Möbius Topological Vacuum Symmetry Breaking: A Research Hypothesis on Non-Orientable Electromagnetic Cavities

This work presents an exploratory theoretical framework investigating whether non-orientable Möbius topology can produce measurable modifications in the electromagnetic vacuum mode spectrum relative to orientable cavities of equal volume. The central research question is: Do non-orientable electromagnetic cavities possess a vacuum mode spectrum distinguishable from that of orientable cavities with equivalent geometric parameters? To address this question, the paper introduces the concept of a topological spectral shift, denoted ΔTopo(ω), as a falsifiable observable that can be tested through computational electromagnetic simulations and future experimental measurements. The framework is structured according to clearly defined confidence levels, separating established physics from plausible, speculative, and highly speculative extensions. Particular emphasis is placed on transparency, falsifiability, and the possibility of null results. No claims of energy extraction, propulsion, or technological application are made in this work. The objective is solely to formulate a mathematically and physically well-defined research programme capable of determining whether non-orientable topology leaves a measurable spectral signature in confined electromagnetic fields. The paper proposes a staged verification pathway, beginning with finite-element computational analysis (Stage 0) and proceeding, contingent on positive results, toward experimental validation. Whether the proposed effect exists or not, the investigation aims to contribute to the broader study of spectral geometry, topology, quantum vacuum structure, and electromagnetic field theory on non-orientable manifolds.