Physical Principles Based on Geometric Properties

TL;DR

This paper explores geometric principles derived from Cartan's approach and conformal transformations, proposing classical principles with quantum-like properties as a foundation for a force-free quantum theory.

Contribution

It introduces four new classical principles based on geometry, including one resembling the Heisenberg uncertainty principle and another akin to Bohr's principle.

Findings

Derived classical principles with quantum-like features

Reinterpreted angular momentum through geometry without postulates

Proposed a geometric basis for a force-free quantum theory

Abstract

In this paper we present some results obtained in a previous paper about the Cartan's approach to Riemannian normal coordinates and our conformal transformations among pseudo-Riemannian manifolds. We also review the classical and the quantum angular momenta of a particle obtained as a consequence of geometry, without postulates. We present four classical principles, identifed as new results obtained from geometry. One of them has properties similar Heisemberg's uncertaintly principle and another has some properties similar to Bohr's principle. Our geometric result can be considered as a possible starting point toward a quantum theory without forces.