NEWTON's trajectories versus MOND's trajectories

TL;DR

This paper examines whether MOND's modified dynamics can be derived from a velocity-dependent coordinate deformation, concluding it cannot due to its intrinsic non-local temporal nature, reaffirming Milgrom's earlier insights.

Contribution

It demonstrates that MOND's dynamics cannot be obtained through local coordinate deformations, emphasizing its non-local temporal character.

Findings

MOND cannot be derived from local coordinate transformations.

MOND's non-locality in time is intrinsic and unavoidable.

Supports Milgrom's previous observations on MOND's non-local nature.

Abstract

MOND dynamics consists of a modification of the acceleration with respect to the one provided by Newtonian mechanics. In this paper we investigate whether it can be derived from a velocity-dependent deformation of the coordinates of the systems. The conclusion is that it cannot be derived this way because of the intrinsic non-local character in time of the MOND procedure. This is a feature pointed out some time ago already by Milgrom himself.