2020/01/09 by Ayal Sharon, Sharon, Ayal
Computer Science · Physics and Astronomy · Psychology · #03A05 #65J20 #81T16 #Computability, Logic, AI Algorithms #FOS: Mathematics #General Mathematics (math.GM) #Philosophy and Theoretical Science #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2001.04282
openalex publication_date 2020/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantum Electrodynamics (QED) renormalizaion is a paradox. It uses the\nEuler-Mascheroni constant, which is defined by a conditionally convergent\nseries. But Riemann's series theorem proves that any conditionally convergent\nseries can be rearranged to be divergent. This contradiction (a series that is\nboth convergent and divergent) is a paradox in "classical" logic,\nintuitionistic logic, and Zermelo-Fraenkel set theory, and also contradicts the\ncommutative and associative properties of addition. Therefore QED is\nmathematically invalid. Zeta function regularization equates two definitions of\nthe Zeta function at domain values where they contradict (where the Dirichlet\nseries definition is divergent and Riemann's definition is convergent). Doing\nso either creates a paradox (if Riemann's definition is true), or is logically\ninvalid (if Riemann's definition is false). We show that Riemann's definition\nis false, because the derivation of Riemann's definition includes a\ncontradiction: the use of both the Hankel contour and Cauchy's integral\ntheorem. Also, a third definition of the Zeta function is proven to be false.\nThe Zeta function has no zeros, so the Riemann hypothesis is a paradox, due to\nmaterial implication and "vacuous subjects".\n