Editing Openai/6908ee36-d3b4-8010-a468-28e0753d08ae (section)

=== Model two adjacent coherence states ∣L⟩,∣R⟩|L\rangle,|R\rangle∣L⟩,∣R⟩ with ===

H=Δ2 σx+ε2 σz,(ε≈0 resonant).H=\frac{\Delta}{2}\,\sigma_x+\frac{\varepsilon}{2}\,\sigma_z,\quad (\varepsilon\approx 0\ \text{resonant}).H=2Δσx+2εσz,(ε≈0 resonant).
The coherent oscillation (tunnel) frequency is Ω=Δ/ℏ\Omega=\Delta/\hbarΩ=Δ/ℏ and the first-passage/half-Rabi latency is

τhop≃πΩ=πℏΔ.\tau_{\text{hop}}\simeq \frac{\pi}{\Omega}=\frac{\pi\hbar}{\Delta}.τhop≃Ωπ=Δπℏ.
So if your measured/assumed latency is τ\tauτ, the implied level splitting is

Δ≃πℏτ.\Delta \simeq \frac{\pi\hbar}{\tau}.Δ≃τπℏ.
With τ=3.71×10−26 s\tau=3.71\times10^{-26}\,\text{s}τ=3.71×10−26s, this back-infers Δ≈5.6×1010 eV\Delta \approx 5.6\times 10^{10}\ \text{eV}Δ≈5.6×1010 eV (∼55 GeV). That’s huge compared with atomic scales, which tells you one of two things must be true:
* The hop is not a full ∣L⟩→∣R⟩|L\rangle\to|R\rangle∣L⟩→∣R⟩ Rabi half-cycle (orthogonalization), or
* The states are separated by an ultra-stiff barrier tied to a much higher internal energy scale than ordinary atomic structure.

This is still useful: once you specify a plausible Δ\DeltaΔ from HU microphysics, the formula gives you τ\tauτ directly.