Coherence Map — Quantum Mechanics

TriadicFrameworks /docs/theories/quantum_mechanics/coherence_map.md#

This map defines how coherence behaves across the QM substrate.

1. Coherence Dimensions#

QM coherence is evaluated across five substrate‑level dimensions:

1.1 Amplitude Coherence#

• phase integrity
• norm preservation
• interference structure
• amplitude geometry stability

1.2 Operator Coherence#

• Hermiticity
• commutation relations
• spectral stability
• unitary evolution consistency

1.3 Basis Coherence#

• orthonormality
• completeness
• unitary basis transitions
• representation invariance

1.4 Measurement Coherence#

• projection rules
• eigenbasis stability
• probability conservation
• collapse consistency

1.5 Entanglement Coherence#

• tensor‑product structure
• reduced states
• correlation geometry
• non‑classicality integrity

2. Coherence Levels (C0–C4)#

C0 — Incoherent#

• amplitude undefined
• operator algebra broken
• basis inconsistent
• measurement rules invalid

C1 — Weak Coherence#

• partial amplitude stability
• basis drift
• decoherence dominant
• measurement unreliable

C2 — Moderate Coherence#

• stable amplitudes
• operators well‑defined
• basis transformations valid
• entanglement fragile

C3 — Strong Coherence#

• full amplitude integrity
• unitary evolution stable
• measurement consistent
• entanglement robust

C4 — Perfect Coherence#

• idealized Hilbert‑space behavior
• no decoherence
• perfect operator algebra
• maximal entanglement stability

C4 is theoretical; real systems approach C3.

3. Coherence Field#

The coherence field is a gradient over:

• amplitude stability
• operator consistency
• basis integrity
• measurement reliability
• entanglement robustness

High gradients indicate coherence instability, typically near:

• measurement
• environment coupling
• basis transitions

4. Collapse Modes#

QM coherence fails through four canonical collapse modes:

M1 — Measurement Collapse#

• projection onto eigenbasis
• non‑unitary
• coherence lost in orthogonal components

M2 — Decoherence Collapse#

• environment coupling
• phase information lost
• mixed states produced

M3 — Basis Drift Collapse#

• unstable basis choice
• representation inconsistency
• loss of amplitude clarity

M4 — Operator Instability Collapse#

• non‑Hermitian drift
• broken commutation structure
• invalid spectral decomposition

5. RTT Regime Coherence#

R1 — Quantum Amplitude Regime#

Coherence strongest.

• unitary evolution stable
• measurement rules valid
• entanglement robust
• decoherence manageable

R2 — QFT Regime#

Coherence embedded in field structure.

• QM coherence becomes mode‑level
• vacuum structure influences stability

R3 — High‑Energy Resonance#

Coherence degrades.

• running couplings distort operator algebra
• amplitude geometry insufficient

R4 — Cosmological Regime#

Coherence incomplete.

• horizon‑scale fields dominate
• measurement rules degrade

6. Diagnostics#

A QM system is coherent when:

• ⟨ψ|ψ⟩ = 1
• U(t) is unitary
• operators are Hermitian
• basis is orthonormal
• entanglement is stable
• decoherence is controlled

A system is incoherent when:

• norm drifts
• operators lose Hermiticity
• basis becomes unstable
• measurement rules fail
• environment dominates

Summary#

Quantum Mechanics coherence is:

• amplitude‑first
• operator‑aligned
• basis‑true
• measurement‑consistent
• entanglement‑aware
• RTT‑dependent

QM coherence is strongest in R1, embedded in R2, degraded in
R3, and incomplete in R4.