Modified Newtonian dynamics

alternative explanation of the non-Newtonian rotation of galaxies

Modified Newtonian dynamics (MOND) is a theory created in 1982 by Mordehai Milgrom and published in 1983 in The Astrophysical Journal. The theory is based on the empirical facts for galaxy rotation curves. In MOND there is violation of Newton's 2nd law of motion when gravitational accelerations are extremely small and the Newtonian approximation is valid. When general relativity theory is needed, MOND does not make predictions, because there is no generally-accepted, relativistic MOND theory.


  • Fundamental to the idea of MOND is that it is an 'effective' theory, playing a role similar to Kepler's laws (as stressed by Felten 1984). The proponents of MOND have yet to develop the analogue of Newtonian mechanics to explain the effective theory. The absence of a full theory seriously limits the predictive power of MOND, and leads various authors to disagree as to what the observational consequences of this revision will be.
  • ... Milgrom and those few who work on it, are quite aware of the pressing need to have a fully consistent theory that goes beyond the Newtonian non-relativistic limit to a theory that can be applied to cosmology. They don't have one. They fully admit it and they agree that this is a big gap, big lack in the theory. There it is. They do insist that on the scales of galaxies and smaller where it is intended to apply it works remarkably well, and they're right. There are just a few people working on this theory. The most active of the young people is Stacy McGaugh at the University of Maryland. If you ever get a chance you might be amused to talk to him.
  • MOND is so successful that, as a minimum, it is telling us the exact functional form of the force in galaxies. Any theory of galaxy and structure formation must therefore be able to reproduce the MOND phenomenology.
  • I've had conversations about MOND with several of the most imaginative theorists I know. Often it went like this: We would be talking about some sober mainstream problem and one of us would mention galaxies. We would look at each other with a glint of recognition and one of would say, "So you worry about MOND, too," as if admitting a secret vice. Then we would share our crazy ideas — because all ideas about MOND that are not immediately wrong turn out to be crazy.
  • In matter of fact, whether MOND is a fundamental theory or not, the very special and central role the constant a0 plays in galaxy dynamics is well established and is here to stay. For instance, you will find it everywhere in the data itself. All round systems, from giant molecular clouds, through globular clusters and elliptical galaxies, to clusters of galaxies lie, in the mass-radius plane, near the line with constant M/R2. The value of this ratio when multiplied by G gives a0. Another example: the baryonic Tully-Fisher relation agrees well (over many orders of magnitude in mass) with a relation of the form α M = V–4. The proportionality constant α has dimensions of G times acceleration and when divided by G gives a0 (this is independent of the previous appearance as it refers to asymptotic regions in the galaxies).
  • Today we can probe regions of physics where space-time curvature is extremely small finding that, again, Newtonian mechanics fails. This may mean that the Theory of General Relativity needs an extension or that we do not yet understand what “space-time” and “mass” are nor how they are fundamentally related. Perhaps it just boils down to the problem of us not understanding the vacuum.
  • Mild failures aside, it is clear that there is a broad range of masses, 106 — 1011 M☉, in which systems adhere to MOND in their systematics. This must be telling us something; logically there are the following possibilities. a) MOND is merely an efficient summary of the way DM is distributed in the said systems? b) MOND reveals the dependence of inertia on acceleration for small accelerations? c) MOND betrays hitherto unknown forces particularly effective at astronomical scales? d) MOND encapsulates departures from standard Newtonian-Einsteinian gravity theory at the mentioned scales?
  • Ten years ago, it was perfectly respectable to speculate that there was no such thing as dark matter, just a modification of gravity. (It couldn’t have been MOND alone, which was ruled out by clusters, but it could have been some more elaborate modification.) That’s no longer true. The Bullet Cluster and the CMB both provide straightforward evidence that there is gravity pointing in the direction of something other than the ordinary matter. The source for that gravity is “dark matter.” It could be simple, like an axion or a thermal relic, or it could be quite baroque, like TeVeS + sprinkles of other dark matter as required, but it’s definitely there.
  • Viewed simply, MOND is an algorithm that, with one additional fundamental parameter having units of acceleration, allows calculation of the distribution of the effective gravitational force in astronomical objects from the observed distribution of baryonic dark matter — and it works remarkably well. This is evidenced primarily by the use of the MOND algorithm in the determination of rotation curves of disk galaxies where the agreement with observed rotation curves is often precise, even in details. The existence of such an algorithm is problematic for CDM because this is not something that dissipationless dark matter on the scale of galaxies can naturally do; it would seem to require a coupling between dark matter and baryonic matter which is totally at odds with the perceived properties of CDM.
  • We do not know to what extent and how MOND affects nongravitational phenomena such as electromagnetism (EM). For example, if there is a consistent way to extend and apply the basic tenets to nongravitational physics.
    • Mordehai Milgrom: (2014). "MOND theory". Canadian Journal of Physics 93 (2): 107–118. (p. 108)
  • Another crucial point is that MOND as we know it now is arguably only an approximate 'effective field theory' that approximates some more fundamental scheme at a deeper stratum — some 'FUNDAMOND' — conceptually, in a similar way to thermodynamics being an approximation of the statistical-mechanics, microscopic description.
  • We have in MOND a formula that has had repeated predictive successes. Many of these have been true a priori predictions, like the absolute nature of the Tully-Fisher relation, the large mass discrepancies evinced by low surface brightness galaxies, and the velocity dispersions of many individual dwarf spheroidal galaxies like Cluster 2. I don't see how this can be an accident. But what we lack is an underlying theoretical basis for the observed MONDian phenomenology: Why does this happen?
  • The key appeal of MOND is that we only need ordinary matter, the matter we can actually see, to explain the universe. But opponents are not happy with the ad-hocness of aspects of the theory, the messiness of the underlying mathematics, and the tweaking of parameters required to make MOND work. Most cosmologists would bet on dark matter, but MOND advocates show little sign of slowing down.

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