Prof. Peter Gerwinski, PhD Bochum University of Applied Sciences What is dark matter? May 16, 2024
First of all, thanks to my colleague Mrs. Feldmüller for this introduction.
Before I start, does our technical equipment work? Can you hear me clearly?
Over the speakers and online, too?
At least we have tested everything extensively, so everything should work.
As was already said, I am Peter Gerwinski, professor for low-level IT systems at this university.
Some students know me already from my courses in Computer Technology.
Later I will teach them Low-Level Programming, Algorithms and Data Structures, Embedded Systems, and Databases and Data Security. These are my subjects here.
In fact, however, I am a physicist. "Dr. rer. nat." means "doctor rerum naturalium", doctor of natural sciences.
I studied physics and made my PhD about Quantum Chaos.
Now I am presenting a subject from astronomy, so you might ask how this is related to quantum physics.
So I am sticking my neck far out and speak about things I do not … things I did not study.
As we will see later, dark matter is related to quantum physics to an amazing degree.
The first thing I will address today: What is the mystery? What is the problem?
After that we will address solutions to this problem, or more precise, suggestions for solutions.
This is one of today's unsolved problems in physics, in astro-physics. Nobody knows what dark matter is.
One mystery of particular interest is pictured here. This is the so-called Bullet Cluster.
As I said, this is a mystery of particular interest. I will say some words about this later.
In fact I found out something new myself.
To say it outright: I claim that I know what dark matter is.
During the last months I have been working on this in my scarce free time.
I started some serious work on this in 2021.
I had just a small idea I wanted to try out. I tried it out, and it worked.
Today I am presenting this in public for the first time.
And then … let's see how to proceed from there.
But first, what is the mystery? What is the problem?
Why is it called “dark matter”?
“Dark” in outer space means: We cannot see it.
Outer space is black. When something does not give light in black outer space, we cannot see it.
“To see” does not only refer to optics, what we can see using our eyes and telescopes,
but also IR, UV, radar, radio, gamma rays, … that does not matter.
We cannot see that dark matter with any telescope.
Okay, so it does not exist. How do we know that there is something?
Dark matter produces gravity. We know there is something in outer space which produces gravity,
but we cannot detect it using any of our telescopes, not even using X-rays or radio waves.
I will now present three methods how to detect, using gravity, that something must be there.
We start in historical order with the virial theorem by which all this was discovered in the first place.
Rotation curves were the key to clarifying that this is real and not just imagined by someone.
Currently we are using so-called gravitational lenses to examine dark matter.
There is more. I just picked out the three most important items.
Let's start with the virial theorem.
This phenomenon can be summarised as: Galaxies are moving too fast.
What does “too fast” mean?
In 1933, Fritz Zwicky, a Swiss astronomer, pictured here,
applied a method which was new at that time to investigate the Coma Cluster of galaxies.
This method is well-established in our time. We are looking at the redshift of galaxies.
The light is redshifted when something is departing from us; it is blueshifted when something is approaching us.
Using this, he investigated how fast these galaxies are.
He found a number way too high, couldn't believe in it first, but then recalculated everything and found out:
Either these galaxies do not form a cluster but are at the same place just by chance.
Or there must be at least 400 times as much mass as can be seen.
Here we see a lot of galaxies. Each of these points is not just a star, but a whole galaxy.
When we count all stars in the galaxies, their combined mass is just 1/400 of what would be needed to keep the cluster together.
He also considered that the galaxies do not form a cluster, but are at the same place just by chance.
Here the famous astronomically large coincidence comes into play.
The probability that these galaxies are at the same place just by chance is 1 in several trillions, quintillions, whatever.
This cannot be. There must be something we cannot see.
Back then, his method was new, so it was said: Maybe he found something, maybe he didn't.
Maybe he simply got something wrong. Not many thoughts were given to this, back then.
This changed in the 1970s.
In 1970, astronomer Vera Rubin investigated single stars in the Andromeda Galaxy.
This picture does not depict the Andromeda Galaxy, but just a generical one.
She investigated how the stars move in the galaxy. Galaxies rotate.
What are the stars doing? I am going to show this in a small animation. Let me switch …
Like this … we just practised this …
Just a moment … one step back …
Okay. That's it.
Here we see a rotating galaxy.
We see the stars. From the brightness we can estimate how much mass is there, how heavy the stars are.
When they are brighter, they are heavier, simply because they are more.
Now we can calculate how fast the stars may rotate, assuming Newton's laws.
We get fast rotation close to the centre and slow rotation in the outskirts.
Vera Rubin measured fast rotation close to the centre, and in the outskirts – the same speed.
This was rather puzzling. The stars move as if there was something in the galaxy much heavier than the other stars.
There must be something additional. This established the concept of “dark matter”.
There is something in the galaxies which causes the stars to move faster than Newton's laws allow.
I am now switching back to the transparencies.
So as of 1970 we know that there must be much more in the galaxy than the visible stars.
Now we switch to our time, where we have space telescopes such as Hubble.
This picture has been combined from Hubble images and images from the Earth-based Magellan telescopes.
This is state of the art. That's the kind of pictures we can create today.
Here we see the cluster of galaxies “Abell 1689”. I hope that my pronunciation is not too wrong.
Probably something like “able 1689”.
This galaxy cluster consists, of course, of galaxies, which in turn consist of stars.
Now we can do what Zwicky did in 1933.
We look how bright these stars are. Then we can calculate their mass.
That's not really precise, but we can estimate that the stars we see here have 4.7·10¹² times the mass of our Sun.
That's 4.7 trillons, or 4.7 million millions, a 1 with 12 zeroes. So many suns are these.
That's a lot. That's not peanuts.
In fact what we can see in visible light is just a small fraction of what can be seen altogether.
This is an X-ray image of the same galaxy cluster. We see some diffuse structure. What is that?
This is intergalactical gas, a gas cloud which does not only fill the space within the galaxies, but the space between the galaxies. Incredibly large.
Its size is several 100 kiloparsec, hundreds of thousands or millions of light years, one big gas cloud.
It is not very dense. On Earth, we would consider this cloud a vacuum. There is nothing.
In outer space, however, this is a gas cloud. Now we can calculate from the brightness how much gas there is.
We find out that it is almost ten times as heavy as the stars are.
The visible stars comprise not much more than one tenth of the total mass.
Almost 90% of the total mass belongs to this gas cloud.
So this whole thing is much heavier than what we can assume considering the stars it contains.
But there is more, yet another method how to put this thing on a balance, the gravitational lensing effect.
I am magnifying this image a little.
When we look at this magnified image, we see some round structures.
Here … and there … round streaks …
This looks as if someone had put down a cup on this. Something is round here.
These are distorted galaxies, the so-called gravitational lensing effect. I am zooming in.
This weird streak is a galaxy located behind the galaxy cluster.
The galaxy cluster bends the light around itself because it is so heavy.
Like through a lens the light takes a way around the cluster, causing these weird streaks.
Now astronomers can calculate how heavy the lens must be.
How heavy must the stuff in the centre be, the stars and the gas, to create precisely this streak?
Here we see the distribution of gravity. This blue glow shows where the biggest mass is.
That fits well. Here are the stars and the gas. Then let's have a look how much it is.
That's again more than ten times as much mass as we already have in the shape of stars and gas.
Whatever there is, 90% of it we cannot see. What we can see, stars and gas, comprises not even 10%.
Just a little more than 5%.
So the universe in this galaxy cluster consists of dark matter by 93.7%.
From the remaining parts, 5.6% are gas. The stars, 0.7%, do not really stand out.
The stars are the lightest thing here.
So we know: Something is there. Now we ask, of course: What is that?
This question has already been asked in the time of Zwicky.
I am now going to present the three most important answers to this.
What approaches are there to explain dark matter?
First, normal matter which just does not give light. Second, new elementary particles, previously unknown.
There is also the possibility that there is a new law of gravity.
These are the three most important approaches.
Let'start with normal matter which just does not give light. What could it be?
For instance a planet without a sun. When a planet does not get illuminated by a sun, we cannot see it.
Then it is dark. Dark matter.
Or, we have seen gas clouds using X-rays. They are emitting X-rays because they are hot.
But when the gas cloud is cold, it does not give light. Then it is just dark.
Then we would not see it, and it would be a candidate for dark matter.
Then there are more exotic object such as neutron stars, or, fully extreme, black holes.
I won't address in detail today what a black hole is. In any case it is black. We do not see it.
It can get visible indirectly by matter falling into the black hole heating up in an accretion disk.
But we cannot see the black hole itself, so it is another candidate for dark matter.
Okay, but now we have one problem with this. As we have seen, in the galaxy cluster there are 93% dark matter.
If all of this are planets without a sun, they would bustle about somewhere all the time.
They would fly through our telescopes all the time. Even if they do not give light, they would obscure something.
For instance if they pass by a star.
If they are just a few we can say: Okay, we didn't discover them yet.
However meanwhile we have very good telescopes such as the Hubble and James Webb space telescopes.
With this kind of instruments we would have detected something if there was anything.
But we did not find anything, so we are stuck with: There is nothing.
All of these candidates certainly exist. We even know a few of them.
However this is not suited to explain 93% of the total matter.
More than 10 times what we can see … We would have detected something.
This is not a good explanation.
These so-called Massive Astrophysical Compact Halo Objects, MACHOs for short, are no working explanation for dark matter.
Well, what else could it be?
This leads us to quantum physics.
What do we consist of? Of atoms.
What do atoms consist of? Of nuclei and electrons orbiting them.
What do atomic nuclei consist of? Of protons and neutrons.
What do protons and neutrons consist of? Of up quarks and down quarks. This means: We are here. That's us.
These are all existing particles, and all of them have been detected at the LHC and elsewhere.
Only a small part of them is visible matter. What about the others? Maybe that's dark matter.
There are, for instance, these candidates, the neutrinos.
They are extremely difficult to detect. They are invisible. This makes them good candidates for dark matter.
But they have some problems. They are very light. It is not even clear whether they have a mass at all.
Again: If they comprise 90% of total matter, they must be extremely many.
But they have yet another problem. They are so fast that they have traversed a galaxy cluster before noticing it.
They practically move at lightspeed all the time.
Because they are so fast, they cannot explain the rotational behaviour of galaxies.
So neutrinos cannot explain rotation curves.
What else could it be? All the other particles are unstable. They decay immediately.
Not the electrons, but all these particles.
These are interaction particles. Forces. They do not have anything to do with this.
What about the Higgs boson. It decays, too, but …
Maybe there are little brothers of the Higgs boson. There are some theories. So-called little Higgs particles.
They would be candidates.
Or there are big brothers of the neutrinos in yet another theory. To solve certain problems …
… one has thought out certain new ideas and, er … stop. Okay … now.
It might be possible to explain neutrino oscillations by assuming yet another kind of neutrinos.
They are heavy. They are even more difficult to detect then normal neutrinos. They might be dark matter.
We have searched for them. As of today, we found nothing.
We have searched for little Higgs particles. We found nothing.
Then there are axions as a theory.
One tries to explain certain properties of the gluons by introducing new particles, so-called axions.
We have searched for them. As of today, we found nothing.
But now comes supersymmetry. It solves all problems.
We try to unify general relativity with quantum field theory using a so-called supersymmetric theory.
It cancels the non-renormalisable divergences of gravity. Neat. A great theory.
Now we build the LHC and check it. We find: There is nothing.
One was absolutely sure that one would find any of these at the LHC.
But we didn't. There is nothing.
As of today there are no sterile neutrinos, no axions, no little Higgs particles, and no supersymmetric partners.
There is nothing.
Probably this is not dark matter.
Of course the jury is still out.
It might be that the next particle collider will find something.
But it is getting more and more unlikely that one of these theories is correct.
Probably each of these is a nice idea, but wrong, unfortunately.
So we still do not know what dark matter is.
There is yet another idea. Maybe this is not a new kind of matter, but a new law of nature.
To understand how a new law of nature can explain additional matter, I am now going a little far afield.
This has been done before in the 19th century.
In 1686, Newton established the law of universal gravitation.
Those who have attended our physics lectures should know this law.
The force is one mass times the other mass times the so-called gravitational constant, divided by the square of the radius, the distance between both masses.
A beautiful law. Newton discovered it in 1686.
In 19th century very smart people did calculations using this law, in particular Le Verrier.
He calculated very thorougly using Newton's law and investigated the orbit of Uranus around the Sun.
Back then, Uranus had been discovered quite recently. Its orbit was surveyed. How does Uranus orbit the Sun?
It was found: Sometimes it is somewhat too early on its orbit; sometimes it is too late.
It might be that there is yet another planet out there which tugs at Uranus.
Its gravity causes Uranus to behave somewhat wiredly.
Le Verrier calculated this very thoroughly.
In 1846 he made a prediction: Look at that place. There might be a new planet.
Gottfried Galle did that. He looked at that place.
Le Verrier said: There might be a new planet. And right beside it there was a new planet.
He found it within half an hour. An incredible triumphe for physics.
Just by calculating Le Verrier predicted: Look there. There is a new planet. Half an hour later the astronomer actually found it.
Yes, we have a new planet. We call it Neptun. Great.
Newton's laws are very good, and the people who can apply them are very good, too.
Let's do this again. The innermost planet, Mercury, behaves weirdly, too.
Sometimes it is early, sometimes late, and there is the so-called perihelion precession.
This looks like a circle. In fact it is an ellipse.
This ellipse slowly rotates around the sun. That's the so-called perihelion precession.
Based on the perihelion precession, Le Verrier calculated that there must be yet another planet, orbiting.
He was so sure about this that he already had a name for the new planet.
The new planet was even mapped on celestial maps already.
The planet Vulcan orbits the Sun closer than Mercury does. It is only a matter of time until we have found it.
One has been searching for it. For 50 years. One found nothing. There is nothing.
One found a few little rocks orbiting the Sun, but nothing which could explain the orbit of Mercury around the Sun.
What now? What is the reason for it? This was found by Einstein.
With his general relativity he established, in 1915, a new law of gravity.
It is almost the same as Newton's one.
Here I am showing the Scharzschild metric by approximation, showing what changes.
This r² becomes r times r minus rₛ.
Instead of taking the square of the distance between the Sun and Mercury, I take that distance and multiply it by itself minus rₛ.
This rₛ is 3 kilometres. On the distance between the Sun and Mercury.
The Earth is about 150 millions of kilometres away from the Sun. Adding 3 kilometres does not really matter.
However these 3 kilometres cause Mercury to behave just a little different from what Newton predicted.
This perfectly explains the orbit of Mercury. This explanation is valid until today.
We are checking this again and again, using better and better telescopes and better and better calculation methods.
Le Verrier used paper and pencil. Today these calculations are carried out by supercomputers.
We always find: It's correct. Mercury behaves exactly as calculated by Einstein in 1915.
So a new natural law explains a deviation in an orbit, we rather wanted to explain by a new mass, a new planet, bustling around somewhere.
In 1983, this gave Milgrom the idea: Maybe we can explain dark matter the same way?
Maybe there is a deviating law of gravity, too.
Not in the vicinity of the Sun, but far, far away, where we would not feel anything, normally.
Maybe something changes there.
I have written down his formula in a somewhat clumsy way to have the F on one side.
Normally we would multiply the µ to the other side. Then there is µ(a/a₀), where a is M·G/r², which is also left over on the right hand side.
When we assume this law of gravity which behaves a little different than Newton at far distances, …
Could this explain dark matter? Let's try out.
What do we need to test? The virial theorem.
We repeat Zwicky's calculations of 1933 for the Coma Cluster. Maybe that works out.
It does. Using modified gravity we can explain the behaviour of galaxy clusters, that the galaxies are flying about way too fast.
When gravity behaves differently at far distances, the cluster stays together. Then it fits.
So modified gravity explains the mystery of 1933.
Next mystery. The stars in the galaxies are rotating much faster then they are supposed to.
So there must be additional mass, or we have a modified law of gravity. Let's try it out.
Wow. We get an excellent result.
The explanation by modified gravity perfectly matches the observations, much better than dark matter does.
So he did it. Milgrom is right. Let's give him a Nobel prize. He's still alive. He succeeded to explain dark matter.
Now we jump to our time where we investigate galaxy clusters using the effect of gravitational lensing.
We find that it does not work at all. It is not just a little wrong, but totally wrong.
What is going totally wrong?
For one thing, the calculated gravity is way too strong.
We have seen that dark matter comprises about 93%. The remaining 7% are gas and stars.
Using modified gravity we do not get 93%, but something like 99% of dark matter.
Nice try, but overshot. It does not work.
But there is something else which does not work. That's why this theory is rated as refuted as of 2006.
The gravity is at the wrong place. What does that mean? This leads us to the so-called Bullet Cluster I mentioned initially.
Here we see the so-called Bullet Cluster, which translates to “Geschoßhaufen” or “Gewehrkugelhaufen” in German.
In fact these are two galaxy clusters which have collided some astronomically short time ago – 100 million years ago.
One is here, and the other one is over there.
This small cluster has fallen through the big one.
It came from the left, and the other one came from the right, and then they passed through each other.
What has this to do with dark matter? Let's have a look how heavy these clusters are.
By counting the stars in the galaxies like Zwicky did, we arrive at 3.8·10¹³ solar masses.
38 trillions, 38 millions of millions times our Sun. That many stars we see here.
Again there are gas clouds.
Something weird stands out. Here are stars, and the gas clouds are besides them.
There are stars, and the gas clouds are besides them again, and they have a weird shape. Why? What happened there?
Let's have a look at a small animation which shows what happened there.
Just a moment …
Here we see the galaxy clusters how they might have looked like before the collision. Now they are about to collide.
These dots are galaxies with stars. The gas clouds are depicted in pink.
The gas clouds drop behind the galaxies at the moment when they pass each other.
They decelerate each other.
I'm showing it again. The gas clouds do not pass each other “just like that”, but they decelerate each other and thus drop behind the galaxies.
The galaxies just move on, passing each other.
There is enough place between the stars. Even if two galaxies collide, they do not even notice. They pass each other as if there was nothing.
The gas clouds do notice it. They heat up each other. Then they emit X-rays. That's why we can see them.
They decelerate each other and drop behind the galaxies.
Here are the stars, and the gas cloud which was between them initially, has dropped behind them.
And the same here: Here are the stars, and the gas cloud has dropped behind them.
The galaxies collided 100 million years ago. The gas clouds have heated up and decelerated each other.
The galaxies did not even notice that there was something.
This also explains this shape.
This small galaxy cluster has passed the big one like a bullet from a shotgun.
This looks like the shock wave of a bullet in the air. This photo was taken using a special camera.
A bullet passes through the air at a supersonic speed, causing shock waves of this kind.
It looks the same as this other shock wave because it was formed the same way.
This small cloud passed the big one like a bullet passes the air.
That's why it is called “Bullet Cluster”.
Now what about dark matter?
We can study it using the effect of gravitational lensing.
In 2006, Clowe et al. – again I hope that I get the pronunciation right – published a groundbreaking work.
They examined where the dark matter is.
It is here, and it is there.
The dark matter, the biggest source of gravity, is located where the stars are, and it is not where the gas is.
We remember: The gas is much heavier than the stars are. Here it is a little less than 10 times as heavy.
The biggest visible mass is here, where the gas clouds are.
The biggest measured mass is here, close to the stars.
This clearly proves that modified gravity is wrong, because then the biggest gravity would have to be with the gas clouds.
Dark matter must exist. It moves together with the stars. It is collision-free, just like the stars.
This means, they pass each other without even noticing.
So as of 2006 it is clear that the theory of modified gravity has been refuted.
The theory of dark matter has been confirmed again, even though we still do not know what it is.
In 2007, Angus and McGough – again I hope that I am pronouncing them correctly – calculated the relative speed between both galaxy clusters.
They passed each other – at what speed?
We can read this off the shape of the shock wave, just like with a rifle bullet. There it works, too.
They calculated 4700 kilometres per second.
That's rather fast, even by astronomic measures. In fact it is too fast.
They cannot be that fast.
Someone must have accelerated them. We can calculate: How much matter is in the universe? Who tugs at whom?
Something must have accelerated them towards each other.
There is noone who could accelerate them that strongly.
Assuming the theory of dark matter, even if there is a lot of dark matter, they can gain at most 2900 km/s.
They are, however, significantly faster.
Assuming the theory of modified gravity, gravity is different. At large distances it is stronger than one would otherwise assume.
This explains that they have been accelerated towards each other over large distances.
Then we can calculate thet they could have gained a relative speed of up to 4800 km/s.
So the Bullet Cluster proves clearly that the theory of dark matter is wrong. There is no dark matter.
It clearly proves that there is modified gravity. That's the only way to explain the Bullet Cluster.
That's the current state of research. To summarise it to a signle word:
Huh? We simply don't know.
The Bullet Cluster proves that dark matter exists and that modified gravity is wrong.
And the very same Bullet Cluster also proves the opposite.
As of today, astrophysicists are at a loss. We have no idea what dark matter is, whether it exists at all, …
or whether there is modified gravity instead. However both has in fact been refuted. We do not know anything.
That's common in science, and that's what makes it interesting. There are actual unsolved mysteries.
It is not that someone knows the solution and did not tell us yet, but the solution is actually unknown.
Now here I could say: This is my answer to the question: What is dark matter? Nobody knows.
But then something strange happened. I am now switching back to 2021.
Back then I held another speech, titled: “6 · 9 = 42. My search for the Theory of Everything”
That was during the pandemy. The speech was only online.
Among other things, I showed this transparency.
What did I find in my search for the Theory of Everything?
I found this so-called noncommutative geometry.
It was developed essentially by Alain Connes, a French mathematician.
What is noncommutative geometry?
We take not only the normal dimensions …
Can you still hear me well? I just got some weird noises … Nothing changed? Okay.
In normal geometry we work with three dimensions, length, width, and height.
Or with just two dimensions. Then we have a sheet with length and width.
Now I can crumple up the sheed, then it is bent.
This sheet has its usual two dimensions.
Now Connes gave it a noncommutative extension, a discrete extra-dimension.
Not the usual third dimension, which would turn the sheet into a solid.
Instead it gets a discrete extra-dimension. What does “discrete” mean?
In length, width, and height, I can think of arbitrary lengths.
When there are 10 cm, there are also 10.01 cm, or 10.275 cm, or whatever.
In this discrete extra-dimension there are just only four points.
A point in this extra-dimension can only be at one of four places.
Taken together with the normal two dimensions, we get a universe consisting of four sheets.
So this is a two-dimensional universe, consisting of four sheets.
Well, what is it good for?
Now we examine which kind of physics is admissable in this universe.
This was achieved by Connes, Chamseddine, and others.
I can recommend Mr. Schücker, who presented this in a way which can be understood well by physicists.
Those who have studied physics have a chance to understand this. Oh – there is someone …
Four-page world. A world consisting of four pages. The whole world consists of these four pages.
Now we can examine what kind of physics is admissable on this world. What could happen there?
The condition is: All forces are geometry. This is a generalisation of general relativity.
On this world, essentially nothing happens, which is boring.
Let's take this world. What is that?
This M denotes Minkowski space. That's a four-dimensional world with length, width, height, and time. In other words, that's us.
Now we attach additional sheets to this world.
These are the 3×3 matrices over the complex numbers. These are the complex numbers themselves.
And these are Hamilton's quaternions. Those who have attended my lecture “Algorithms and Data Structures“ might remember that I mentionend them briefly.
So this is our world with additional sheets. Neat.
Now when I do general relativity on this world, what kind of physics do I get? What is admissible?
When I am lucky, I get general relativity again. Maybe we get something different. Let's see.
We obtain a somewhat longer formula.
It starts here and continues at the bottom. I am extracting it in isolation.
So this is the admissible physics on this small formula we just saw.
That small formula could be converted to this one. Neat. What does that do for us? What is that?
This is the Standard Model of elementary particles, the Standard Model of quantum field theory.
This tiny formula implies the whole Standard Model. When you deal with it for longer you can recognise it.
Above there are quarks and leptons. These are the up quark, the down quark, and the electron. That's us.
Then there are forces between them. This is the so-called electroweak interaction.
That's both electromagnetism and the weak interaction in the atomic nuclei and even smaller elementary particles.
This is the strong interaction which holds the atomic nuclei together.
First, up and down quarks form protons and neutrons this way.
Then it holds them together. So this is nuclear energy.
And this is the Higgs mechanism, the Higgs boson and the mechanism which gives the particles mass.
I consider this an extreme surprise.
We take some tiny formula out of the air. We take a universe with some weird sheets.
Then we get this formula, and it is perfectly correct.
That's totally surprising.
So from the third line on, this is the Standard Model of quantum field theory.
Great. And what are the other lines? For instance what's that at the top?
That's general relativity.
In 1996, Connes and others have unified general relativity with quantum field theory.
So this problem has been solved for a long time.
Why is this unknown? Why didn't that guy get a Nobel Prize in Physics for that?
Well, he got a Fields Medal, but for very different things. That's kind of a Nobel Prize in Mathematics.
Why doesn't anybody know this theory?
This theory has the same problem as general relativity itself has. It is said to be non-quantisable.
Nevertheless I consider this a Theory of Everything. From my point of view, he found it – if we want to speak about a “Theory of Everything” at all.
Why is it unknown? Because it is non-quantisable.
What does that mean? The normal way to deal with this kind of formulas is to draw pictures like this. Maybe you have already seen them.
This is a so-called Feynman diagram, intended to depict how an electron and a muon exchange a graviton.
This means: A tiny electron and an equally tiny muon interact via their gravity.
This calculation method, using these diagrams, does not work as soon as general relativity comes into play.
As it stands, noncommutative geometry does not change this.
So he didn't solve a problem. He only wrote down something where it was clear already …
Everyone can put a plus sign in between. Then why am I interested in this?
In 2021 I developed, or completed, a different quantisation method.
I have been researching this since 2009, and in 2021 I found:
Using a very different method, it is possible to treat this quantum-mechanically, or to treat quantum field theory the same way as general relativity.
So I did not quantise gravity, but I gravitised non-gravity – or I geometrised it, or however you want to name it.
This was a short version of my speech of 2021.
Back then I stopped at the middle line. What is that?
This is what I wrote on my transparency back then. This is new. Nobody knows what it is.
But I found some hints in scientific articles that this might be dark matter in the form of modified gravity.
I didn't pursue this. In 2021 I said that this should be addressed by someone who has already learned the ropes.
Working my way into it would take way too long. I do not have that much time.
Then I couldn't resist and read up the ropes, and I found: Yes, it is indeed dark matter.
I'm sorry, but I accidentally solved this mystery on the side.
What does all this mean? We have seen that the first line of that formula is general relativity. It looks like this.
This is the so-called Lagrange density. There you must set up the Euler-Lagrange equations for fields, do some approximations, and calculate the metric.
Eventually the force law emerges. It is almost Newton's law, except for these 3 kilometres rₛ. This difference explains the orbit of Mercury around the Sun.
Now we must apply this to that.
This was already done by Schwarzschild in 1915, and now we have a new formula.
Now we must calculate the same again. Maybe we get a different force law.
Fortunately I didn't have to do this by myself. This was done by … er … the names will appear soon …
One is named Mannheim and the other one Kazanas or similar …
“Kazanas” was correct. So a few years ago, Kazanas and Mannheim did that.
They obtained this force law.
It is really simple. If you look at this formula, and if you know what these R mean … they are really complicated …
It is amazing that a force law this simple comes out.
It is general relativity plus a constant force which does not depend on the distance. There is no r.
This means that each of us – and our Sun – excerts a force on an object in the Andromeda galaxy.
This does not sound very plausible, so the first thought is: Too bad. This theory must be wrong.
In fact this constant force is extremely tiny.
For our Sun I calculated a gravitational acceleration of 2.4·10⁻²² m/s².
For comparison: The Earth has 9.81 m/s². That's much more powerful gravity.
When I drop a ball from a height of 1 m, it would take 2900 years – under the gravity of the Sun – to reach the ground.
That's extremely extremely extremely tiny gravity.
Then the second thought is: This might be correct, but who is interested in that?
Such a tiny force does not cause anything. Nothing happens.
Except: We consider something extremely big, like a galaxy cluster.
In 1989, Kazanas and Mannheim calculated that this is a possible explanation for dark matter.
This is one of the theories of modified gravity.
So it has the same problems as all theories of modified gravity.
The explanation of the virial theorem works with this kind of modified gravity.
The rotation curves match perfectly. Excellent.
Gravitational lenses do not match at all. We obtain utter rubbish.
What kind of rubbish? The modified gravity is too strong and at the wrong place.
Now we are back where we were. But something is different. My first thought when I saw this formula was …
Okay, later. First, let me show why it is utter rubbish. The modified gravity is too strong.
I have selected a paper by Dutta and Islam from 2018.
They have calculated for the galaxy cluster Abell 1689, which I already presented, how big the calculated gravity must be.
We calculate the gravity for this galaxy cluster. Depending on how we calculate we get one of these blue curves.
They are about the same. Using two different models we find out that the curve goes like this.
Now we compare it to the measured curve.
When we evaluate gravitational lenses, look for circles on Hubble images and calculate how strong the gravity must be,
then we obtain this curve. These are two workgroups, one around Limousin and one around Umetsu, French and Japanese astronomers.
There are many more curves. I will show some later.
They measured this curve. Well, that's not exactly a good match.
Even with a lot of phantasy one would not claim that this calculation was correct.
It goes really, really wrong. The gravity is way to strong, as we see here.
The curve is going up. It should go down. What is going wrong here?
Now comes my thought. This L, this Lagrange density contains an R. This other one contains an R².
And this and that are kind of R², too. So this L contains kind of R² three times.
This R denotes gravity. It is the Ricci scalar of curvature.
This is the Riemann tensor, and this is the Ricci tensor. All these R denote gravity, curvature of space.
How curved is our space? When I look around, I do not really perceive it as curved, but mostly straight.
This means that this R is tiny.
Space curvature means that when I step to the right, and suddenly the time is different.
Or I go two metres forward and end up behind myself or something like that. We do not have such effects.
When we calculate this R we get a really tiny number.
Now this contains R², which then is even much smaller.
For instance if R is 1/1000, then R² is 1/1000000. In fact it is even much smaller than that.
From this I conclude that this so-called conformal gravity, this new formula for gravity, is only relevant when the gravity is very strong.
When is gravity strong? For instance when we approach the Sun.
On Earth we can still say: Something fell on my head. So gravity is strong.
In an intergalactic gas cloud, gravity is not strong, but rather weak.
This means, my first conclusion when I saw this formula was:
Conformal gravity holds for stars, but not for gas clouds. They do not take part.
They are too light – per volume. They are not dense enough.
In several papers I read that there is no real difference between stars and gas clouds. Both are masses.
Those who say there is no difference should try to fly across them.
When you fly across a gas cloud, you do not feel it. It is too tenuous.
When you try to fly across a star, you do feel it. Better don't do that.
Using this, we can explain the remaining parts.
We can explain the graviational lensing effect being too strong, and we can even explain the Bullet Cluster.
I will show you.
This is Abell 1689 again and a lot of measured curves.
This time I took the surface mass density rather than gravitational acceleration.
There are more data for this. One is by … oh, now I must speak Dutch … Nieuwenhuizen.
Alamo-Martínez et al., Umetsu, Broadhurst, … there are many measured curves.
The red curve was calculated by myself.
I do not claim that it matches the data perfectly, but it is not worse than the other curves. It blends in quite well.
The curves do not really agree. Some are lower, some are higher.
It is not perfect, but it matches quite well. Much worse curves have been praised in the news:
“Wow! Dark matter has been explained!” Then someone else looks at that curve and says: “This does not fit at all.” My curve is better.
It is quite good. I calculated it for two more galaxy clusters, too, and it looks quite similar. It really fits.
I calculated it for three galaxy clusters. Each time I obtained a curve which fits the data quite well. So this might be correct.
Now let's take the Bullet Cluster. Above we see again the image by Clowe et al. from 2006.
This image was said to refute modified gravity because then the strongest gravity should be at the gas clouds, because there is the biggest mass.
Now I used my formula to calculate where the biggest gravity is. It is here and there.
The images do not match perfectly, but I can say with an easy conscience that there is some similarity between them.
So the Bullet Cluster, too, can be explained using modified gravity, using so-called conformal gravity,
which emerges as a side product from noncommutative geometry.
We are virtually perfectly on schedule. This is what I wanted to tell you.
I accidentally found a new explanation for dark matter because of my interest in noncommutative geometry.
So far my results suggest that this explanation is correct.
This is of course not the end of this story. I will verify this further.
For instance that image of the Bullet Cluster is not similar enough for my taste. Something is still wrong.
Probably I am overlooking some small thing. For instance there is one problem …
I am calculating the gravity from the stars. For this we must know where the stars are.
For instance when I look at that point, is that a big galaxis farther away or a small galaxis which is closer?
That's not really clear. Now when I consult literature …
Well, gravitational lensing … gas clouds … okay, stars exist, too, but the gravitational lens is much more interesting.
You do not find anything about stars. I have the impression that astronomers do not like stars.
They like gas clouds, black holes, gravitational lenses, neutron stars. But plain stars bustling about …
It is really difficult to find out which of them belong to the galaxy cluster and which ones do not.
In any case I have to check this further.
I am, however, somewhat confident about this.
First, I must build up my understanding how to check which stars belong to the cluster and which ones do not.
The more I learn about this, the better my results get. So it looks good so far.
One day, I will have something I can write down and publish. Then it will appear in the journals.
So far this has not been published anyware. This speech was the first time I went public with this.
With this I thank you for your attendance. I am now available for your questions. Thank you.