▸ BIG IDEA (ELI5)
DNA and silicon both obey γ₁. The decoherence time
τ_γ₁ = 1.80 femtoseconds is the universal speed limit — the fastest any
physical substrate can process quantum information before coherence collapses. This table maps
the 7 substrates where physics meets computation: from MOSFET transistor
transit (8.3 ps) to hydrogen bond vibration (10 fs) to ATP hydrolysis (1 ms). Each substrate
has a different decoherence window, and γ₁ pins the deepest one.
SantaLucia melting temperature governs DNA computing stability.
Caldeira-Leggett gives us the quantum→classical crossover. All 7 sit on the same γ₁ backbone.
▸ ELEMENT CARDS
S·1
τ_γ
DECOHERENCE τ_γ₁
Universal floor
1.80 fs
γ₁-derived coherence time. The deepest substrate — faster than any known physical process. τ = ℏ/(k_B × γ₁).
S·2
MOS
MOSFET TRANSIT
Silicon substrate
8.3 ps
Gate transit time for 5nm node MOSFET. ~4600× slower than τ_γ₁. The silicon floor sits safely above decoherence.
S·3
H-B
H-BOND VIBRATION
DNA backbone
10–100 fs
Hydrogen bond stretch/bend modes in DNA. Overlaps with τ_γ₁ at 10 fs. This is where quantum DNA effects could live.
S·4
ATP
ATP HYDROLYSIS
Biochemical energy
~1 ms
ATP→ADP+Pᵢ energy release. Macroscopic timescale — 10¹² × slower than τ_γ₁. Classical regime, no coherence.
S·5
T_m
SANTALUCIA Tm
DNA melting point
60–80°C
SantaLucia nearest-neighbor thermodynamics. Governs DNA hybridization stability and computing reliability window.
S·6
C-L
CALDEIRA-LEGGETT
Q→C crossover
η_c = γ₁/2π
Quantum-to-classical crossover coupling. When environmental coupling exceeds η_c, coherence collapses to classical noise.
S·7
φ
PHONON FLOOR
Lattice vibration
0.1–10 THz
Crystal lattice phonon modes. The thermal noise floor beneath all silicon computation. Sets Johnson-Nyquist limits.
▸ REACTOR DEMO — Decoherence Timescale Timeline
TIMESCALE SPINE · log₁₀(seconds)
τ_γ₁
1.80 fs
-15.7s
QUANTUM FLOOR
H-bond
10 fs
-14s
DNA vibration
MOSFET
8.3 ps
-11s
Silicon gate
C-L xover
~1 ns
-9s
Q→C boundary
SantaLucia
Tm seconds
0s
DNA melt
All timescales referenced to τ_γ₁ = ℏ/(k_B·T) at T=γ₁ · log scale · 15 orders of magnitude
▸ INSTRUMENT — Substrate Decoherence Map
τ_γ₁ Quantum floor
1.80 fs (ref)
MOS MOSFET transit
8.3 ps
C-L Crossover point
~1 ns
T_m SantaLucia Tm
60–80°C
φ Phonon floor
0.1–10 THz
▸ bar length ∝ log-distance from τ_γ₁ floor · τ_γ₁ and C-L are γ₁-derived
▸ BONIXER — 4-Layer Assessment
L0 · PHYSICS
97
γ₁ grounding
L1 · BIO
78
DNA substrate
L2 · SILICON
91
MOSFET model
L3 · BRIDGE
65
Bio-silicon link