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In the 1800s, detailed observations of the planet Mercury showed that its orbit was slightly different than Newtonian mechanics predicted-- a difference of about 43 arcseconds per century. The study was rigorous enough to rule out any observation errors.
Le Verrier, the astronomer who made these observations, wondered how to explain the difference. A decade earlier, he had noticed a similar irregularity in the orbit of Uranus, which led to the discovery of Neptune, whose gravity caused these perturbations. So Le Verrier reasoned that something similar must be going on for Mercury, and he posited the existence of Vulcan, a tiny planet close to the Sun.
Many attempts were made for decades to observe Vulcan. It was even included on some maps of the Solar System at the time (https://www.loc.gov/resource/g3180.ct003790). But it was never conclusively observed.
When Einstein published his theory of relativity in 1915, the mystery of Mercury's orbit was finally explained-- Newtonian mechanics were simply incomplete, and the irregularity of Mercury's orbit was due to relativistic effects.
Could it be that something similar is happening today? Observations of gravity on galactic scales doesn't quite align with what relativity would predict, so we use dark matter to fill the gaps. We've tried for decades to detect dark matter, with no dice. Is our theory of gravity simply incomplete?
MOND may not be the solution, but I'm still skeptical about dark matter.
As new papers come out the needle goes back and forth, and I guess that she will make a new video if she hasn't already, with the needle moving one step towards dark matter.
I find it interesting how it doesn't seem to settle. Dark matter is still the favorite, but there is a lot of back and forth between "MOND is dead" and "we found new stuff we couldn't explain with dark matter, but it matches MOND predictions".
Galaxies are typically so far away from another they're almost like point sources to each other, hence Newtonian gravity explains their motion very well.
However, inside galaxies things do not behave as expected, as stars in almost all the galaxies we've measured does not move like Newtonian (nor GR) behaves based on the matter in the galaxy we see. One alternative to the mainstream theories of dark matter is to modify Newtonian gravity, called MOND.
This work tested if MOND fit the motion of galaxies in galaxy clusters. They found it did not.
MOND already does not explain other phenomena that dark matter can so it's not terribly surprising. Here[1] is a nice accessible talk going through all the evidence for dark matter.
But it is technically a possibility that there's two things are going on, something MOND-like as well as dark matter, so worth checking.
[1]: https://pirsa.org/26030070
There are ways of adapting MOND to match general relativity, should it turn to be correct at explaining what it is supposed to explain (like the movement of galaxies).
The test here is for the inverse square law of gravity. The rival theory in this case isn't GR, but MOND: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics