MOND is the non-quantum modification to gravity that has captivated the most attention from the physics community since Einstein’s General Relativity. MOdified Newtonian Dynamics (or MilgrOmiaN Dynamics) was first proposed in 1982 by Milgrom as a modification to inertia or to gravity (in particular, to the inverse squared law force of gravity), explicitly constructed to obtain flat galactic rotation curves to explain the dark matter observations in galaxies. If fact, it is built directly out of an observation, the Tully-Fisher law, by which there is an empirical relationship between the asymptotic rotation velocity of galaxies and their mass or luminosity. These velocities are proportial to the fourth root of the gravitational mass.
In essence, MOND modifies gravity in a certain low acceleration regime through a fundamental constant of acceleration (also referred to as an acceleration scale constant or Hubble acceleration), in a way in which Newtonian gravity transitions from an inverse squared law to a simple inverse law through an interpolating function dependent on the true acceleration and the acceleration constant.
Evidence in favor of MOND in contrast to physical dark matter is found in several observations.
Galactic rotation curves generally exhibit no mass discrepancy at their interior, which is very difficult to explain with physical dark matter (also known as the cuspy halo problem), which should clump together and exist in larger amounts in the center of galaxies (of course, one could hypothesize any desired stable distribution of physical dark matter to fit observations, since it is not observable).
MOND is sometimes critized as “curve-fitting” (as if, for instance, Planck’s law wasn’t, which started one of the greatest revolutions in theoretical physics). MOND fits the data with a single free parameter, its acceleration constant (in contrast to physical dark matter models which have many more). It is a fact that, if one wants to modify gravity to explain dark matter in rotation curves, this modification must always departure from Newtonian gravity at a particular acceleration scale. This is always correct and it is the true great achievement of MOND, without even stating how must gravity behave beyond this scale (apart from being stronger), because there are multiple choices for its interpolating function in the original MOND proposal, different interpretations such as modified inertia or just modified gravity, and different frameworks that reduce to MOND. The mass discrepancy in galaxies always appears at lower accelerations than a particular “threshold” value. This correlation between acceleration and mass discrepancy should not be expected to arise naturally with physical dark matter.
The Tully-Fisher relationship is an observational correlation between the mass or luminosity of a galaxy and its rotational velocity, which MOND’s formulation results in, but there is no reason why it should arise with physical dark matter. Moreover, MOND explains the Renzo’s rule, by which features in the baryonic mass distribution and features in the rotation curve are strongly correlated. Again, there is no reason by which physical dark matter should result in this correlation. For both of these cases, physical dark matter (which accounts for most of the matter in the galaxies) should clump by its own gravity, leading to deviations from these relationships. Although the Tully-Fisher relationship was known for certain type of galaxies before Milgrom worked out MOND, MOND predicted this relationship for all galaxy types after its formulation.
There are many more indications that support MOND, such as observed flat rotation curves extending beyond the supposed dark matter halo, tidal dwarf galaxies exhibiting dark matter effects that shouldn’t exist according to physical dark matter models, early galaxy formation as observed by the James Web Telescope, and many more. Results for binary system tests are inconclusive at this present date (2025).
It is often claimed that MOND has been falsified and its wrong, because it does not explain galaxy cluster dynamics or the evidence of dark matter in the CMB at the early universe. Firstly, one must understand MOND as an effective theory, the same way Newtonian gravity (or gravitoelectromagnetism, or linearized gravity) is an effective theory or approximation of General Relativity. We know this is the case for sure, since the original MOND formulation is not only non-relativistic, but also fails to satisfy basic conservation laws. But theories which satisfy conservation laws that result in MOND´s approximation can be built (examples are AQUAL and QUMOND). In other words, a more fundamental theory of modified gravity, FundaMOND, must reduce to MOND as an approximation in the galaxy’s regime, while its complete formulation must explain galaxy cluster dynamics, if physical dark matter does not exist. The topic of the CMB will be discussed later.
Since MOND alleviates the mass-luminosity discrepancies in galaxy cluster dynamics (from a factor of 10: to a 2-3:1), and by using MOND, the discrepancy decreases with increasing distance from the center of the clusters, some MOND supporters suggest that a physical form of dark matter could exist in these systems. This physical dark matter could explain the evidence for dark matter in the early universe from the CMB. While some may think that there is no point in using MOND to explain some dark matter observations, and physical dark matter to explain other dark matter observations, not only this could be true, but it is more reasonable than to propose physical dark matter for the case of individual galaxies, where the cuspy halo problem shows that by using Newtonian gravity, the mass discrepancy increases with distances far away from the galactic center, because physical dark matter should concentrate more in both galaxy centers and cluster centers. Dark matter should “clump” by gravity, with higher densities where there is more baryonic matter, and this works in galaxy clusters considering that MOND holds, but not within galaxies.
While this could be a solution to the CMB, the effects of dark matter in the early universe could also be explained by the fact that most attempts to construct a FundaMOND theory rely on additional or extra fields, which must be accompanied by a particle related to that field according to quantum field theory, which could be the physical dark matter particle of the CMB power spectrum. A varying acceleration constant in MOND could also solve early universe structure formation which is claimed to be due to physical dark matter.
If one prefers to think that galaxy clusters are empty of physical dark matter, then the original MOND formulation must be modified and gravity should be even stronger for these systems than in MOND. One may even think that a FundaMOND theory should take into account this modification of MOND, and that MOND is just an approximation, for instance, in which extra terms or higher order terms are missing. It was Bekenstein who, in the same way that Milgrom identified the difference between the solar system and the outer part of galaxies as the latter having lower gravitational field intensities (or accelerations) than the first, identified that the interior of galaxy clusters have deeper potential wells than the solar system or individual galaxies (and proposed an AQUAL scale dependent critical acceleration based on potential and a constant of speed). This means that MOND, which is based on gravitational field intensities, may be missing a correction or a term based on gravitational potentials, which FundaMOND could contain. The main troublesome one encounters with this idea is that if a correction to MOND is based on the depth of potential wells, it must yield Newtonian gravity for neutron stars, which have even deeper potential wells than clusters. This could be in principle solved if FundaMOND only differentiates from MOND in the low acceleration regime, which is the case for galaxy clusters but not for neutron stars.
The collision of two clusters named the Bullet cluster is usually portraited as evidence against MOND, because the mass discrepancies in the system (inferred from weak lensing analysis of background galaxies) do not appear where the observed bulk of most baryons is (the inner central gas). But MOND does not predict that the discrepancies must be where baryons are. Instead, it predicts that the discrepancies must be where accelerations are small (which is usually found far away from the observed baryonic bulks). Bekenstein’s scale dependent critical acceleration violates Newton shell theorem (the gravitational field at a surrounding surface does not fix uniquely the mass within it, but matter elsewhere can influence the result), which could solve the Bullet’s cluster dynamics (in this cluster, the problem is that there is gravitational field whose sources do not seem to be inside but outside the gravitational field). Still, standard MOND does not explain the Bullet cluster (as it doesn’t fully explain other galaxy clusters, colliding or not). The Bullet cluster, not only doesn’t rule out modified gravity or a FundaMOND theory, but it is also difficult to favor physical dark matter, due to the difficulties to model the dynamical system with dark matter.
Why is then MOND strongly criticized if it has not only not been proved wrong, but there is evidence for MOND and against physical dark matter? There are over 50 mayor experiments (counting current and past efforts) dedicated to detecting dark matter, which have received enormous amounts of funding for institutions and research centers. In contrast, the required funding for theoretical works of modifying gravity to explain dark matter are miniscule. Is the dark matter search promoted just for the profitability of traditional institutions? Is the scientific community reluctant to modify the established theories?
Milgrom himself often supported the idea of MOND as modifying inertia instead of gravity, although the latter might seem simpler (or less of a sin) to do. Newtonian inertia was already modified by special relativity, and there are many more examples in physics of modified, acquired, or effective inertia observations. Could there be a modified theory of inertia leading to MOND? Many other attempts to modify gravity, such as Brans-Dicke theory, were motivated and phenomenologically grounded on Mach’s principle. We explain the relationship between modified inertia theories with Mach’s principle and MOND a next post here.
Common misconceptions:
MOND is not that there exists a minimum acceleration all stars have when orbiting around galaxies.
MOND does not mean that there is always an extra tiny acceleration that becomes noticeable in the outskirts of galaxies.
MOND predicts galaxies with no dark matter, if there is an acceleration that pushes them into the Newtonian regime (e.g., a nearby mother galaxy pulling it).
References:
Morderhai Milgrom, MOND – A Pedagogical Review, 2001
Morderhai Milgrom, Scholarpedia – The MOND paradigm of modified dynamics