Thank you to CuriosityStream for supporting PBS! What if there is no such thing as dark matter.  What if our understandingÂ
of gravity is just wrong? New work is taking anotherÂ
shot at that Einstein guy. Let’s see if we’ve finally scored a hit. 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 - assumingÂ
they are held together by the gravity of their visible mass alone. They would need at least 5 times as muchÂ
matter to provide the gravity needed to hold these 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 comeÂ
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 UniversalÂ
Gravitation, the gravitational field drops off with the square of distance fromÂ
the mass producing that gravity. In most galaxies, stars are somewhat concentratedÂ
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 - orbitalÂ
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 gravityÂ
breaks down when the gravitational field gets too strong - there you need his general theoryÂ
of relativity, which explains gravity as the curvature in the fabric of space and timeÂ
rather than just as 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 downÂ
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 they start to plateau out. This can be done with a modification to eitherÂ
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 recoverÂ
the observed rotation curves for spiral galaxies very nicely without the need for extra mass. And you only need to tune a single parameter -Â
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. One:
it needs to give the right answer in more than one special case. So MOND would need to do away with the needÂ
for physical dark matter in the other places we see evidence for dark matter. Two: it needs to be consistent with  the other known laws and theoriesÂ
of physics that are experimentally verified. And three: it needs to make testable predictionsÂ
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 relativityÂ
- 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 beyondÂ
the observations that inspired it? This is actually where we can turn this around. Spiral galaxies all follow this tight relationshipÂ
between their speed of rotation and their luminosity - the brighter they are the faster
they spin. This is the Tully-Fisher Law. It’s a little surprising that the Tully-Fisher LawÂ
is such a tight relationship because the rotation velocity depends on the dark matter haloÂ
while the luminosity depends on the stars. Now those two are connected, but some believeÂ
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 relationshipÂ
between rotation speed and luminosity. That was a completely unexpectedÂ
and un-engineered outcome of MOND. So, while the Tully-Fisher Law was alreadyÂ
known, we can sort of count it as a prediction of MOND. And this one success has been enough to inspireÂ
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 hitÂ
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 momentÂ
to work with Mordehai Milgrom in fixing MOND. The first step was to reformulateÂ
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 actionÂ
allows equations of motion to be extracted in a way that automatically obeys all of our
conservation laws. And done the right way the result can also
work with relativity. Bekenstein and Milgrom achieved thisÂ
by adding a second field to gravity. In Einstein’s description, the gravitational field is what we call a tensorÂ
field - a multi-component object that describes the curvature of spacetime. These guys added a new scalar field - a fieldÂ
that’s just a single numerical value everywhere in space. And it was a good start - the resultingÂ
“AQuaL - for “a quadratic Lagrangian” gave the same results as MOND, except thatÂ
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 cameÂ
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 TensorÂ
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 awkwardÂ
causality-breaking nature of AQuaL. It acted like Newtonian mechanics on solar
system scales, like MOND on galactic scales, and like regular general relativityÂ
for gravitational lensing. It was not without problems though - for exampleÂ
the physicist Michael Seifert claimed that TeVeS and other MOND proposals produceÂ
instabilities in the presence of matter,  which would, for example, make long-lived stars impossible. But the main problem with TeVeSÂ
is cosmological in nature. One of the most important pieces of evidenceÂ
for dark matter as a particle is seen in the light that comes from the very early universe. The cosmic microwave background radiationÂ
reveals a lumpiness that tells us how matter pulled itself together under itsÂ
own gravity at the earliest times. Back then, light and matter were lockedÂ
together due to the extreme densities. Regular matter was kept from collapsing intoÂ
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 cooledÂ
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 reason, most forms of MONDÂ
- including TeVeS, come up short. And this is where the new guys come in. In 2020 Constantinos Skordis and Tom ZĹ‚osnikÂ
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 thatÂ
in the early universe, that field behaved a bit like a type of matter, which ZĹ‚osnik
calls “dark dust”. It was able to clump in the rightÂ
way to kickstart cluster formation. But then later its behavior shifted so thatÂ
it now behaves more like Bekenstein’s TeVeS proposal. More work is needed to see if the newly-dubbledÂ
RelMOND - relativistic MOND - works for galaxy clusters and keeps stars from explodingÂ
- 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 claimÂ
to address this, but the Bullet Cluster might be the most awkward resultÂ
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 ofÂ
dark matter particles that have to be carefully fine-tuned to produce the phenomena that MONDÂ
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’tÂ
detected dark matter 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 ofÂ
the others who have supported MOND theories. We can’t dismiss them out of hand. I personally withhold my judgement - becauseÂ
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 continueÂ
our exploration of reality, whether we’re led beyond the standard model by dark matterÂ
particles, or beyond general relativity by hidden gravitational modes of space time. A big thank you to CuriosityStream for supporting
PBS! CuriosityStream is SmartTV for your SmartTV. The subscription streaming service offers
documentaries and non¬fiction titles from various filmmakers, with topics including
History, Nature, Science, Food, Technology, Travel, and more. For instance, CuriosityStream has Black Holes:
Messages from The Edge of Space, which examines not only black holes, but neutrino astronomy. It takes a deep dive into the science of blackÂ
holes and takes you into the Antarctic lab where astrophysicists detected neutrinos in
the ice of the South Pole. There are also collections of curated programs
selected by experts. For more information, go toÂ
curiositystream.com/PBSSPACETIMEÂ and use the code SPACETIME for a trial. Before we get to comments, we want to tell
you about PBS’s new medical show called Vitals. It’s always been important to stay healthy. But it’s gotten harder to tell what medical
information is based in science and what is unhelpful pseudoscience. Fortunately, Vitals, PBS’s brand new health
and wellness show, is here to help. Co-hosts Dr. Alok Patel and nurse Sheena WilliamsÂ
will bust medical myths, explore the latest science and answer all your burning health
questions in every episode. Check out Vitals in the link in the description,
and tell them that Space Time sent you! Our last episode was all about the principleÂ
of least action, and how this one simple idea sort of leads to all of physics. Let’s see what you had to say. J Smith asks, if the configuration  space Lagrangian seems to bridgeÂ
quantum mechanics and relativity, what's missing to make thisÂ
a theory of everything? Rather than answer this myself, I willl read
the reply by Fernando, the co-writer of that episode. In simple terms, the universe at its very
core seems to be a set of symmetries which are manifest in the Lagrangian. This means that if we knew all the symmetriesÂ
the universe follows we could describe it perfectly, but we don't know all the symmetriesÂ
and we are not sure how those symmetries fit with each other. Well put, Fernando. It’s the symmetries of the Lagrangian via
Noether’s theorem that yields our conservation laws and ultimately, well, all of physics. Check our episodes on Noether’s theorem,
quantum invariance, and the electroweak force for some details, but we probably need to
go even deeper. Jackie Johnson asks - in the case of gravitationalÂ
lensing, isn't the light still traveling in a straight line? Isn’t it spacetime that bends, not light? That’s a valid way to think of it. Light does travel a straight line if you look
at an infinitesimally small patch of space. Imagine light traveling through curved space
as like an and walking across a disco ball. The ant’s path around a disco ball looksÂ
curved, even if it travels in perfectly straight lines across each mirror. Well, in space the disco ball mirrors are
infinitesimally small, but over those regions the path is straight. A few people pointed out an error - I said
that the action reduces to an integral over proper time in general relativity. That was right - but I then went on to call
this a “principle of least proper time” by analogy to the principle of least action. In fact, in general relativity objects in
gravitational fields tend to maximize, not minimize their proper time. That’s still consistent with the whole action
thing because the proper name is the principle of stationary action - and the maximum is
also a stationary point - of proper time and of the action. But I was still misleading. Thanks for correcting me on that. Many of you point out that you’re already
adherents of the principle of least action. As in you take the fastest, easiest, or laziest
path to any outcome. Me too! Like, for example, when I come up with a joke
to end the comment section  …
/u/cptnpiccard , I've noticed you haven't posted these on your usual lightning quick manner. Everything good on your end?
I really enjoyed that. Thank you!