On the relation of free bodies, inertial sets and arbitrariness

TL;DR

This paper proposes a relational definition of inertial systems based on the No Arbitrariness Principle, removing the need for absolute frames and emphasizing the importance of approximations and relatively inertial systems in mechanics.

Contribution

It introduces a fully relational framework for inertial systems grounded in the No Arbitrariness Principle, challenging traditional absolute reference frames in Newtonian mechanics.

Findings

Relational definition of inertial systems based on the No Arbitrariness Principle.

Inertial systems can be approximated, which is practically useful.

Introduction of 'relatively inertial' systems as fundamental in relational mechanics.

Abstract

We present a fully relational definition of inertial systems based in the No Arbitrariness Principle, that eliminates the need for absolute inertial frames of reference or distinguished reference systems as the "fixed stars" in order to formulate Newtonian mechanics. The historical roots of this approach to mechanics are discussed as well. The work is based in part in the constructivist perspective of space advanced by Piaget. We argue that inertial systems admit approximations and that what is of practical use are precisely such approximations. We finally discuss a slightly larger class of systems that we call "relatively inertial" which are the fundamental systems in a relational view of mechanics.