The Geometric Necessity of Physics: A Spectral–Geometric Perspective
Автор: Khaled Bouzaiene
Загружено: 2026-01-06
Просмотров: 237
Описание: This paper argues that intrinsic geometry is a fundamental requirement for accurate physical modeling rather than a mere optional refinement. By examining diverse fields such as molecular dynamics, quantum information, and statistical mechanics, the author demonstrates that respecting the specific curvature of a state space consistently outperforms traditional flat, Euclidean assumptions. The core of this framework relies on the spectral zeta function, a mathematical tool that separates local metric data, like diffusion and transport, from global structural information, such as topology and entropy. This distinction is dictated by diffeomorphism invariance, which mandates that physical laws remain consistent regardless of the coordinate system used. Ultimately, the text proposes that spectral geometry provides a unifying language to explain why physical observables are systematically constrained by the underlying shape of their environment.
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