MOND and natural scales of distance and mass

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, i.e. [Formula: see text] — the Planck constant, [Formula: see text] — the speed of light and [Formula: see text] — the MOND acceleration constant. When the gravitational constant [Formula: see text] 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.