A Derivation of Modified Newtonian Dynamics

TL;DR

This paper compares classical MOND with a graviton-based toy model, suggesting that MOND naturally emerges from the graviton picture for symmetric systems, providing a potential physical mechanism for galactic gravity.

Contribution

It demonstrates that MOND can be derived from a graviton-based model, offering a physical basis for the modified dynamics in galactic systems.

Findings

MOND aligns with the graviton model in symmetric systems

The graviton picture offers a candidate mechanism for galactic gravity

MOND can be derived without empirical transition functions

Abstract

Modified Newtonian Dynamics (MOND) is a possible solution for the missing mass problem in galactic dynamics; its predictions are in good agreement with observations in the limit of weak accelerations. However, MOND does not derive from a physical mechanism and does not make predictions on the transitional regime from Newtonian to modified dynamics; rather, empirical transition functions have to be constructed from the boundary conditions and comparison to observations. I compare the formalism of classical MOND to the scaling law derived from a toy model of gravity based on virtual massive gravitons (the "graviton picture") which I proposed recently. I conclude that MOND naturally derives from the "graviton picture" at least for the case of non-relativistic, highly symmetric dynamical systems. This suggests that - to first order - the "graviton picture" indeed provides a valid candidate for the physical mechanism behind MOND and gravity on galactic scales in general.