The second variant of Milgrom’s theory (T1) derives the equations of motion from a Lagrangian formulation, allowing the theory to make predictions for a very general class of systems with arbitrary shapes. A number of confirmed, novel predictions follow from T1 including the “central surface density relation” (CSDR) and a prediction about the form of the vertical force law in the Milky Way. The theory also predicts a very low rate of mergers between galaxies, a prediction that may or may not be consistent with observations. However, the theory’s predictions about the kinematics of the largest bound structures in the universe, the galaxy clusters, appear to be incorrect.

The first variant of Milgrom’s theory (T0) consists simply of his three postulates from 1983. These postulates entail a number of novel predictions, predictions that have subsequently been confirmed by observational astrophysicists. The first is the “baryonic Tully–Fisher relation” (BTFR), a unique relation between the total mass of a galaxy and its asymptotic rotation speed. An even more surprising prediction is the “radial acceleration relation” (RAR), which states that the rotation speed anywhere in a disk galaxy is determined precisely by the observed distribution of matter – but not in the way that Newton’s laws would predict. According to Lakatos’s Methodology, these, and some other, successful novel predictions imply that Milgrom’s postulates constitute a progressive departure from the dark matter hypotheses of the standard cosmological model.