Physics turns slowly like one of those giant freighters that draw the knots of trade linking the world. A freighter cannot change course quickly because the laws of physics prevent it from doing so. Physics, however, does not change course quickly only because human nature resists such change. That is to say that physics can change quickly if there is sufficient reason for it to do so. It would seem that we have come upon such a moment.

A recent article posted to ArXiv.org on the Radial Acceleration Relation presents the real possibility that a longstanding analytical error is about to be corrected. This in turn will require a major revision of the standard model of cosmology. Dark matter, it would appear, is about to take its place alongside luminiferous aether and caloric fluid in the dustbin of history. At least that is how it should be, but then there is that business about human nature resisting change.

In their abstract of the article, the authors state:

We report a correlation between the radial acceleration traced by rotation curves and that predicted by the observed distribution of baryons. The same relation is followed by 2693 points in 153 galaxies with very different morphologies, masses, sizes, and gas fractions. The correlation persists even when dark matter dominates. Consequently, the dark matter contribution is fully specified by that of the baryons.

Note the peculiarity of the last two sentences. On the one hand dark matter is said to dominate and on the other, the dark matter contribution is said to be fully specified by the baryons (ordinary matter). The two statements would seem to be contradictory. Dark matter cannot be said to dominate if its contribution is specified by baryons. This conflicted stance is repeated and elaborated on in the full text before being settled, somewhat tenuously, in favor of the empirical results:

Regardless of its theoretical basis, the radial acceleration relation exists as an empirical relation. The acceleration scale g† is in the data. The observed coupling…..demands a satisfactory explanation. The radial acceleration relation appears to be a law of nature, a sort of Kepler’s law for rotating galaxies.

This is all well and good; dark matter has been cast off as an explanation for the galactic rotation curves because it is superfluous. But the desire evidenced here to reduce the behavior of galactic systems to a set of simple laws is fundamentally misguided. Kepler’s laws are simple because they treat a fundamentally simple solar system. Galaxies are complex systems and need to be treated as such and first assessed qualitatively to determine the scope of an appropriate quantitative model which is unlikely to be simple.

The dark matter claim with regard to galaxies is rooted in the inappropriate use of the Keplerian method in deriving the expected rotation curves for galaxies. Kepler derived his laws heuristically from Brahe’s empirical data of planetary movement. In the solar system 98% of the mass is concentrated at the center (the sun) and the residual 2% is widely dispersed over orders of magnitude (relative to the solar diameter) from the center.*

Kepler’s laws, then, can only be reasonably considered to apply to similar physical systems. Galaxies are not at all physically similar to the solar system in their mass distribution characteristics and mass distribution is the primary determinant of the gravitational effect. Therefore the use of the heuristically derived Keplerian method in determining expected values for galactic rotation curves is simply wrong. The scandal, and there is a scandal here, is that this error is scientifically obvious because of the obvious dissimilarities between the two physical systems. It should not have persisted, unchallenged, for nearly 40 years.

Indeed, the dark matter hypothesis should never have been widely accepted in the absence of any empirical evidence for its existence. That it has been not only accepted, but fully incorporated into the standard model of cosmology indicates just how deeply, what might be called the mathematician’s delusion has come to predominate in the modern scientific academy.

Whatever the rationalization, the empirical finding of a rotational acceleration relation in galaxies obviates the need for galactic dark matter while also raising questions regarding the dark matter associated with galactic clusters. If, after all, there is no dark matter in galaxies, then how can there be any in galactic clusters?

The problem theorists are now faced with is that they have no qualitative model on which to build a new quantitative model. All they have is MOND, which is just a mathematical tweak to the existing model. It is the mathematical equivalent of an epicycle in Ptolemaic cosmology; it has no explanatory power.

A reasonable first qualitative assessment of the behavior of the outer regions of galaxies would be to say that they exhibit some form of viscosity that is directly related to the even more viscous inner galactic core. This suggests a quantitative treatment analogous to fluid dynamics, which might in turn be extensible to galactic clusters. Whether anyone in the scientific academy will attempt such an approach is, of course, an open question related to the human element mentioned in the first paragraph.

*A more elaborate presentation of the Keplerian argument can be found here. I also want to acknowledge that it was an earlier paper by the author, James Dwyer that, to my knowledge, first pointed out the Keplerian problem with the prevailing analytical approach to galactic rotation curves.