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, 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.

Modified Newtonian dynamics and hadronic scales

“…8 in [21]), which is achieved for δ = 1/3. Furthermore, there is an important conceptual difference between the ways the characteristic mass and distance scales were estimated in [21] and in Eqs (8,9) above. Namely, the condition used in [21] (see also [22]) was that of mathematical simplicity, i.e.…”

“…Indeed, while the set (m P , l P ) depends both on hc and h/c, the set (m CM , r CM ) depends on h/c only. Within the scheme of [21] this latter set is obtained by requesting the absence of hc from formula…”

“…Furthermore, there is an important conceptual difference between the ways the characteristic mass and distance scales were estimated in [21] and in Eqs (8,9) above. Namely, the condition used in [21] (see also [22]) was that of mathematical simplicity, i.e. the independence of the characteristic scales of one of three constants (h, c, and the cosmological constant Λ).…”

“…On the other hand, the estimate of Eqs (8,9) is based on a physical condition: the identification of mass and distance appearing in the MOND and in the quantum mass-distance relations (7). Thus, when compared to [21], the derivation leading to hadronic scales seems to be more physical than the derivations leading to Planck scales and other scales discussed in [21].…”