MPT in the Laboratory

This correspondence note identifies a precise mathematical and physical connection between Metric Phase Transition Theory (MPT) and the Rydberg atom ring experiment of Chao, Ge et al. (arXiv:2512.04637), which demonstrates false vacuum decay and bubble nucleation in a programmable ring of 87Rb atoms. The correspondence operates at four levels: VACUUM STRUCTURE: The two spin states of the Rydberg system map directly to the two vacuum states of the MPT metric field (psi=0 at the core, psi=1 at the horizon), both created by the same mechanism -- a symmetry-breaking gradient lifting vacuum degeneracy. TOPOLOGICAL KINKS: Domain walls in the Rydberg ring are the direct condensed-matter analogues of MPT metric kinks (baryons). The topological protection mechanism is identical in both systems. THE DECAY LAW: The experimentally observed exponential suppression of the false vacuum decay rate, gamma proportional to exp(-lambda * V/Delta_l) with lambda = 0.225, has the same functional form as the MPT dark energy density formula rho_Lambda = m_pi^4 * (1/kappa_23)^kappa_23, derived independently. Both arise from the same physical mechanism: exponentially suppressed collective tunnelling through a resonant bubble of critical size. THE COUPLING CONSTANT: Via the Jordan-Wigner transformation, the transverse field Ising chain maps exactly to the sine-Gordon model at xi = 1/2. This is precisely the MPT coupling constant, derived independently from the Casimir invariant C = j(j+1) = 1 and N_c = 3. The note includes a full instanton analysis explaining the measured lambda = 0.225 (showing it arises from the generalised Ising regime, long-range 1/r^6 interactions, and finite ring size, rather than a discrepancy), the continuum limit (lambda -> 2/pi = 0.637 as Omega/V -> 0), and the mapping of MPT phase boundaries to the Rydberg parameter space. Three specific testable predictions are stated for future Rydberg experiments: Prediction 1: Changes in slope of ln(gamma) versus V/Delta_l at V/Delta_l = 8.565 (the MPT Phase I/II boundary, kappa_12 = 1/16*alpha, exact) and V/Delta_l = 29.37 (the Phase II/III boundary, kappa_23). Both are within or near the current experimental range. Prediction 2: As Omega/V -> 0 (continuum limit), the measured lambda should converge to 2/pi = 0.6366, the sine-Gordon instanton action at xi = 1/2. Prediction 3: In a Z3 Rydberg ring experiment (as suggested by Chao et al. in their outlook), the long-time vacuum sector populations should approach 5:27:68 rather than the equal 1:1:1 expected from a symmetric Z3 model, reflecting the MPT cosmic energy budget Omega_b : Omega_DM : Omega_Lambda. The note is honest about what the correspondence does and does not establish. It does not claim experimental confirmation of MPT cosmology. The energy scales differ by approximately 10^60. It claims that the mathematical structure underlying the MPT dark energy formula has been directly observed in a laboratory, and that three specific predictions follow for the Rydberg platform. Companion to: Rogers, G.H., "Metric Phase Transition Theory," Zenodo, April 12, 2026. DOI: 10.5281/zenodo.19538655