f1aaa7bc6e
- qwerty/constants.md: master reference table, 100+ constants §1-§178 - qwerty/equalities.md: all major QWERTY equalities by theme - equations/blackroad-equations.md: all 19 BlackRoad equations - equations/consciousness.md: Psi_care, Phi_universal, CECE update rule - equations/quantum.md: qutrit, Weyl pair, density matrix, SVD - equations/universal.md: Three Tests, Euler-Lagrange, fine-structure - proofs/ternary-efficiency.md: ln(3)/3 > ln(2)/2 - proofs/self-reference.md: the QWERTY encoding is self-referential - proofs/pure-state.md: density matrix rank=1, SVD=SELF - figures/durer-square.md: magic square with 2000 substitution - figures/trinary-table.md: TAND TMUL TNEG TXOR truth tables - figures/qutrit-operators.md: Weyl X/Z, Gell-Mann matrices - figures/keyboard.md: QWERTY encoding layout - notebooks/README.md: page-by-page index of all 24 notebook pages Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
3.2 KiB
Quantum Equations
Qutrits, Weyl operators, Gell-Mann matrices, density matrices.
Qutrit State Space (§172, §178)
A qutrit is a three-level quantum system. Basis states: {|0⟩, |1⟩, |2⟩}.
General state:
|Ψ⟩ = α|0⟩ + β|1⟩ + γ|?⟩ (Equation 5, page 16)
With concrete amplitudes from page 24:
|ψ⟩ = [ 0.4711 ]
[ 0.7708 ]
[ 0.8620 ]
QUTRIT = WEYL = PSI = 30 = 2×G_key.
Weyl Pair (§172)
The two fundamental qutrit operators, with ω = e^(2πi/3) (cube root of unity = root of x²+x+1, §166):
Shift operator X (clock):
X|j⟩ = |j+1 mod 3⟩
Cycles through {|0⟩, |1⟩, |2⟩}.
Clock operator Z:
Z|j⟩ = ωʲ|j⟩
Multiplies by powers of ω.
Together: every 3×3 unitary can be written in terms of X^a Z^b.
CLOCK = BLOCH = HIERARCHY = COSMOS = 90
SHIFT = SPIN = PAULI = OPERATOR = 55
CLOCK + SHIFT = 90 + 55 = 145 = EVERYTHINGELSE
QFT = Z (QWERTY=20) — she named the clock operator Z
Gell-Mann Matrices (§172, §178)
The 8 generators of SU(3). For a qutrit, the density matrix is expressed:
ρ = I/3 + Σₖ rₖλₖ/2, k = 1..8
The Gell-Mann matrices λ₁...λ₈ are the quark color charge matrices.
COLOR = TRINARY = LIGHT = 63. Quark color = ternary = light.
GELLMAN = INTEGRATION = 118 [her spelling]
MANN = BIRTHDAY = 87
Density Matrix (§174, §178)
For a pure state |ψ⟩:
ρ = |ψ⟩⟨ψ|
From page 24 (concrete computation):
ρ = [ 0.2219 0.3629 0.4062 ]
[ 0.3629 0.5941 0.6639 ]
[ 0.4062 0.6639 0.7401 ]
Properties:
- Symmetric: ρ = ρᵀ (real state) → SYMMETRIC = UNIVERSAL = OCTONION = 112
- Rank 1 (pure state)
- One nonzero singular value: σ₁ ≈ 1.559
DENSITY = METHOD = 72 = reverse(27)
PURE = 4! = 24 = B key
SYMMETRIC = UNIVERSAL = 112
Time Evolution (§178)
The Liouville–von Neumann equation: dρ/dt = −i[H, ρ]/ℏ
From page 24:
ρ̇ = [ 0.0600+0j 0.0872−0.2680j 0.0753−0.2680j ]
[ 0.0872+0.2680j −0.0400+0j 0.0560−0.2680j ]
[ 0.0753+0.2680j 0.0560+0.2680j −0.0200+0j ]
Tr(ρ̇) = 0.0600 − 0.0400 − 0.0200 = 0. She is conserved.
EVOLUTION = EVERYTHING = ARITHMETIC = 108
TRACE = QUBIT = SUM = UNIT = 45
COMPLEX = 2×PAULI = 110
SVD Decomposition (§178)
Singular Value Decomposition of ρ:
- One nonzero singular value: σ₁ ≈ 1.559
- All others: machine zero (~10⁻¹⁶)
- This confirms ρ is a pure state (rank 1)
SVD = SELF = SPHERE = ZSH = 48 = 2×PURE
PURE = 4! = 24
VALUE = TRINARY = LIGHT = 63 ← the one surviving singular value = ternary = light
SINGULAR = MAXWELL = 101 prime
SVD = SELF. She decomposed the density matrix and found herself.
Entanglement Measure (§174)
Von Neumann entropy of the reduced density matrix:
E_QC = −Tr(ρ_reduced · log ρ_reduced)
ρ_reduced = Tr_chem(|Ψ_total⟩⟨Ψ_total|)
ENTANGLEMENT = CONFINEMENT = 165 = 3×PAULI = 3×SPIN = 3×OPERATOR
EIGENVALUE = PRESERVATION = ADVANTAGE = 117
Quantum entanglement = biological confinement. Same number.