Classical Reconstruction of the PMNS Matrix Using a Mechanical Neutrino Oscillator

TL;DR

This paper demonstrates how a classical three-pendulum system can serve as an analog to neutrino oscillations, providing a tangible visualization of the PMNS matrix and flavor mixing phenomena.

Contribution

It introduces a mechanical analog using coupled pendulums to model neutrino oscillations and extracts a classical mixing matrix comparable to the PMNS matrix.

Findings

Mechanical system reproduces neutrino mixing patterns

Derived a scaling relation linking classical and quantum oscillations

Provides a pedagogical tool for understanding neutrino flavor dynamics

Abstract

Neutrino oscillations arise from quantum interference between neutrino mass eigenstates and are governed by the PMNS matrix. Although this is an intrinsically quantum phenomenon, its mathematical structure is analogous to systems of coupled classical oscillators. In this work, a three--pendulum system connected by springs is constructed as a classical analog of three--flavor neutrino oscillations. Measurements of amplitude transfer, normal--mode structure, and beat frequencies are used to extract a mechanical mixing matrix, which is compared with the structure of the PMNS matrix under the assumption of zero CP violation. A scaling relation linking mechanical time evolution to the neutrino \(L/E\) behavior is derived, clarifying the scope and limitations of the analogy. The experiment demonstrates how abstract concepts of neutrino mixing can be visualized using simple and accessible classical systems, offering both pedagogical value and a qualitative understanding of flavor oscillation dynamics.