Theory of non-local point transformations - Part 2: General form and Gedanken experiment

TL;DR

This paper extends the axiomatic framework of non-local point transformations to curved spacetimes, enabling ideal phase-space transformations in classical systems, with applications to various metric tensors.

Contribution

It introduces a general form of non-local point transformations applicable to curved spacetimes and discusses their potential for ideal phase-space transformations in classical dynamics.

Findings

Applicable to diagonal and non-diagonal metric tensors

Allows ideal phase-space transformations in classical systems

Extends the axiomatic construction for non-local transformations

Abstract

The problem is posed of further extending the axiomatic construction proposed in Part 1 for non-local point transformations mapping in each other different curved space times. The new transformations apply to curved space times when expressed in arbitrary coordinate systems. It is shown that the solution permits to achieve an ideal (Gedanken) experiment realizing a suitable kind of phase-space transformation on point-particle classical dynamical systems. Applications of the theory are discussed both for diagonal and non-diagonal metric tensors.