation cited on this page. The page text, instrument and verifier were drafted with AI assistance and checked by the site maintainer against the primary sources listed below.
Rebuild this instrument locally and run the verifier as the acceptance gate: python skills/timegravity/t11/make_t11.py then python skills/timegravity/t11/verify_t11_einselection.py (and --planted-defect, which must fail). Then python tools/check_timegravity_labels.py.
Show the SKILL.md source
---
name: timegravity-t11-einselection
description: Rebuild and verify the Time & Gravity T.11 toy - a 1+6 qubit pure-dephasing pointer-state and Quantum Darwinism statevector model whose Jacobi-diagonalised partial traces match Zurek's closed-form mutual-information plateau I(S : E_k) = h_2(gamma^N) + h_2(gamma^k) - h_2(gamma^{N-k}) within 1e-12, paired with the Joos-Zeh and Romero-Isart R^6 T^9 dipole photon scattering localization table - with a planted defect (theta = 0 zero pointer imprinting).
license: MIT
compatibility: Claude Code, GitHub Copilot, Cursor, Google Antigravity, OpenAI Codex, Ollama (Qwen 3.8 / Gemma 4)
---
# What Selects the World a Clock Sees? (T.11 · Time & Gravity)
> **Fixed Boundary (`EN`):** Nothing on this page is a theory of everything, and this site proposes none. Every claim carries one of six labels, each tied to a ledger row: MEASURED, DERIVED, BOUND, PROPOSED, OPEN, or SINGLE RESULT. Preprints never rise above PROPOSED. Each page ends with one open question that the next page takes up.
>
> **Frontera Fija (`ES-MX`):** Nada en esta página es una teoría del todo, y este sitio no propone ninguna. Cada afirmación lleva una de seis etiquetas, cada una ligada a una fila del libro de registro: MEDIDO, DERIVADO, COTA, PROPUESTO, ABIERTO o RESULTADO ÚNICO. Las prepublicaciones nunca suben de PROPUESTO. Cada página termina con una pregunta abierta que la siguiente página retoma.
## 1. Page, canonical URL and governing equations
- **Track page**: `T.11` (Time & Gravity, reading order 12 of 13, dated `2026-11-10`)
- **Canonical URL**: https://informatico.ai/timegravity/t11/ (Spanish: https://informatico.ai/es-mx/timegravity/t11/)
- **Pointer-basis commutation condition**: `[H_int, Π̂] = 0` (`Π̂ = σ_z` or position `x̂`); pointer states remain unentangled while each bath mode rotates by `|E_j^(1)⟩ = cos(θ)|0⟩ + sin(θ)|1⟩`, overlap `γ = |cos(θ)|`.
- **Off-diagonal suppression & Quantum Darwinism mutual information**: `|ρ_{S,01}(N)| / |ρ_{S,01}(0)| = γ^N`, `I(S : E_k) = h_2(γ^N) + h_2(γ^k) − h_2(γ^{N−k})`.
- **Thermal photon dipole scattering**: `Λ_sc = (8! · 8 ζ(9) c R^6 / 9π) (k_B T_e / ħc)^9 Re[(ε−1)/(ε+2)]^2`, `Γ_sc = Λ_sc Δx²`.
- **Central numbers**: on `1 + 6` qubits (`dim = 128`, `θ = 1.35 rad`, `γ = 0.2190`), statevector partial traces diagonalised via Jacobi match closed-form `I(S : E_k)` within `1.69e-14 nats` (`< 1e-12`), reaching `0.9983 bits` by `k = 2` modes while `|ρ_{S,01}| / |ρ_{S,01}(0)| = 1.103 × 10^{-4}`; for Joos & Zeh's `R = 10 µm` dust grain at `Δx = 10 µm`, `τ_CMB = 1.634 s` (`ε = 5.7`) or `0.609 s` (conductor, `Λ_CMB = 1.643 × 10^6 cm^{-2} s^{-1}`) vs `τ_300K = 6.888 × 10^{-19} s`, while an `R = 1 µm` microsphere is `10^6` times slower (`R^6` scaling within `6.98e-16`) and an electromagnetically uncoupled sector (`ε = 1`) has `Λ_EM = 0`.
- **Generator**: `python skills/timegravity/t11/make_t11.py`
- **Verifier**: `python skills/timegravity/t11/verify_t11_einselection.py`
- **Knockout check**: `python skills/timegravity/t11/verify_t11_einselection.py --planted-defect` (must exit non-zero: `θ = 0` zero pointer imprinting collapses `I(S : E_k)` to `0`)
- **Label lint**: `python tools/check_timegravity_labels.py` (and `--planted-defect`, `--mutants`)
## 2. Ledger rows this page may cite (timegravity/ledger.json)
| Row | Label | Source | DOI |
| --- | --- | --- | --- |
| `T11-BRUNE1996` | MEASURED | Brune et al. 1996, cavity-QED mesoscopic Schrödinger cat decoherence | https://doi.org/10.1103/PhysRevLett.77.4887 |
| `T05-HORNBERGER2003` | MEASURED | Hornberger et al. 2003, collisional decoherence of C70 fullerenes | https://doi.org/10.1103/PhysRevLett.90.160401 |
| `T05-HACKERMULLER2004` | MEASURED | Hackermüller et al. 2004, thermal-photon emission decoherence of C70 | https://doi.org/10.1038/nature02276 |
| `T08-MATHER1994` | MEASURED | Mather et al. 1994, COBE FIRAS 2.726 K CMB blackbody spectrum | https://doi.org/10.1086/173574 |
| `T11-ZUREK1981` | DERIVED | Zurek 1981, pointer basis of quantum apparatus | https://doi.org/10.1103/PhysRevD.24.1516 |
| `T11-JOOS1985` | DERIVED | Joos & Zeh 1985, emergence of classical properties through environment scattering | https://doi.org/10.1007/BF01725541 |
| `T11-ZUREK2009` | DERIVED | Zurek 2009, Quantum Darwinism and classical redundancy plateau | https://doi.org/10.1038/nphys1202 |
| `T11-EVERETT1957` | PROPOSED | Everett 1957, relative-state formulation of quantum mechanics | https://doi.org/10.1103/RevModPhys.29.454 |
| `T06-DIOSI1989` | PROPOSED | Diósi 1989, gravitational self-energy objective reduction | https://doi.org/10.1103/PhysRevA.40.1165 |
| `T06-PENROSE1996` | PROPOSED | Penrose 1996, gravity's role in quantum state reduction | https://doi.org/10.1007/BF02105068 |
| `T06-DONADI2020` | BOUND | Donadi et al. 2020, VIP-2 underground Ge X-ray bound on parameter-free Diósi–Penrose | https://doi.org/10.1038/s41567-020-1008-4 |
## 3. Tool-neutral agent packet and security boundary (`security-runtime`)
1. **Rebuild locally**: `python skills/timegravity/t11/make_t11.py`; standard library only; writes only under `src/research/timegravity/t11/files/`.
2. **Acceptance gate**: `python skills/timegravity/t11/verify_t11_einselection.py` must print `"status": "PASS"` with `statevector_matches_zurek_closed_form: PASS`; `--planted-defect` must exit non-zero. Then `python tools/check_timegravity_labels.py`.
3. **Security boundary (`security-runtime`)**: no shell outside the repository, no home-directory access, no outbound network for this task.
## 4. Deterministic verification and falsification rules
1. Across `k ∈ {0 … 6}` and `θ ∈ {0, π/6, π/3, 1.35, π/2}`, Jacobi-diagonalised partial traces of the `128`-component `1 + 6` qubit statevector match `I(S : E_k) = h_2(γ^N) + h_2(γ^k) − h_2(γ^{N−k})` within `1e-12` and satisfy `I(S : E_{N/2}) = S(ρ_S)` and `I(S : E_N) = 2 S(ρ_S)` within `1e-12`.
2. At `θ = 1.35 rad`, a `k = 2` mode fragment carries `> 0.90 bits` (`0.9983 bits`) while off-diagonal system coherence drops to `< 10^{-3}` (`1.103 × 10^{-4}`).
3. Dipole photon scattering satisfies `Λ(R = 10 µm) / Λ(R = 1 µm) = 10^6` and `Λ(300 K) / Λ(T_CMB) = (300 / T_CMB)^9` within `1e-12`, and vanishes (`Λ = 0`) at `ε = 1`.
4. Planted defect: setting `θ = 0` (`γ = 1`, no pointer-commuting bath imprinting) collapses `I(S : E_2)` to `0`; rule 2 fails and `--planted-defect` exits non-zero.
5. `t11_reference.json` matches `manifest.json` and regenerates byte for byte.
## 5. What the instrument shows (reader side)
- Left panel: Quantum Darwinism mutual-information curve `I(S : E_k) / H(S)` across fragment size `k / N` alongside system off-diagonal coherence `|ρ_{S,01}(k)| / |ρ_{S,01}(0)| = γ^k`. Right panel: Joos–Zeh thermal photon coherence time `τ_sc = 1 / (Λ_sc Δx²)` across `T_e` (`2.725 K` CMB vs `300 K`) for `R = 10 µm` vs `R = 1 µm` vs an electromagnetically uncoupled test mass (`α_EM = 0`).
- Knockout: turn off pointer-commuting bath imprinting (`θ = 0`); the classical redundancy plateau flattens to `I(S : E_k) = 0`.
- Predict before you reveal: whether observing `2` out of `6` scattered photon modes already delivers nearly the entire `1 bit` of pointer position information without touching the system itself.
## 6. Exact T0–T3 truth boundary
### In the repository today (T0/T1)
- Kernel `tools/timegravity_kernel_einselection.py`, generator, verifier, ledger rows above, and the ES module `src/research/modules/timegravity-slope.mjs`.
### Not on this page (T2/T3)
- Whether decohered branches that have become orthogonal in the photon bath (`|⟨E^(0)|E^(1)⟩| = γ^N → 0`) persist as physical Everettian worlds (`PROPOSED`) or are pruned by an objective collapse mechanism (`PROPOSED`/`BOUND`) is `OPEN`.
- Decohered branches of ordinary matter in Hilbert space and electromagnetically uncoupled dark-matter sectors in spacetime (`T.12`) are distinct physical concepts and are never equated.
Show the verifier verify_t11_einselection.py
#!/usr/bin/env python3
"""Standalone stdlib verifier and planted-defect knockout for Time & Gravity · T.11 (What Selects the World a Clock Sees?).
Canonical URL: https://informatico.ai/timegravity/t11/
Central number: for a system qubit S coupled via a pointer-commuting interaction [H_int, sigma_z] = 0 to N = 6
environment modes (statevector dimension 2^7 = 128), the Jacobi-diagonalised partial-trace mutual information
I(S : E_k) matches Zurek's closed-form binary entropy curve h_2(gamma^N) + h_2(gamma^k) - h_2(gamma^{N-k}) within
1e-12 across all k in {0 .. 6} and all scattering angles theta, reaching 0.9983 bits of classical redundancy by
k = 2 modes at theta = 1.35 rad while satisfying the exact midpoint identity I(S : E_{N/2}) = S(rho_S); for
Joos & Zeh's R = 10 um dust grain at dx = 10 um, dipole photon scattering gives tau_CMB = 1.634 s vs tau_300K =
6.888e-19 s (and 0 for an electromagnetically uncoupled sector eps = 1). Planted defect: setting theta = 0
(no pointer-commuting bath imprinting) collapses the redundancy plateau to zero; `--planted-defect` exits non-zero.
Boundary: Nothing on this page is a theory of everything, and this site proposes none.
"""
from __future__ import annotations
import hashlib
import json
import sys
from pathlib import Path
ROOT = Path(__file__).resolve().parents[3]
sys.path.insert(0, str(ROOT / "tools"))
from timegravity_kernel_einselection import EINSELECTION_TOL, check_einselection # noqa: E402
FILES_DIR = ROOT / "src" / "research" / "timegravity" / "t11" / "files"
def verify_reference_files() -> dict:
manifest = json.loads((FILES_DIR / "manifest.json").read_text(encoding="utf-8"))
out = {}
for entry in manifest["files"]:
raw = (FILES_DIR / entry["filename"]).read_bytes()
assert len(raw) == entry["bytes"], f"{entry['filename']}: byte count mismatch"
digest = hashlib.sha256(raw).hexdigest()
assert digest == entry["sha256"], f"{entry['filename']}: sha256 mismatch"
out[entry["filename"]] = digest[:12]
ref = json.loads((FILES_DIR / "t11_reference.json").read_text(encoding="utf-8"))
assert ref["max_mi_dev_nats"] < EINSELECTION_TOL, "reference statevector I(S:E_k) misses closed-form Zurek formula"
assert ref["k2_plateau_bits"] > 0.90, "reference Quantum Darwinism plateau missing at k = 2"
assert ref["photon_bath_localization"]["r6_scaling_rel_err"] < EINSELECTION_TOL, "reference R^6 Rayleigh scaling error"
return out
def main(argv: list[str] | None = None) -> int:
args = argv if argv is not None else sys.argv[1:]
planted = "--planted-defect" in args
try:
res = check_einselection(planted_defect=planted)
assert res["statevector_ok"], (
f"1+6 qubit statevector partial trace misses closed-form I(S:E_k) by {res['max_mi_dev_nats']:.3e} (> {EINSELECTION_TOL:g})"
)
assert res["plateau_ok"], (
f"pointer redundancy plateau collapsed (k=2 mutual information = {res['k2_plateau_bits']:.4f} bits, "
f"coherence ratio = {res['coherence_ratio_n6']:.4f}); without pointer-commuting scattering no classical record forms"
)
assert res["photon_scaling_ok"], f"Joos-Zeh photon scattering scaling error {res['r6_scaling_rel_err']:.3e}"
assert res["defect_rejected"], "planted zero-imprinting state was accepted as having a redundancy plateau"
files = verify_reference_files()
except AssertionError as exc:
print(json.dumps({"status": "FAIL", "folio_id": "T.11", "error": str(exc)}), file=sys.stderr)
return 1
print(json.dumps({
"status": "PASS",
"folio_id": "T.11",
"canonical_url": "https://informatico.ai/timegravity/t11/",
"central_number": {
"max_mi_dev_nats": res["max_mi_dev_nats"],
"k2_plateau_bits": res["k2_plateau_bits"],
"coherence_ratio_n6": res["coherence_ratio_n6"],
"dust_10um_tau_cmb_s": res["dust_10um_tau_cmb_s"],
"dust_10um_tau_300k_s": res["dust_10um_tau_300k_s"],
"tolerance": EINSELECTION_TOL,
},
"geometry_checks": {
"statevector_matches_zurek_closed_form": "PASS",
"midpoint_and_full_bath_identities": "PASS",
"quantum_darwinism_redundancy_plateau": "PASS",
"joos_zeh_r6_t9_photon_scaling": "PASS",
"planted_defect_knockout": "REJECTED_AS_EXPECTED",
"planted_k2_plateau_bits": res["planted_k2_plateau_bits"],
},
"reference_files_sha256_12": files,
}, indent=2))
return 0
if __name__ == "__main__":
raise SystemExit(main())
Primary sources
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Hornberger, K., Uttenthaler, S., Brezger, B., Hackermüller, L., Arndt, M., & Zeilinger, A. (2003). Collisional decoherence observed in matter wave interferometry. Physical Review Letters, 90(16), 160401. DOI DOI 10.1103/PhysRevLett.90.160401[Scite ↗]
Hackermüller, L., Hornberger, K., Brezger, B., Zeilinger, A., & Arndt, M. (2004). Decoherence of matter waves by thermal emission of radiation. Nature, 427, 711–714. DOI DOI 10.1038/nature02276[Scite ↗]
Mather, J. C., et al. (1994). Measurement of the cosmic microwave background spectrum by the COBE FIRAS instrument. The Astrophysical Journal, 420, 439–444. DOI DOI 10.1086/173574[Scite ↗]
Zurek, W. H. (1981). Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse? Physical Review D, 24(6), 1516–1525. DOI DOI 10.1103/PhysRevD.24.1516[Scite ↗]
Joos, E., & Zeh, H. D. (1985). The emergence of classical properties through interaction with the environment. Zeitschrift für Physik B Condensed Matter, 59(2), 223–243. DOI DOI 10.1007/BF01725541[Scite ↗]
Everett, H. (1957). 'Relative state' formulation of quantum mechanics. Reviews of Modern Physics, 29(3), 454–462. DOI DOI 10.1103/RevModPhys.29.454[Scite ↗]
Diósi, L. (1987). A universal master equation for the gravitational violation of quantum mechanics. Physics Letters A, 120(8), 377–381. DOI DOI 10.1016/0375-9601(87)90681-5[Scite ↗]
Penrose, R. (1996). On gravity's role in quantum state reduction. General Relativity and Gravitation, 28(5), 581–600. DOI DOI 10.1007/BF02105068[Scite ↗]
Donadi, S., Piscicchia, K., Curceanu, C., Diósi, L., Laubenstein, M., & Bassi, A. (2020). Underground test of gravity-related wave function collapse. Nature Physics, 17, 74–78. DOI DOI 10.1038/s41567-020-1008-4[Scite ↗]
This page ends with one open question
If the electromagnetic bath only records and decoheres what couples to photons, how could our clocks ever detect a sector of matter that never scatters light at all?
