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# Milgrom vs Newton

The formula for the force of gravitational interaction invented by Newton: F = gMm / r ^ 2, where F is the force of interaction, g is the gravitational constant, M and m are the masses of interacting bodies, r is the distance between them, which lies at the heart of modern physics. But, the more observations, the worse this formula reflects the real interaction of objects. It was to correct the behavior of stupid nature in accordance with this «smart» formula that «dark matter» was invented.

Israeli scientist Mordehai Milgrom questioned the universality of Newton’s formulas, primarily the formula for Newton’s second law F = ma, where F is the force, m is the mass of an object, and a is its acceleration. In the case of stars moving around the center of the galaxy, the force F entering the equation is the force of gravity. Since stars violating Newton’s law move with very small accelerations, he suggested that in systems where the acceleration falls below a certain critical value a0, the formula F = ma should be replaced by the formula F = ma2 / a0. Milgrom’s formula correctly reflected the movements of galaxies.

Of course, the overwhelming number of scientists did not accept Milgrom’s idea, because his modified Newtonian dynamics (MOD) did not correspond to relativistic theories. (There were also attempts at a relativistic modification of the MOND. For example, this was done by Jacob Berkenstein.)

In March 2018, the journal Nature published an article with the results of observation of the irregular dwarf galaxy NGC1052 – DF2.
Scientists have calculated the velocity dispersion (σ) for NGC1052 – DF2 using the method of calculating the net gravitational force for N bodies. It turned out that the influence of NGC1052 reduces the variance for MOND to 15 kilometers per second, bringing it closer to the observed values. In this case, the difference between the theoretical and measured σ was about two standard deviations and was statistically insignificant.

An employee of the University of Maryland (USA) Stacy McGaugh showed in his observation that modified Newtonian dynamics (MOD) can explain the real rotation of galaxies without «dark matter» and more accurately.

MOND offers a completely different way of solving the problem — changing traditional dynamics. In this theory, a new constant is introduced with the dimension of acceleration, a0, and the following is established: at high (much greater than a0) accelerations, the «old» law is in effect, and at low accelerations, its modified version. In other words, the well-known formula F = m • a is changed to F = m • μ (a / a0) • a, where the factor μ (a / a0) takes on the value 1 if a is much greater than a0, and a / a0 if a less than a0.

Milgrom’s formula is just as heuristic as Newton’s, that is, it is also invented. It is not for nothing that Milgrom called his theory modified Newtonian dynamics, that is, he corrected Newton, and did not abandon any unnatural formulas. Milgrom did not try to find a natural formula in which mass would not be multiplied by mass, time by time, speed by speed, and similar mathematical actions were applied, which were in no way correlated with the realities of nature, but Milgrom’s formula showed the very possibility of looking for a natural formula, denying the monopoly Newton’s formula!