Is our understanding of gravity wrong: We’ve now been searching for dark matter for over half a century. We’ve dubbed this hypothetical stuff dark matter, and of course, we’ve talked about dark matter many times on this channel – from the evidence for its existence to some of the speculative ideas of what it might be made of – from exotic particles to black holes.
The so-called rotation curve should drop – orbital speed should diminish with distance from the center. Dark matter is supposed to add extra mass that’s more evenly distributed through galaxies, strengthening the gravitational field in the outskirts to explain the high rotation speeds. Dark matter flattens rotation curves.
The idea is straightforward enough – what if there exists a minimum possible acceleration that can be produced by the gravitational force?
This can be done with a modification to either Newton’s law of universal gravitation – in which case gravity has a minimum strength – or by a modification to Newton’s 3rd law of motion, in which case the acceleration produced by a force has a minimum strength.
And you only need to tune a single parameter – which is effectively the minimum acceleration
– to get the correct rotation curves for nearly all galaxies. That’s very promising, but in order to be taken seriously, a new hypothesis like MOND needs to do a few things. So MOND would need to do away with the need for physical dark matter in the other places we see evidence for dark matter.
If you tune MOND to work for galaxies and then apply it to galaxy clusters, you do get rid of the need for some of the dark matter but not all of it. You still need about 20% of the current dark matter required to explain all the gravity we see in clusters. There are some other pieces of evidence for dark matter that O-G MOND also fails for, but I’ll come back to those.
Is MOND consistent with the rest of physics?
“MOND in what we call the “weak field limit.
And it’s not consistent with general relativity – in that general relativity does not reproduce
It’s not looking good for MOND.
Does MOND make any predictions beyond the observations that inspired it?
It’s a little surprising that the Tully-Fisher Law is such a tight relationship because the rotation velocity depends on the dark matter halo while the luminosity depends on the stars. That was a completely unexpected and un-engineered outcome of MOND. So, while the Tully-Fisher Law was already known, we can sort of count it as a prediction of MOND. The next critical step was to get a version of MOND that didn’t contradict so much of the rest of physics.
For that Jacob Bekenstein came to the rescue. You may remember Bekenstein from such hit ideas as the Bekenstein bound, which connects black hole information content to entropy, as well as other black-hole-related awesomeness. In 1984 he diverted his attention for a moment to work with Mordehai Milgrom in fixing MOND. The first step was to reformulate MOND using Lagrangian mechanics.
In Einstein’s description, the gravitational field is what we call a tensor field – a multi-component object that describes the curvature of spacetime. These guys added a new scalar field – a field that’s just a single numerical value everywhere in space. “And it was a good start – the resulting “AQuaL – for “a quadratic Lagrangian” gave the same results as MOND, except that conservation laws were obeyed, and because this was a relativistic theory it was possible to see if it gave the right result for the bending of light by galaxies, which wasn’t even possible with the original MOND. Not to be deterred, Bekenstein came back over 20 years later with an update.
It acted like Newtonian mechanics on solar system scales, like MOND on galactic scales, and like regular general relativity for gravitational lensing.
It was not without problems though – for example, the physicist Michael Seifert claimed that
One of the most important pieces of evidence for dark matter as a particle is seen in the light that comes from the very early universe. The cosmic microwave background radiation reveals a lumpiness that tells us how matter pulled itself together under its own gravity at the earliest times. Their big change was that they allowed the scalar field to change its behavior over time. They managed to tweak their equations so that in the early universe, that field behaved a bit like a type of matter, which Złosnik calls “dark dust”.
Of course, there are MOND proposals that claim to address this, but the Bullet Cluster might be the most awkward result for modified gravity folks.
Who’s right?
Although our experiments haven’t detected dark matter yet, there are still plenty of possibilities for what it might be beyond our standard model of particle physics.
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