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.

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.

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.

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.

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.