MOND: A consequence of the geometric Leibniz Clock

TL;DR

This paper proposes that gravitating particles act as geometric Leibniz Clocks, and demonstrates that this concept naturally reproduces key features of MOND galaxy dynamics, linking geometry and gravity.

Contribution

It introduces the geometric Leibniz Clock as a foundational concept that explains MOND phenomena without additional hypotheses.

Findings

Reproduces flat galaxy rotation curves

Derives the baryonic Tully-Fisher relation

Identifies a critical acceleration scale

Abstract

Leibniz considered the notion of the 'empty physical space' to be a meaningless abstraction, and he held firmly to the view that the only significant thing was the set of relationships between 'objects', whatever these 'objects' might be. Similarly, he was equally clear in expressing his views about Newton's universal time, which he also considered to be a meaningless abstraction. In effect, for him, time was no more than a synonym for ordered change within a material system. The process of giving quantitative realization to this duality of non-Newtonian ideas forms the core of this work. A primary result arising is that every gravitating particle is no more than a clock - the geometric Leibniz Clock - which provides all the basic things: it conserves energy and angular momentum and satisfies the Weak Equivalence Principle. When the Clock is applied to model the concept of a galactic object within which all motions are circular, the characteristic properties of the MOND galaxy (asymptotic flatness, a critical acceleration scale, the baryonic Tully-Fisher relationship) are quantitatively reproduced in the resulting Leibniz galaxy. In short, the characteristic essence of MOND has its source in the geometric Leibniz Clock.