MOND and Natural Scales of Distance and Mass

TL;DR

This paper explores a MOND-related framework for defining natural scales of distance and mass based on fundamental constants, proposing scales independent of specific physical interactions.

Contribution

It introduces a novel approach linking MOND to natural scales derived from fundamental constants, extending the concept of units beyond interaction-based systems.

Findings

Defines MOND-induced scales using h, c, and a_M

Identifies additional scales when G is included, such as the Planck and nanometer scales

Connects these scales to classical and quantum regimes

Abstract

We describe a MOND-related approach to natural scales of distance and mass, viewing it as a logical step following Planck's modification of the Stoney system of units. The MOND-induced scales are not based on the strength of any physical interaction (electromagnetic, gravitational, or otherwise). Instead, they are specified by three physical constants of a general nature that define the scales of action, speed, and acceleration, ie. h -- the Planck constant, c -- the speed of light, and a_M -- the MOND acceleration constant. When the gravitational constant G is added, two further distance scales (apart from the size of the Universe) appear: the Planck scale and a nanometer scale that fits the typical borderline between the classical and the quantum descriptions.