2025 Nobel Prize: Macroscopic Quantum Tunnelling in Superconducting Circuits — E8 Intelligence Research

FINDING: 2025 Nobel Prize in Physics awarded for macroscopic quantum tunnelling — the demonstration that quantum behaviour (superposition, tunnelling) persists in superconducting circuits large enough to be held in the hand. | MATH: Tunnelling probability through a barrier: T ≈ exp(−2∫√(2m(V(x)−E))/ħ dx). Macroscopic circuit regime governed by the Josephson relations: I = I_c sin(φ), dφ/dt = 2eV/ħ. Quantised energy levels in the "phase particle" potential U(φ) = −E_J cos(φ) − (ħ I_ext/2e)φ. Escape rate from a metastable well (Kramers/quantum regime): Γ ∝ exp(−B/ħ) where B is the Euclidean action of the bounce solution. | CONNECTION: The Josephson phase φ is a compact U(1) variable — a circle S¹. The washboard potential is a cosine lattice, i.e. a 1D periodic structure with the same translational symmetry class as crystallographic lattices. The tunnelling action B/ħ is dimensionless and scales with the ratio of barrier height to plasma frequency ω_p = √(2eI_c/ħC). No direct 0.618/1.618 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com