# Regimes — Quantum Mechanics  
### TriadicFrameworks /docs/theories/quantum_mechanics/regimes.md

Quantum Mechanics (QM) is the **R1 amplitude grammar** of the RTT stack.  
It defines how amplitudes, operators, and measurement behave when no  
stable excitations exist. QM is not a particle theory and not a wave  
theory — it is an **operator‑based amplitude geometry**.

This file defines QM’s regime behavior across R1 → R4.

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# R1 — Quantum Amplitude Regime  
### (Pure amplitude geometry • no stable excitations)

In R1:

- states are amplitude vectors  
- operators define all observable structure  
- evolution is unitary  
- measurement is projection  
- basis changes are geometric  
- no stable excitations exist  
- no field modes exist  
- no renormalization flow exists  

This is **canonical Quantum Mechanics**.

**Interpretation:**  
QM is fully valid only in R1.

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# R2 — Field‑Emergence Regime  
### (QM becomes the low‑energy limit of QFT)

In R2:

- stable excitation modes appear  
- creation/annihilation operators become meaningful  
- propagators emerge  
- vacuum structure becomes defined  
- symmetry geometry becomes non‑trivial  

QM survives only as:

- the amplitude limit  
- the single‑mode approximation  
- the low‑energy truncation of QFT  

**Interpretation:**  
QM is embedded inside QFT.

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# R3 — High‑Energy Resonance Regime  
### (QM insufficient • resonance surfaces dominate)

In R3:

- running couplings dominate  
- symmetry restoration begins  
- excitation surfaces merge  
- vacuum flattens  
- amplitude‑only descriptions fail  

QM cannot describe:

- resonance topology  
- running couplings  
- high‑energy field behavior  

**Interpretation:**  
QM is no longer a complete grammar.

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# R4 — Cosmological Regime  
### (QM incomplete • horizon‑scale fields dominate)

In R4:

- horizon‑scale fields dominate  
- vacuum becomes cosmological  
- amplitude structure loses meaning  
- measurement rules become incomplete  
- QM cannot describe large‑scale coherence  

**Interpretation:**  
QM requires cosmology or quantum gravity.

---

# Summary

Quantum Mechanics behaves as:

- **R1:** pure amplitude grammar (fully valid)  
- **R2:** low‑energy limit of QFT  
- **R3:** insufficient (resonance dominates)  
- **R4:** incomplete (cosmological fields dominate)  

QM is the **substrate amplitude layer** from which QFT emerges and to  
which QFT collapses when excitations lose stability.