Modified Newtonian dynamics

The modified Newtonian dynamics, abbreviated MOON, is a physical hypothesis to explain the rotational behavior of galaxies through modifications of the equations of motion of matter in the gravitational field. MOND was proposed in 1983 by Mordehai Milgrom as an alternative to the postulate of dark matter.

The theory is controversial and rejected by many followers of the standard cosmological model. It is sometimes pointed out a similar situation as in previous sociological paradigm shifts.

Background

Rotational velocity of galaxies

Since the 80s of the 20th century, measurements of the rotation of galaxies, that the rotation speeds did not meet the expectations. The orbits of the stars in a galaxy are caused only by the gravity of the aggregated matter in the galaxy. Using the observed mass distribution (stars, nebulae ), the gravitational force, and thus the path of the star can be calculated.

It turned out that the stars at the edge of the galaxy circulated faster than according to the theory predicted. One speaks of the " flattening of the rotation speed " as opposed to the expected " drop in the speed of rotation ".

Modified dynamics instead of dark matter

Since both the Newtonian law of gravitation as well as Albert Einstein's general relativity theory are well verified theories about the behavior of matter under gravity, take most astronomers an invisible ( ie dark ) matter component in the halo around the galaxies to explain the flat rotation curves. Also observations on larger scales, such as clusters of galaxies or the large-scale structure of the universe, provided strong evidence for the existence of dark matter.

Instead of additional, non-visible mass suggested Mordehai Milgrom 1983 provides that a change in the Newtonian laws of motion could be the cause for the observed rotation curves. According to the MOND hypothesis, the change takes only at very small accelerations, as they occur in the astronomical scale, a relevant influence on the movements.

Proponents of MOND hypothesis argue that the Newtonian theory of gravitation has already experienced in 1686 three modifications. At very close distances physicists use only quantum mechanics, at very high speeds Einstein's special theory of relativity and close to very large masses his general theory of relativity. A fourth modification in the above-mentioned extreme range was therefore not excluded.

The hypothesis

The Newtonian law of motion states that an object of constant mass, if it is subjected to a force undergoes an acceleration:

This law has generally proved correct. However, it is only to prove difficult or impossible to experimentally at extremely small accelerations. However, such extremely small accelerations acting on the gravitational interaction between distant stars.

Milgrom suggested that the law of motion to:

Amend, where

Is a function which takes 1 for high values ​​() for small values ​​(). The exact shape of the function is not specified in the literature and are most often used. is a constant which is determined below which accelerate the modification is relevant.

Assuming that there is no dark matter and instead apply the MOND hypothesis, can be determined from astronomical measured rotation curves of galaxies. Milgrom received from measurements of many galaxies.

Since all processes of everyday life take place during acceleration, here the law of motion remains unchanged. Far away from the center of a galaxy is the situation, however, is different. According to the law of gravity applies where:

Where the gravitational constant, the mass of the galaxy and the mass of the star is considered. is the distance between the centroid of the galaxy and the star.

With the modified law of motion is created:

Since in this situation just to so apply, one obtains:

And thus

So is

, The relationship between speed, acceleration and the distance to center of force for a circular path is:

This results in

It follows that the rotational speed does not depend on the distance in the far distance.

Tensor - vector - scalar theory of gravity

A relativistic formulation of MOND was proposed by Jacob Bekenstein 2004. She is known as tensor - vector - scalar theory of gravity.

Review of the theory by observations

The Cluster -Merger 1E 0657-558 provides the ability to test alternative theories of gravity against the dark matter. On the one hand, the distribution of the visible baryonic matter was measured, and on the other hand the gravitational potential of the cluster using the deflection of light in its gravitational field (where the nature of the MOND theory has been considered). The mass ratio between galaxies contained and the surrounding plasma is 2:15 to 3:15. That is, the galaxies make up only a small fraction of the baryonic mass of the cluster. It was also observed that the plasmas of the two progenitor clusters have combined to form a new cluster, while the galaxies survived the collision of the two previous clusters more or less kollisionslos.

The gravitational potential does not follow the baryonic mass distribution of the plasma, but that of the galaxies. By modifying the law of gravity this is not explainable. However, it can be explained by the fact that the source of the gravitational potential is not only the visible baryonic matter but also dark matter. Even when the MOND hypothesis were true, there must be invisible ( dark ) matter.

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