On measuring standards in Weyl's geometry

TL;DR

This paper revisits the measurement standards in Weyl's geometry, proposing solutions to nonintegrability issues and establishing a framework where atoms can serve as standards, thus supporting classical gravity and electromagnetism theories.

Contribution

It introduces approaches to eliminate nonintegrability of length in Weyl's geometry, enabling atoms to act as reliable measuring standards within a consistent geometric framework.

Findings

Atoms can serve as measuring standards in Weyl's geometry.

Weyl's space provides a solid foundation for classical gravitation and electromagnetism.

Solutions to nonintegrability improve the applicability of Weyl's geometry in physics.

Abstract

In Weyl's geometry the nonintegrability problem and difficulties in defining measuring standards are reconsidered. Approaches removing the nonintegrability of lengthin in the interior of atoms are given, so that atoms may serve as measuring standards. The Weyl space become a well founded framework for classical theories of gravitation and electromagnetism,