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In physics, modified Newtonian dynamics (MOND) is a theory that proposes a modification of Newton's laws to account for observed properties of galaxies. Created in 1983 by Israeli physicist Mordehai Milgrom,〔. . .〕 the theory's original motivation was to explain the fact that 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. == Overview == 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.〔Babcock, H, 1939, "(The rotation of the Andromeda Nebula )", Lick Observatory bulletin ; no. 498〕 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 lead 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 μ(x) → 1 for x >> 1, and consistency with astronomical observations requires μ(x) → x for x << 1. Beyond these limits, the interpolating function is not specified by the theory, although it is possible to weakly constrain it empirically.〔G. Gentile, B. Famaey, W.J.G. de Blok (2011). "THINGS about MOND", Astron. Astrophys. 527, A76. 〕〔B. Famaey, J. Binney (2005), "Modified Newtonian Dynamics in the Milky Way", MNRAS, 〕 Two common choices are: : ("Simple interpolating function"), and : ("Standard interpolating function"). Thus, in the deep-MOND regime (a << a0): :. Applying this to an object of mass m in circular orbit around a point mass M (a crude approximation for a star in the outer regions of a galaxy), we find: : that is, the star's rotation velocity is independent of its distance r from the centre of the galaxy – the rotation curve is flat, as required. By fitting his law to rotation curve data, Milgrom found a0 ≈ 1.2 x 10−10 m s−2 to be optimal. This simple law is sufficient to make predictions for a broad range of galactic phenomena. Milgrom's law can be interpreted in two different ways. One possibility is to treat it as a modification to the classical law of inertia (Newton's second law), so that the force on an object is not proportional to the particle's acceleration a but rather to μ(a/a0)a. In this case, the modified dynamics would apply not only to gravitational phenomena, but also those generated by other forces, for example electromagnetism.〔M. Milgrom, "MOND - Particularly as Modified Inertia", 〕 Alternatively, Milgrom's law can be viewed as leaving Newton's Second Law intact and instead modifying the inverse-square law of gravity, so that the true gravitational force on an object of mass m due to another of mass M is roughly of the form GMm/(μ(a/a0)r2). In this interpretation, Milgrom's modification would apply exclusively to gravitational phenomena. By itself, Milgrom's law is not a complete and self-contained physical theory, but rather an ad-hoc empirically-motivated variant of one of the several equations that constitute classical mechanics. Its status within a coherent non-relativistic theory of MOND is akin to Kepler's Third Law within Newtonian mechanics; it provides a succinct description of observational facts, but must itself be explained by more fundamental concepts situated within the underlying theory. Several complete classical theories have been proposed (typically along "modified gravity" as opposed to "modified inertia" lines), which generally yield Milgrom's law exactly in situations of high symmetry and otherwise deviate from it slightly. A subset of these non-relativistic theories have been further embedded within relativistic theories, which are capable of making contact with non-classical phenomena (e.g., gravitational lensing) and cosmology.〔B. Famaey and S. McGaugh, "Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions", 〕 Distinguishing both theoretically and observationally between these alternatives is a subject of current research. The majority of astronomers, astrophysicists and cosmologists accept ΛCDM〔(Pavel Kroupa – The vast polar structures around the Milky Way and Andromeda, YouTube, Nov. 18, 2013 ) Pavel Kroupa claims that the majority opinion is wrong and that empirical evidence rules out the ΛCDM model.〕 (based on General Relativity, and hence Newtonian mechanics), and are committed to a dark matter solution of the missing-mass problem. MOND, by contrast, is actively studied by only a handful of researchers. The primary difference between supporters of ΛCDM and MOND is in the observations for which they demand a robust, quantitative explanation and those for which they are satisfied with a qualitative account, or are prepared to leave for future work. Proponents of MOND emphasize predictions made on galaxy scales (where MOND enjoys its most notable successes) and believe that a cosmological model consistent with galaxy dynamics has yet to be discovered; proponents of ΛCDM require high levels of cosmological accuracy (which concordance cosmology provides) and argue that a resolution of galaxy-scale issues will follow from a better understanding of the complicated baryonic astrophysics underlying galaxy formation.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Modified Newtonian dynamics」の詳細全文を読む スポンサード リンク
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