What If Our Understanding of Gravity Is Wrong? (Script) (Patreon)

What if there is no such thing as dark matter.What if our understanding of gravity is just wrong? New work is taking another shot at that Einstein guy. Let’s see if we’ve finally scored a hit.

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We’ve now been searching for dark matter for over half a century. In the early 60s, Vera Rubin proved that the spiral galaxies are rotating so fast that they should fling themselves apart - assuming they are held together by the gravity of their visible mass alone. They would need at least 5 times as much matter to provide the gravity needed to hold galaxies together. And the gravity of visible matter is also way too weak to hold galaxy clusters together, or to bend the path of light to the degree seen in gravitational lenses - when more distant light sources are warped by an intervening mass.

It sure looks like 80% of the mass in the universe is completely invisible to us. 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.

But what if we’ve been thinking about this the wrong way all the time? The expected rotation rates of galaxies come from applying our laws of gravity based on the observed mass. So … the mass could be wrong. Or the laws of gravity could be wrong. After all, if your scientific theory doesn’t fit observations we should reject our theory, right?

And for nearly as long as astronomers have been hunting for dark matter, others have been hunting for an alteration to our theory of gravity that can explain the effect of dark matter without the actual matter.  Today, we’re going to look into that long history - what has worked and what has utterly failed - and finally at a new proposal that purports to fix those failures once and for all.

According to Isaac Newton’s Law of Universal Gravitation, the gravitational field drops off with the square of distance from the mass producing that gravity. In most galaxies, stars are somewhat concentrated towards the centers, which means gravity should weaken towards the outskirts. That means the orbital velocities of stars out there should be lower in order to keep them in orbit. The so-called rotation curve should drop - orbital speed should diminish with distance from 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.

But what if gravity doesn’t obey Newton’s law of gravity? Well, we actually know that it doesn’t. Albert Einstein found that Newtonian gravity breaks down when the gravitational field gets too strong - there you need his general theory of relativity, which explains gravity as the curvature in the fabric of space and time rather than a classical force. But Einsteinian gravity looks exactly like Newtonian gravity when gravitational fields get weak. But what if Einstein missed something? What if Newtonian gravity breaks down both for very strong AND very weak fields?

This is the idea behind Modified Newtonian Dynamics, or MOND, proposed by Israeli physicist Mordehai Milgrom in 1982. The idea is straightforward enough - what if there exists a minimum possible acceleration that can be produced by the gravitational force? In MOND, force or acceleration drop off with distance squared until, at very low values it starts to plateau out. 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.

If you tune the modification right you recover the observed rotation curves for spiral galaxies very nicely without the need for extra mass. 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

1. It needs to give the right answer in more than one special case. So MOND would need to do away with the need for physical dark matter in the other places we see evidence for dark matter.
2. It needs to be consistent with the other known laws and theories that are experimentally verified.
3. It needs to make testable predictions beyond the phenomena that it was tuned for.

Let’s take these one by one.

First, how does MOND do with respect to the other evidence for dark matter? Not … great actually. 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 requirement to explain all the gravity we see in clusters.

Now you might think that cutting down the invisible mass requirement by 80% is pretty good - and it is helpful to be honest. But the fact that you still need some type of physical dark matter in clusters is seen as a strong point against MOND in its first incarnation at least.

There are some other pieces of evidence for dark matter that O-G MOND also fails for, but I’ll come back to those.

For now Point 2. Is MOND consistent with the rest of physics? No - it’s totally broken. It doesn’t respect conservation of energy or momentum or angular momentum. And it’s not consistent with general relativity - in that general relativity does not reproduce MOND in what we call the “weak field limit”. Instead it does what it was designed to do - it reproduces good ol’ Newtonian gravity.

It’s not looking good for MOND. But let’s address point 3 anyway. Does MOND make any predictions beyond the observations that inspired it? This is actually where we can turn this around. Spiral galaxies all follow this tight relationship between their speed of rotation and their luminosity - the brighter they are the faster they spin. This is the Tully-Fisher relation. It’s a little surprising that the Tully-Fisher is such a tight relationship because the rotation velocity depends on the dark matter halo while the luminosity depends on the stars. Now those two are connected, but some believe that their connection shouldn’t be so perfect to give the extremely tight Tully-Fisher law. On the other hand, if you tune MOND to get the flat rotation curves of spiral galaxies, you automatically get the correct relationship between rotation speed and luminosity.

That was a completely unexpected, un-engineered outcome of MOND. So, while the Tully-Fisher relation was already known, we can sort of count it as a prediction of MOND.

And this one success has been enough to inspire others to dig deeper into the idea over the years. 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. What on earth does that mean, you ask? Fortunately we just did an episode on the awesome power of the Lagrangian. There we saw that the principle of least action allows equations of motion to be extracted in a way that automatically obeys all of our conservation laws.

Bekenstein and Milgrom achieved this by adding a second field to gravity. 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. And it did not. AQuaL also had the unfortunate prediction of faster-than-light waves in this added scalar field, which broke causality.

Not to be deterred, Bekenstein came back over 20 years later with an update. If adding one field doesn’t work, why not add another? In 2005 Bekenstein introduced TeVeS, for Tensor Vector Scalar gravity - based on the fact that it describes gravity with three fields - a tensor, a vector, and a scalar. The introduction of the new field fixed the problem with gravitational lensing and also tamed the awkward causality-breaking nature of AQuaL. 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 TeVeS and other MOND proposals produce instabilities in the presence of matter, which would, for example, make long-lived stars impossible.

But the main problem with TeVeS is cosmological nature. One of the most important pieces of evidence for dark matter as a particle is seen in the light we see from the extremely early universe. The cosmic microwave background radiation reveals a lumpiness that tells us how matter pulled itself together under its own gravity and it’s earliest time. Back then, light and matter were locked together due to the extreme densities. Regular matter was kept from collapsing into any structures by the pressure of the intense radiation of that era. But dark matter doesn’t interact with light, so it would have been able to collapse just fine. And after the universe had expanded and cooled enough for regular matter to be released from the clutch of light, it could have followed the dark matter into its deep gravitational wells and get to the business of forming galaxies. But if dark matter isn’t real, and regular matter controls gravity completely, then no structure should have been able to form at those early times. For this reasons, most forms of MOND - including TeVeS, come up short.

And this is where the new guys come in. In 2020 Constantinos Skordis and Tom Złosnik proposed a new relativistic version of MOND, and just last month their paper passed peer review. 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”. It was able to clump in the right way to kickstart cluster formation. But then later its behavior shifted so that it behaves more like Bekenstein’s TeVeS proposal. More work is needed to see if the newly-dubbled RelMOND - relativistic MOND - works for galaxy clusters and keeps stars from exploding - but the authors are optimistic.

OK, so, problem solved. We don’t need dark matter, anymore? Not so fast. Modified gravity theories still can’t explain the Bullet Cluster - and I don’t have time to get into that and we’ve covered it before. So I’ll just say that when galaxy clusters collide and the dark matter gets ripped away from the light matter - it makes you doubt that dark matter is just light matter acting funny. Of course there are MOND proposals which claim to address this, but the Bullet Cluster might be the most awkward result for modified gravity folks.

At this point the two theories are in a bloody theoretical knife fight, where the knife is Occam’s razor. Proponents of dark-matter-as-particle say that MOND proposals are now so elaborate and fine-tuned that we can’t take them seriously. But MOND proponents say that it’s the behavior of dark matter particles that have to be carefully fine-tuned to produce the phenomena that MOND predicts naturally - like the flatness of rotation curves and the Tully-Fisher law. Who’s right? Well the majority of experts are pretty firmly in the dark-matter-as-particle camp. Although our experiments haven’t detected the dark matter particle yet, there are still plenty of possibilities for what it might be beyond our standard model of particle physics. And we’ve been through those before. But Bekenstein was no slouch, nor are many of the others who have supported MOND theories. We can’t dismiss them out of hand.

I personally withhold my judgement - because it’s OK to be uncertain, and because it’ll be equally exciting whichever way this gets resolved. One way or another we opened paths to continue our exploration of reality, whether we’re led beyond the standard model by dark matter particles, or beyond general relativity by hidden gravitational modes of space time.