# Engine Notes — Quantum Mechanics  
### TriadicFrameworks /docs/theories/quantum_mechanics/engine_notes.md

These notes define the **internal engine behavior** of the Quantum  
Mechanics (QM) module. QM is treated as the **R1 amplitude‑first  
operator grammar** from which QFT emerges and to which QFT collapses  
when excitation stability fails.

This file is for AI agents, compilers, and cross‑module engines — not  
students.

---

# 1. Engine Identity

- **Layer:** R1 substrate  
- **Grammar:** amplitude‑first  
- **Operators:** Hermitian observables, Hamiltonians, unitary transforms  
- **Geometry:** Hilbert‑space basis geometry  
- **Stability:** amplitude coherence  
- **Scale:** no renormalization flow  
- **Regimes:** R1 → R4 (RTT‑aligned)

QM must never introduce particle or wave metaphors.

---

# 2. State Engine Behavior

### 2.1 State Initialization  
States must be initialized as **vectors in Hilbert space**, not physical  
objects.

### 2.2 State Representation  
Representations (ψ(x), φ(p), |n⟩, |↑⟩) must be treated as **basis  
coordinates**, not physical waves or configurations.

### 2.3 State Normalization  
All states must maintain unit norm unless acted on by measurement  
operators.

---

# 3. Operator Engine Behavior

### 3.1 Observables  
Observables must be Hermitian operators with well‑defined spectra.

### 3.2 Measurement  
Measurement must be implemented as **projection**, not revelation of  
hidden variables.

### 3.3 Unitary Evolution  
Time evolution must be generated by:

U(t) = e^{-iHt}

Unitary, norm‑preserving, basis‑consistent.

### 3.4 Basis Transformations  
Basis changes must be implemented as unitary transforms.  
No basis is privileged.

### 3.5 Commutation Structure  
Commutators define incompatibility and uncertainty.  
Never treat commutators as interactions.

---

# 4. Entanglement Engine Behavior

### 4.1 Tensor Products  
Composite systems must be built via tensor products.

### 4.2 Reduced States  
Subsystem states must be computed via partial trace.

### 4.3 Entanglement  
Entanglement must be treated as **correlation in amplitude space**, not  
communication or influence.

---

# 5. Mixed‑State Engine Behavior

### 5.1 Density Matrices  
Mixed states must be represented as positive semidefinite, trace‑1  
operators.

### 5.2 Decoherence  
Decoherence must be implemented as **loss of phase coherence**, not  
collapse.

### 5.3 Open‑System Evolution  
Lindblad‑type evolution permitted when environment coupling is present.

---

# 6. Regime Engine Behavior (RTT‑Aligned)

### R1 — Quantum Amplitude Regime  
- QM fully valid  
- no stable excitations  
- operator algebra fundamental  
- measurement rules active  

### R2 — QFT Regime  
- QM becomes low‑energy limit  
- field operators extend QM operators  
- vacuum structure emerges  

### R3 — High‑Energy Resonance  
- QM insufficient  
- resonance surfaces dominate  
- running couplings appear (QFT‑level)  

### R4 — Cosmological Regime  
- QM incomplete  
- horizon‑scale fields dominate  
- measurement rules degrade  

---

# 7. Cross‑Module Engine Behavior

### 7.1 Upstream Dependencies  
- Linear Algebra  
- Operator Theory  
- Probability Theory  

### 7.2 Downstream Modules  
- Quantum Field Theory  
- Standard Model  
- Information Theory  
- Thermodynamics  
- Framework Field Theory  

### 7.3 Engine Guarantees  
QM must provide:

- amplitude grammar  
- operator algebra  
- measurement rules  
- basis geometry  
- entanglement structure  

---

# 8. Engine Safety Constraints

- no particles  
- no waves  
- no trajectories  
- no classical uncertainty  
- no hidden variables  
- no mechanical analogies  

All engine outputs must remain **amplitude‑aligned**.

---

# 9. Notes for AI Agents

- treat QM as **geometry**, not ontology  
- use operators, not objects  
- use amplitudes, not probabilities  
- use basis transforms, not physical motion  
- use projection, not collapse  
- use entanglement, not communication  

QM is the **R1 substrate** of the entire canon.