Modified Newtonian dynamics

Modified Newtonian dynamics (MOND) is a theory that proposes a modification of Newton's laws to account for observed properties of galaxies. It is an alternative to the theory of dark matter in terms of explaining why galaxies do not appear to obey the currently understood laws of physics. F N = m μ ( a a 0 ) a . {displaystyle F_{N}=mmu left({frac {a}{a_{0}}} ight)a.}     (1) G M m r 2 = m ( v 2 r ) 2 a 0 ⟹ v 4 = G M a 0 {displaystyle {frac {GMm}{r^{2}}}=m{frac {left({frac {v^{2}}{r}} ight)^{2}}{a_{0}}}quad Longrightarrow quad v^{4}=GMa_{0}}     (2)It has been long suspected that local dynamics is strongly influenced by the universe at large, a-la Mach's principle, but MOND seems to be the first to supply concrete evidence for such a connection. This may turn out to be the most fundamental implication of MOND, beyond its implied modification of Newtonian dynamics and general relativity, and beyond the elimination of dark matter. Modified Newtonian dynamics (MOND) is a theory that proposes a modification of Newton's laws to account for observed properties of galaxies. It is an alternative to the theory 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 theory's 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 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. MOND is an example of a class of theories known as modified gravity, and is an alternative to the hypothesis that the dynamics of galaxies are determined by massive, invisible dark matter halos. Since Milgrom's original proposal, MOND has successfully predicted a variety of galactic phenomena that are difficult to understand from a dark matter perspective. However, MOND and its generalisations do not adequately account for observed properties of galaxy clusters, and no satisfactory cosmological model has been constructed from the theory. The accurate measurement of the speed of gravitational waves compared to the speed of light in 2017 ruled out many theories which used modified gravity to explain dark matter.However, both Milgrom’s bi-metric formulation of MOND and nonlocal MOND are not ruled out according to the same study. Several independent observations point to the fact that the visible mass in galaxies and galaxy clusters is insufficient to account for their dynamics, when analysed using Newton's laws. This discrepancy – known as the 'missing mass problem' – was first identified for clusters by Swiss astronomer Fritz Zwicky in 1933 (who studied the Coma cluster), and subsequently extended to include spiral galaxies by the 1939 work of Horace Babcock on Andromeda. These early studies were augmented and brought to the attention of the astronomical community in the 1960s and 1970s by the work of Vera Rubin at the Carnegie Institute in Washington, who mapped in detail the rotation velocities of stars in a large sample of spirals. While Newton's Laws predict that stellar rotation velocities should decrease with distance from the galactic centre, Rubin and collaborators found instead that they remain almost constant – the rotation curves are said to be 'flat'. This observation necessitates at least one of the following: 1) There exists in galaxies large quantities of unseen matter which boosts the stars' velocities beyond what would be expected on the basis of the visible mass alone, or 2) Newton's Laws do not apply to galaxies. The former leads to the dark matter hypothesis; the latter leads to MOND. The basic premise of MOND is that while Newton's laws have been extensively tested in high-acceleration environments (in the Solar System and on Earth), they have not been verified for objects with extremely low acceleration, such as stars in the outer parts of galaxies. This led Milgrom to postulate a new effective gravitational force law (sometimes referred to as 'Milgrom's law') that relates the true acceleration of an object to the acceleration that would be predicted for it on the basis of Newtonian mechanics. This law, the keystone of MOND, is chosen to reduce to the Newtonian result at high acceleration but leads to different ('deep-MOND') behaviour at low acceleration: Here FN is the Newtonian force, m is the object's (gravitational) mass, a is its acceleration, μ(x) is an as-yet unspecified function (known as the 'interpolating function'), and a0 is a new fundamental constant which marks the transition between the Newtonian and deep-MOND regimes. Agreement with Newtonian mechanics requires