On Tunneling in the Quantum Multiverse

TL;DR

This paper reinterprets quantum tunneling within the Everettian Many-Worlds framework, treating barrier scattering as a branching process that yields reflected and tunneled worlds with weights given by environmental correlations. It derives the tunneling probability as $P_T = \sum_{i>k} (c_i^{\mathcal{E}})^2$ and the tunneling time from a branching duration $t_B \sim \hbar/\Delta E_B$, resulting in a practical link between decoherence dynamics and observed tunneling times. The analysis extends to macroscopic quantum tunneling in superconducting circuits, where a temperature-dependent branching count $N_B(T)$ predicts a macroscopic tunneling time $t_T^{\text{macro}}$ of order tens to hundreds of picoseconds under realistic conditions, offering a temporal bridge between foundational quantum theory and experiments. Overall, the work provides a cohesive, if controversial, narrative that connects the Born-rule probabilities to branch weights and presents a measurable, branching-based timescale for both microscopic and macroscopic tunneling phenomena.

Abstract

Prompted by the longstanding interpretational controversy in quantum mechanics, quantum tunneling is heuristically addressed within the Everettian quantum multiverse. In this framework, the universal wavefunction splits into decohered reflected and transmitted branches under the environmetal effect after encountring a potential barrier. The observed tunneling is then experienced by the observer located in a tunneled world. The tunneling probability and the tunneling time are investigated in terms of the tunneled world relative weights and the branching duration, respectively. The macroscopic quantum tunneling, recently honored, is also discussed and the corresponding macroscopic tunneling time is approached based on the obtained results and known data.