5 Milgrom’s Empirical Law and “Kepler Laws” of Galactic Dynamics

Up to this point in this review, the challenges that we have presented have been purely based on observations, and fully independent of any alternative theoretical framework. However, at this point, it would obviously be a step forward if at least some of these puzzling observations could be summarized and empirically unified in some way, as such a unifying process is largely what physics is concerned with, rather than simply exposing a jigsaw of apparently unrelated empirical observations. And such an empirical unification is actually feasible for many of the unpredicted observations presented in the previous Section 4.3, and goes back to a rather old idea of the Israeli physicist Mordehai Milgrom.

Almost 30 years ago, back in 1983 (and thus before most of the aforementioned observations had been carried out), simply prompted by the question of whether the missing mass problem could perhaps reflect a breakdown of Newtonian dynamics in galaxies, Milgrom [293Jump To The Next Citation Point] devised a formula linking the Newtonian gravitational acceleration gN to the true gravitational acceleration g in galaxies. Such attempts to rectify the mass discrepancy by gravitational means often begin by noting that galaxies are much larger than the solar system. It is easy to imagine that at some suitably large scale, let’s say on the order of 1 kpc, there is a transition from the usual dynamics applicable in the comparatively-tiny solar system to some more general theory that applies on the scale of galaxies in order to explain the mass discrepancy problem. If so, we would expect the mass discrepancy to manifest itself at a particular length scale in all systems. However, as already noted, there is no universal length scale apparent in the data (Figure 10View Image) [382, 266, 406, 279Jump To The Next Citation Point, 270]. The mass discrepancy appears already at small radii in some galaxies; in others there is no apparent need for dark matter until very large radii. This now observationally excludes all hypotheses that simply alter the force law at a linear length-scale.

 5.1 Milgrom’s law and the dielectric analogy
 5.2 Galactic Kepler-like laws of motion

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