Modified Newtonian Dynamics

MOND is a redirect to this article. For the companion of the earth see moon .

The modified Newtonian dynamics , abbreviated to MOON (pronounced with a short "O"), is a physical hypothesis that is supposed to explain the rotational behavior of galaxies by modifying the equations of motion of matter in the gravitational field . MOON was proposed in 1983 by Mordehai Milgrom as an alternative to the dark matter postulate .

The hypothesis is controversial.

background

Speed ​​of rotation of galaxies

Diagram showing the discrepancy between the calculated and measured rotational speed of spiral galaxies

Measurements of the rotation of galaxies since the 1980s have shown that the speeds of rotation are not as expected. The orbits of the stars in a galaxy are only caused by the gravity of the matter that is clumped together in the galaxy . Using the observed mass distribution (stars, gas nebula ), the gravitational force and thus the orbit of the stars can be calculated.

It turned out that the stars on the edge of the galaxies orbited faster than the theory predicted. One speaks of the “flattening of the rotational speed” as opposed to the expected “drop in the rotational speed”.

Modified dynamics instead of dark matter

Since both Newton's law of gravity and Albert Einstein's general theory of relativity are well-proven theories about the behavior of matter under gravity, most astronomers assume an invisible (i.e. dark) component of matter in the halo around the galaxies to explain their flat rotation curves . Observations on larger scales, for example of galaxy clusters or the large-scale structure of the universe, also provided strong indications of the existence of dark matter.

Instead of an explanation by additional, invisible mass, Mordehai Milgrom suggested in 1983 that the observed rotation curves could also be represented by changing Newton's laws of motion. The MOON hypothesis states that only with very small changes in the accelerations , as they occur on an astronomical scale, relevant influences on the movements result.

Proponents of the MOON hypothesis claim that Newton's theory of gravity has already undergone three modifications by 1686. In the case of very small distances, physicists only use quantum mechanics , in the case of very high speeds, Einstein's special theory of relativity, and near very large masses, his general theory of relativity . A fourth modification in the extreme range mentioned above cannot therefore be ruled out.

In the meantime, Erik Verlinde has further developed the MOND. This theory says that dark matter , like gravity, is a consequence of dark energy .

The hypothesis

Newton's law of motion states that an object of constant mass , when exposed to a force , experiences an acceleration : ${\displaystyle m}$ ${\displaystyle F}$ ${\displaystyle a}$

${\displaystyle F=m\,a}$

This law has generally been shown to be correct. However, with extremely small accelerations it is difficult or impossible to prove experimentally. However, such extremely small accelerations work in the gravitational interaction between distant stars.

Milgrom suggested the law of motion to:

${\displaystyle F=m\,\operatorname {\mu } (|a|/a_{0})\,a}$

where a (for positive arguments) is a positive, smooth , monotonic function that takes approximately 1 for high values ​​( ) and approximately for small values ​​( ). The exact form of the function is not specified, most frequently in the literature and used. is a (positive) constant that determines the acceleration below which the modification becomes relevant. ${\displaystyle \operatorname {\mu } (x)}$ ${\displaystyle x\gg 1}$ ${\displaystyle x}$ ${\displaystyle x\ll 1}$ ${\displaystyle \operatorname {\mu } (x)}$ ${\displaystyle \operatorname {\mu } (x)={\frac {x}{1+x}}}$ ${\displaystyle \operatorname {\mu } (x)={\frac {x}{\sqrt {1+x^{2}}}}}$ ${\displaystyle a_{0}}$

Assuming that there is no dark matter and that the MOON hypothesis applies instead, the rotation curves of galaxies can be determined from astronomically measured curves. Milgrom obtained from measurements of many galaxies . ${\displaystyle a_{0}}$ ${\displaystyle a_{0}=1{,}2\cdot 10^{-10}\,\mathrm {m} \,\mathrm {s} ^{-2}}$

Since all processes of everyday life take place during acceleration , the law of motion remains unchanged here. Far from the center of a galaxy, however, the situation is different. According to the law of gravitation: ${\displaystyle a\gg a_{0}}$

${\displaystyle F=m\,{\frac {G\,m_{\mathrm {G} }}{r^{2}}},}$

where is the gravitational constant, the mass of the galaxy and the mass of the star under consideration. is the distance between the center of gravity of the galaxy and that of the star. ${\displaystyle G}$ ${\displaystyle m_{\mathrm {G} }}$ ${\displaystyle m}$ ${\displaystyle r}$

With the modified law of motion we get:

${\displaystyle {\frac {G\,m_{\mathrm {G} }}{r^{2}}}=\operatorname {\mu } (|a|/a_{0})\,a.}$

Because in this situation right , so to apply, is obtained for positive (the gravitational acceleration is always positive): ${\displaystyle a\ll a_{0}}$ ${\displaystyle a/a_{0}\ll 1}$ ${\displaystyle a}$

${\displaystyle \operatorname {\mu } (|a|/a_{0})\approx {\frac {a}{a_{0}}}}$

and thus

${\displaystyle {\frac {G\,m_{\mathrm {G} }}{r^{2}}}={\frac {a^{2}}{a_{0}}}.}$

So is

${\displaystyle a={\frac {\sqrt {G\,m_{\mathrm {G} }\,a_{0}}}{r}}.}$

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

${\displaystyle a={\frac {v^{2}}{r}}.}$

This results in equation with the previous equation

${\displaystyle v^{2}={\sqrt {G\,m_{\mathrm {G} }\,a_{0}}}\qquad \mathrm {bzw.} \qquad v={\sqrt[{4}]{G\,m_{\mathrm {G} }\,a_{0}}}.}$

From this it follows that the speed of rotation at a large distance from the center of gravity, i.e. when there is very little acceleration due to gravity, is a system constant that only depends on the mass at the center of gravity.

Tensor-vector-scalar gravitation theory

A relativistic formulation of MOND was proposed by Jacob Bekenstein in 2004 . It is called tensor vector scalar gravitation theory.

Verification of the theory through observation

→ Main article : 1E 0657-558

The cluster merger 1E 0657-558 offers the possibility to test alternative theories. These are two galaxy clusters that have penetrated each other, with the galaxies moving largely without collision, while the intergalactic gas of the two clusters interacted via shock waves and remained in the middle. On the one hand, the visible mass of the galaxies and the gas was measured in the optical spectral range or in X-ray light. The galaxy to gas mass ratio is between 2:15 and 3:15, i.e. H. the gas predominates. On the other hand, the gravitational potential determined by the deflection of the light showed that the mass predominates in the galaxies. This is compatible with the version of the cosmological standard model , in which dark matter occurs in the form of heavy, non- baryonic particles, while the MOON hypothesis had predicted the center of light deflection in gas.

literature

• Mordehai Milgrom: Does Dark Matter Really Exist? Scientific American 8/2002; German speaking: Is there such a thing as dark matter? In: Spectrum of Science , No. 10/2002, p. 34.
• Anthony Aguirre: “Moon” is controversial, but by no means absurd . In: Spectrum of Science , No. 10/2002, p. 39.

Web links

• New doubts about dark matter. In: World of Physics. September 30, 2009, accessed October 1, 2009 (for Nature publication). 
• Theory of gravity. New discussion about the existence of dark matter . Spiegel Online , October 1, 2009.
• The MOON pages
• Another success for alternative to dark matter. In: World of Physics. Retrieved October 5, 2012 . 
• Dark Matter: a Debate , 3sat .online, November 25, 2010 ( Simon White and Pavel Kroupa in an interview with Ottmar Gendera).

Individual evidence

1. ↑ Mordehai Milgrom: Dynamics with a non-standard inertia-acceleration relation: an alternative to dark matter . In: Ann.Phys. , 229, 1994, pp. 384-415, doi: 10.1006 / aphy.1994.1012 ( arxiv : astro-ph / 9303012 ).
2. ↑ Benoit Famaey, Stacy McGaugh: Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions . In: Living Reviews in Relativity , 15, 2012, p. 10, doi: 10.12942 / lrr-2012-10 ( arxiv : 1112.3960v2 ).
3. ↑ Study throws standard cosmological theory into crisis . Press release of the Univ. Bonn, May 5, 2009.
4. ↑ Natalie Wolchover: The beginning of the end of dark matter . February 2017. Accessed February 2017. Spektrum.de
5. ^ Jacob D. Bekenstein: The modified Newtonian dynamics - MOND - and its implications for new physics . In: Contemporary Physics , 47, 2006, p. 387, doi: 10.1080 / 00107510701244055 ( arxiv : astro-ph / 0701848 ).
6. ^ Douglas Clowe et al .: A Direct Empirical Proof of the Existence of Dark Matter . In: Astrophys. J. , 648, 2006, pp. L109-L113, doi: 10.1086 / 508162 ( arxiv : astro-ph / 0608407 ).