Gao, Shan (2025) Why Magnetic Monopoles Cannot Exist: A Gauge Potential Perspective. [Preprint]
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Abstract
Magnetic monopoles, hypothetical entities with isolated magnetic charges (Dirac) or effective charges from field configurations (’t Hooft-Polyakov), are posited to symmetrize electromagnetism and explain electric charge quantization, yet remain undetected. This paper demonstrates that such monopoles—Abelian Dirac and non-Abelian ’t Hooft-Polyakov—are incompatible with a potential-centric ontology, where the gauge potential \( A_\mu \), fixed in one true gauge, the Lorenz gauge, is the fundamental physical entity mediating local interactions, as evidenced by the Aharonov-Bohm effect. We derive a no-go result, showing that magnetic monopoles require singular (e.g., Dirac strings) or non-unique (e.g., Wu-Yang patches) potentials in all gauges to resolve a Stokes’ theorem contradiction, violating the ontology’s requirement for unique, non-singular potentials in the true gauge. This result extends to sphalerons in SU(2) \(\times\) U(1) electroweak theory and D-branes in string theory, whose Ramond-Ramond potentials \( C_{p+1} \) exhibit an AB-like effect but require singular or non-unique potentials due to non-zero flux, leading to a theoretical self-contradiction independent of experimental evidence. In contrast, cosmic strings, with a non-singular, single-valued \( A_\mu \) in a single gauge, satisfying Stokes’ theorem and the ontology’s criteria. Instantons and skyrmions are compatible as non-physical or emergent constructs, and emergent monopoles in spin ice, producing flux in an effective field, are also consistent with the ontology. Our findings explain the absence of magnetic monopoles and baryon number violation in standard electroweak processes, align with experimental null results, and suggest that D-branes’ theoretical inconsistency challenges their physical realizability, offering testable predictions for gauge theories and deepening our understanding of their ontological implications.
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