Göttingen 2025 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 12: Concepts of Physics

MP 12.1: Talk

Thursday, April 3, 2025, 16:15–16:35, ZHG002

The Limits of Mathematics in Physics — •Grit Kalies¹ and Duong D. Do² — ¹HTWD University of Applied Sciences, Dresden, Germany — ²The University of Queensland, Brisbane, Australia

Mathematics is considered the language of physics. Starting from idealizations and kinematics, geometric-mathematical physics emerged. By analyzing processes regarding their causes and the functional dependencies of energies, we identify shortcomings in the basic energy concepts of physics, which cannot be remedied with mathematics. While formal transformations of process equations such as integration are mathematically correct, they do conceal vital physical information, suggesting that mathematics should be used with caution. We propose a physically justified approach that reconciles the mechanical, quantum mechanical and thermodynamic energy concepts and provides a revised interpretation of E = mc^2. Our results suggest that geometric approaches were built too early on a shaky physical foundation, leading to undesirable developments in recent centuries. G. Kalies, D. D. Do, AIP Adv. 14, 115225 (2024)