Look at this picture:
It looks as if dark matter is observed. But what is actually observed? doesn't this picture prove MOND and emergent gravity (both assuming a different gravity tied to normal, non-dark matter only) wrong?
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The purple is a "weak lensing" map. To quote from the original authors:
Weak gravitational lensing is a method which can be used to measure the surface mass in a region by utilizing the fact that the path of a light bundle passing a gravitational potential will be bent by the potential. As a result, images of background galaxies which are near a massive structure, such as a cluster of galaxies, are deflected away from the structure, enlarged while preserving the surface brightness, and distorted such that they are stretched tangentially to the center of the potential. This third effect, known as gravitational shear (γ), causes the background galaxies’ ellipticities to deviate from an isotropic distribution, and the magnitude and direction of these deviations is used to measure the mass of the structure(s) causing the lensing.
So, cluster has a lot of mass. Background galaxies (those that are coincidentally behind the cluster) have their images distorted. If there was no mass, then the shapes of the galaxies would be "isotropic" one region would look the same as another. But the mass causes these to be distorted in particular directions and so presents a way to map the amount of mass. The map is created to fit the observations of the distortions of background galaxies, and this is the best fit.
Notably and significantly for dark matter is the fact that the collision of the bullet cluster has caused the visible matter to partially separate from the dark matter. So we see background galaxies being distorted by what looks like empty space! This is why it is considered good evidence for the reality of dark matter as a "thing" and not as a modification of gravity.
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$\begingroup$ Then what's the big deal with MOND still? Or is there no "still"? $\endgroup$ Commented Jun 7, 2021 at 0:59
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2$\begingroup$ @Barbierium: I'd assume that people working on MOND theories aren't going to totally give up on them just because some experimental evidence appears to support the existence of dark matter. Dark matter still hasn't been conclusively proven. (And it's not impossible that both DM and MOND are real. Although I think most physicists don't really expect that MOND will turn out to be real, i.e. most think general relativity does describe reality even over large scales. I don't really follow the field, though, but that's what I recall from a New Scientist interview with someone working on it.) $\endgroup$ Commented Jun 7, 2021 at 4:48
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2$\begingroup$ To be more precise: most (but not all) of the visible matter is hot gas, and this is indeed separated from the dark matter. Some of the visible mass is stars (in the galaxies), which behaves more or less like the dark matter does. So it not really “empty space” where the background galaxies are being distorted; there are cluster galaxies there. (But, of course, they don’t have nearly enough mass by themselves to explain the distortions of the background galaxies…) $\endgroup$ Commented Jun 7, 2021 at 10:25
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$\begingroup$ @Barbierium Some MOND theories can actually explain the Bullet Cluster. It takes some fiddling, but gravitational force can be decoupled from mass by adding extra fields (though it can be argued that this formulation is simply a reformulation of the Dark Matter hypothesis). The CMB Power Spectrum and Large-scale structure considerations (among others) pretty much rule-out MOND though. $\endgroup$– user0Commented Jun 7, 2021 at 15:54