On the Theoretical Inconsistencies of Cooper Pairing in Superconductivity

The BCS theory of superconductivity, which relies on the formation of Cooper pairs mediated by lattice phonons, has stood for decades as the cornerstone of our understanding of superconductivity in conventional metals. However, critical inspection reveals that several theoretical and experimental inconsistencies persist in this framework, especially when extended to high-temperature and unconventional superconductors. This paper rigorously analyzes these inconsistencies, with emphasis on the inadequacy of phonon-mediated interactions to overcome Coulomb repulsion, the questionable nature of the long-range coherence implied by the size of Cooper pairs, and the breakdown of BCS predictions in strongly correlated systems. We present a calculation-intensive critique, highlighting the need for a deeper, possibly non-phononic mechanism for electron pairing or collective quantum behavior in superconductors. The BCS theory of superconductivity, premised on the formation of Cooper pairs via weak electron-phonon coupling, has long served as the canonical framework for understanding low-temperature superconductors. However, we argue that this framework is conceptually and physically insufficient—even for conventional materials. This paper presents a detailed theoretical critique grounded in explicit calculations, exposing contradictions in the length and energy scales involved, the lack of real-space localization of paired electrons, and the incompatibility between the BCS ground state and a physically bound pair in position space. We emphasize that the superconducting energy gap may better reflect a many-body correlation scale rather than a two-body binding energy. Further, we discuss topological and quantum field theoretic obstructions to pairing and reframe superconductivity as a macroscopic quantum coherent state independent of pair formation. Our approach challenges the narrative that Cooper pairing is a necessary cause of superconductivity and instead highlights the role of collective phase coherence, entanglement, and broken gauge symmetry as possible fundamental mechanisms.