# Modified Newtonian dynamics

Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining why galaxies do not appear to obey the currently understood laws of physics.
Created in 1982 and first published in 1983 by Israeli physicist Mordehai Milgrom, the hypothesis' original motivation was to explain why the velocities of stars in galaxies were observed to be larger than expected based on Newtonian mechanics. Milgrom noted that this discrepancy could be resolved if the gravitational force experienced by a star in the outer regions of a galaxy was proportional to the square of its centripetal acceleration (as opposed to the centripetal acceleration itself, as in Newton's second law) or alternatively, if gravitational force came to vary inversely linearly with radius (as opposed to the inverse square of the radius, as in Newton's law of gravity). In MOND, violation of Newton's laws occurs at extremely small accelerations, characteristic of galaxies yet far below anything typically encountered in the Solar System or on Earth.

## Quotes

* 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.
** Douglas Scott, Martin White, Joanne D. Cohn, and Elena Pierpaoli: (2001). "Cosmological Difficulties with Modified Newtonian Dynamics (or: La Fin du MOND?)". arXiv preprint astro-ph/0104435. p. 3
* ... 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.
** Jim Peebles: Oral History Interviews: Jim Peebles - Session I, Interviewed by Christopher Smeenk (4 April 2002).
* 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.
** Riccardo Scarpa: (2006). "Modified Newtonian dynamics, an introductory review". AIP Conference Proceedings 822 (1): 253–265. arXiv.org preprint, (See "Introduction" section.)
* 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.
** Lee Smolin: The Trouble with Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next. 2006. p. 213.
* In matter of fact, whether MOND is a fundamental theory or not, the very special and central role the constant a$_0$ 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/R$^2$. The value of this ratio when multiplied by G gives a$_0$. 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 a$_0$ (this is independent of the previous appearance as it refers to asymptotic regions in the galaxies).
** Moti Milgrom: Comment on p. 344 in D'Onofrio, Mauro & Burigana, Carlo, eds. (2009). Questions of Modern Cosmology. Springer.
* 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.
** Pavel Kroupa: (1 September 2010)"The Fritz Zwicky Paradox: the fourth failure of Newton (MOND, MOG, etc)". The Dark Matter Crisis blog.
* Mild failures aside, it is clear that there is a broad range of masses, 10$^6$ — 10$^{11}$ 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?
** Jacob D. Bekenstein: (13 January 2012)"Tensor-vector-scalar-modified gravity: from small scale to cosmology". arXiv.org. (quote from p. 4)
* 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.
** Sean M. Carroll: (9 May 2012)"Dark Matter vs. Modified Gravity: A Trialogue, Preposterous Universe blog".
* 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.
** Robert H. Sanders: (2014). "A historical perspective on modified Newtonian dynamics". Canadian Journal of Physics 93 (2): 126–138. DOI:10.1139/cjp-2014-0206. page 2 of arXiv.org preprint
* 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.
** Mordehai Milgrom: (2019). "MOND vs. dark matter in light of historical parallels". arXiv preprint arXiv:1910.04368. (pp. 9–10)
* ... one really has to stand on one's head to reconcile MOND with what is well-established about relativistic physics, and the results are pretty obscure and far-fetched looking.
** Edward Witten: quoted in Witten, Milgrom, Brown, and Kroupa on Modified Newtonian Dynamics (MOND), 2015
* 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?
** Stacy McGaugh: (20 February 2017)"Emergent Gravity hits a pothole". Triton Station blog.
* I think the existence of (something like) dark matter is incontrovertible. It would be nice to understand why Modified Newtonian dynamics (MOND) works so well.
** Zohar Komargodski, as quoted by Luis Álvarez-Gaumé and Maria Shtilman, in: (Fall 2017)"Conversation with Zohar Komargodski". Simons Center for Geometry and Physics (SCGP) Newsletter X: 10–13. (quote from p. 13)
* 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.
** Luke A. Barnes and Geraint F. Lewis: The Cosmic Revolutionary's Handbook: (Or: How to Beat the Big Bang). Cambridge University Press. 4 February 2020. p. 231. ISBN 978-1-108-48670-5.
* Milgromian theorists have understood for a long time that there is just no way that a formless entity such as dark matter can spontaneously rearrange itself – and keep rearranging itself – so as to produce the striking regularities that we observe in the kinematics of nearby galaxies.
** David Merritt, A non-Standard model, Aeon, 19 July 2021
* ... the interpretation of MOND as modified inertia (MI) ... ... Who is afraid of modified inertia? The interpretation of MOND as MI was on the table from the very inception of MOND ...
** Mordehai Milgrom, (2023). "MOND as manifestation of modified inertia"". arXiv preprint arXiv:2310.14334. (quote from abstract and p. 4)