Galactic rotation curves, the baryon-to-dark-halo-mass relation and
  space-time scale invariance
  Low-acceleration space-time scale invariant dynamics (SID, Milgrom 2009a)
predicts two fundamental correlations known from observational galactic
dynamics: the baryonic Tully-Fisher relation (BTFR) and a correlation between
the observed mass discrepancy and acceleration (MDA) in the low acceleration
regime for disc galaxies. SID corresponds to the deep MOdified Newtonian
Dynamics (MOND) limit. The MDA data emerging in cold/warm dark matter (C/WDM)
cosmological simulations disagree significantly with the tight MDA correlation
of the observed galaxies. Therefore, the most modern simulated disc galaxies,
which are delicately selected to have a quiet merging history in a standard
dark-matter-cosmological model, still do not represent the correct rotation
curves. Also, the observed tight correlation contradicts the postulated
stochastic formation of galaxies in low-mass DM halos. Moreover, we find that
SID predicts a baryonic to apparent virial halo (dark matter) mass relation
which agrees well with the correlation deduced observationally assuming
Newtonian dynamics to be valid, while the baryonic to halo mass relation
predicted from CDM models does not. The distribution of the observed ratios of
dark-matter halo masses to baryonic masses may be empirical evidence for the
external field effect, which is predicted in SID as a consequence of the forces
acting between two galaxies depending on the position and mass of a third
galaxy. Applying the external field effect, we predict the masses of galaxies
in the proximity of the dwarf galaxies in the Miller et al. sample. Classical
non-relativistic gravitational dynamics is thus best described as being
Milgromian, rather than Newtonian.
