MOND as manifestation of modified inertia

Abstract: Practically all the full-fledged MOND theories propounded to date are of the modified-gravity (MG) type: they modify only the Newtonian, Poisson action of the gravitational potential, or the general-relativistic Einstein-Hilbert action, leaving other terms (inertia) intact. Here, I discuss the interpretation of MOND as modified inertia (MI). My main aim is threefold: (a) to advocate exploring MOND theories beyond MG, and appreciating their idiosyncrasies, (b) to highlight the fact that secondary predictions of such theories can differ materially from those of MG theories, (c) to demonstrate some of this with specific MI models. I discuss some definitions and generalities concerning MI. I then present instances of MI in physics, and the lessons we can learn from them for MOND. I then concentrate on a specific class of nonrelativistic, MOND, MI models, and contrast their predictions with those of the two workhorse, MG theories -- AQUAL and QUMOND. The MI models predict possibly a stronger external-field effect -- e.g. on low acceleration systems in the solar neighborhood -- such as very wide binary stars -- and on vertical motions in disc galaxies. More generally, the workings of the effect are rather different, and depend in different ways on dimensionless characteristics of the system, such as frequency ratios of the external and internal fields, eccentricity of trajectories, etc. These models predict a {\it much} weaker effect of the Galactic field in the inner Solar System than is predicted by AQUAL/QUMOND. I also show how noncircular motions -- such as those perpendicular to the disc -- modify the standard, algebraic mass-discrepancy-acceleration relation (aka RAR) that is predicted by MI for exactly circular orbits. These differences, and more that are discussed, can potentially offer ways to distinguish between theories.