Modified Newtonian dynamics
Modified Newtonian dynamics (MOND) is a theory that proposes a modification of Newton's second law to account for observed properties of galaxies.
Another notable attempt was by Constantinos Skordis [d] and Tom Złośnik [d] in 2021, which proposed a relativistic model of MOND compatible with cosmic microwave background observations.
[14] 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.
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.
MOND predicts stellar velocities that closely match observations for an extraordinarily wide range of distances from galactic centers of mass.
Within the Solar System, the v 4 = GMa0 equation makes the effect of the a0 term virtually nonexistent; it is overwhelmed by the enormous—and highly Newtonian—gravitational influence of the Sun as well as the variability of Earth's surface gravity.
A change in the laws of gravity below this acceleration is far too small to be resolved with even the most sensitive free-fall-style absolute gravimeters available to national labs, like the FG5-X, which is accurate to just ±2 μGal.
Such disturbances in local gravity due to tidal distortions are even detectable as variations in the rate of a Shortt double-pendulum clock, which was a national timekeeping standard in the late 1920s.
A subset of these non-relativistic hypotheses have been further embedded within relativistic theories, which are capable of making contact with non-classical phenomena (e.g., gravitational lensing) and cosmology.
[20] 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.
[6][21] Since MOND was specifically designed to produce flat rotation curves, these do not constitute evidence for the hypothesis, but every matching observation adds to support of the empirical law.
Each of the theories described here reduce to Milgrom's law in situations of high symmetry (and thus enjoy the successes described above), but produce different behavior in detail.
[45] AQUAL generates MONDian behavior by modifying the gravitational term in the classical Lagrangian from being quadratic in the gradient of the Newtonian potential to a more general function.
This is called the "quasi-linear formulation of MOND", or QUMOND,[46] and is particularly useful for calculating the distribution of "phantom" dark matter that would be inferred from a Newtonian analysis of a given physical situation.
Such "modified inertia" theories, however, are difficult to use because they are time-nonlocal, require energy and momentum to be non-trivially redefined to be conserved, and have predictions that depend on the entirety of a particle's orbit.
Since Milgrom's law is non-linear in acceleration, MONDian subsystems cannot be decoupled from their environment in this way, and in certain situations this leads to behaviour with no Newtonian parallel.
[36] The external field effect is best described by classifying physical systems according to their relative values of ain (the characteristic acceleration of one object within a subsystem due to the influence of another), aex (the acceleration of the entire subsystem due to forces exerted by objects outside of it), and a0: The external field effect implies a fundamental break with the strong equivalence principle (but not necessarily the weak equivalence principle).
In this regard, Milgrom has commented:[54] 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.Indeed, the potential link between MONDian dynamics and the universe as a whole (that is, cosmology) is augmented by the observation that the value of a0 (determined by fits to internal properties of galaxies) is within an order of magnitude of cH0, where c is the speed of light and H0 is the Hubble constant (a measure of the present-day expansion rate of the universe).
Recent work on a transactional formulation of entropic gravity by Schlatter and Kastner[55] suggests a natural connection between a0, H0, and the cosmological constant.
Some effort has gone towards establishing the presence of a characteristic acceleration scale as a natural consequence of the behavior of cold dark matter halos,[56][57] although Milgrom has argued that such arguments explain only a small subset of MOND phenomena.
[59] Finally, some researchers suggest that explaining the empirical success of Milgrom's law requires a more radical break with conventional assumptions about the nature of dark matter.
Astronomers measured the distribution of stellar and gas mass in the clusters using visible and X-ray light, respectively, and in addition mapped the inferred dark matter density using gravitational lensing.
For example, it has been claimed that MOND offers a poor fit to the velocity dispersion profile of globular clusters and the temperature profile of galaxy clusters,[74][75] that different values of a0 are required for agreement with different galaxies' rotation curves,[76] and that MOND is naturally unsuited to forming the basis of cosmology.
