WEBVTT Kind: captions Language: en 00:00:05.000 --> 00:00:10.000 Prof. Peter Gerwinski, PhD Bochum University of Applied Sciences What is dark matter? May 16, 2024 00:00:10.000 --> 00:00:14.000 First of all, thanks to my colleague Mrs. Feldmüller for this introduction. 00:00:14.000 --> 00:00:20.000 Before I start, does our technical equipment work? Can you hear me clearly? 00:00:20.000 --> 00:00:25.000 Over the speakers and online, too? 00:00:25.000 --> 00:00:31.000 At least we have tested everything extensively, so everything should work. 00:00:31.000 --> 00:00:38.000 As was already said, I am Peter Gerwinski, professor for low-level IT systems at this university. 00:00:38.000 --> 00:00:42.000 Some students know me already from my courses in Computer Technology. 00:00:42.000 --> 00:00:51.000 Later I will teach them Low-Level Programming, Algorithms and Data Structures, Embedded Systems, and Databases and Data Security. These are my subjects here. 00:00:51.000 --> 00:00:57.000 In fact, however, I am a physicist. "Dr. rer. nat." means "doctor rerum naturalium", doctor of natural sciences. 00:00:57.000 --> 00:01:04.000 I studied physics and made my PhD about Quantum Chaos. 00:01:04.000 --> 00:01:11.000 Now I am presenting a subject from astronomy, so you might ask how this is related to quantum physics. 00:01:11.000 --> 00:01:20.000 So I am sticking my neck far out and speak about things I do not … things I did not study. 00:01:20.000 --> 00:01:27.000 As we will see later, dark matter is related to quantum physics to an amazing degree. 00:01:27.000 --> 00:01:35.000 The first thing I will address today: What is the mystery? What is the problem? 00:01:35.000 --> 00:01:42.000 After that we will address solutions to this problem, or more precise, suggestions for solutions. 00:01:42.000 --> 00:01:50.000 This is one of today's unsolved problems in physics, in astro-physics. Nobody knows what dark matter is. 00:01:50.000 --> 00:02:00.000 One mystery of particular interest is pictured here. This is the so-called Bullet Cluster. 00:02:00.000 --> 00:02:05.000 As I said, this is a mystery of particular interest. I will say some words about this later. 00:02:05.000 --> 00:02:09.000 In fact I found out something new myself. 00:02:09.000 --> 00:02:14.000 To say it outright: I claim that I know what dark matter is. 00:02:14.000 --> 00:02:24.000 During the last months I have been working on this in my scarce free time. 00:02:24.000 --> 00:02:30.000 I started some serious work on this in 2021. 00:02:30.000 --> 00:02:34.000 I had just a small idea I wanted to try out. I tried it out, and it worked. 00:02:34.000 --> 00:02:39.000 Today I am presenting this in public for the first time. 00:02:39.000 --> 00:02:44.000 And then … let's see how to proceed from there. 00:02:44.000 --> 00:02:50.000 But first, what is the mystery? What is the problem? 00:02:50.000 --> 00:02:54.000 Why is it called “dark matter”? 00:02:54.000 --> 00:02:58.000 “Dark” in outer space means: We cannot see it. 00:02:58.000 --> 00:03:07.000 Outer space is black. When something does not give light in black outer space, we cannot see it. 00:03:07.000 --> 00:03:14.000 “To see” does not only refer to optics, what we can see using our eyes and telescopes, 00:03:14.000 --> 00:03:22.000 but also IR, UV, radar, radio, gamma rays, … that does not matter. 00:03:22.000 --> 00:03:28.000 We cannot see that dark matter with any telescope. 00:03:28.000 --> 00:03:33.000 Okay, so it does not exist. How do we know that there is something? 00:03:33.000 --> 00:03:41.000 Dark matter produces gravity. We know there is something in outer space which produces gravity, 00:03:41.000 --> 00:03:51.000 but we cannot detect it using any of our telescopes, not even using X-rays or radio waves. 00:03:51.000 --> 00:04:00.000 I will now present three methods how to detect, using gravity, that something must be there. 00:04:00.000 --> 00:04:07.000 We start in historical order with the virial theorem by which all this was discovered in the first place. 00:04:07.000 --> 00:04:16.000 Rotation curves were the key to clarifying that this is real and not just imagined by someone. 00:04:16.000 --> 00:04:25.000 Currently we are using so-called gravitational lenses to examine dark matter. 00:04:25.000 --> 00:04:32.000 There is more. I just picked out the three most important items. 00:04:32.000 --> 00:04:37.000 Let's start with the virial theorem. 00:04:37.000 --> 00:04:41.000 This phenomenon can be summarised as: Galaxies are moving too fast. 00:04:41.000 --> 00:04:44.000 What does “too fast” mean? 00:04:44.000 --> 00:04:50.000 In 1933, Fritz Zwicky, a Swiss astronomer, pictured here, 00:04:50.000 --> 00:04:57.000 applied a method which was new at that time to investigate the Coma Cluster of galaxies. 00:04:57.000 --> 00:05:03.000 This method is well-established in our time. We are looking at the redshift of galaxies. 00:05:03.000 --> 00:05:09.000 The light is redshifted when something is departing from us; it is blueshifted when something is approaching us. 00:05:09.000 --> 00:05:13.000 Using this, he investigated how fast these galaxies are. 00:05:13.000 --> 00:05:25.000 He found a number way too high, couldn't believe in it first, but then recalculated everything and found out: 00:05:25.000 --> 00:05:29.000 Either these galaxies do not form a cluster but are at the same place just by chance. 00:05:29.000 --> 00:05:35.000 Or there must be at least 400 times as much mass as can be seen. 00:05:35.000 --> 00:05:43.000 Here we see a lot of galaxies. Each of these points is not just a star, but a whole galaxy. 00:05:43.000 --> 00:05:53.000 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. 00:05:53.000 --> 00:05:58.000 He also considered that the galaxies do not form a cluster, but are at the same place just by chance. 00:05:58.000 --> 00:06:03.000 Here the famous astronomically large coincidence comes into play. 00:06:03.000 --> 00:06:11.000 The probability that these galaxies are at the same place just by chance is 1 in several trillions, quintillions, whatever. 00:06:11.000 --> 00:06:17.000 This cannot be. There must be something we cannot see. 00:06:17.000 --> 00:06:25.000 Back then, his method was new, so it was said: Maybe he found something, maybe he didn't. 00:06:25.000 --> 00:06:31.000 Maybe he simply got something wrong. Not many thoughts were given to this, back then. 00:06:31.000 --> 00:06:36.000 This changed in the 1970s. 00:06:36.000 --> 00:06:47.000 In 1970, astronomer Vera Rubin investigated single stars in the Andromeda Galaxy. 00:06:47.000 --> 00:06:54.000 This picture does not depict the Andromeda Galaxy, but just a generical one. 00:06:54.000 --> 00:07:00.000 She investigated how the stars move in the galaxy. Galaxies rotate. 00:07:00.000 --> 00:07:08.000 What are the stars doing? I am going to show this in a small animation. Let me switch … 00:07:10.000 --> 00:07:15.000 Like this … we just practised this … 00:07:16.000 --> 00:07:20.000 Just a moment … one step back … 00:07:22.000 --> 00:07:27.000 Okay. That's it. 00:07:34.000 --> 00:07:39.000 Here we see a rotating galaxy. 00:07:39.000 --> 00:07:49.000 We see the stars. From the brightness we can estimate how much mass is there, how heavy the stars are. 00:07:49.000 --> 00:07:54.000 When they are brighter, they are heavier, simply because they are more. 00:07:54.000 --> 00:08:04.000 Now we can calculate how fast the stars may rotate, assuming Newton's laws. 00:08:04.000 --> 00:08:12.000 We get fast rotation close to the centre and slow rotation in the outskirts. 00:08:12.000 --> 00:08:20.000 Vera Rubin measured fast rotation close to the centre, and in the outskirts – the same speed. 00:08:20.000 --> 00:08:30.000 This was rather puzzling. The stars move as if there was something in the galaxy much heavier than the other stars. 00:08:30.000 --> 00:08:36.000 There must be something additional. This established the concept of “dark matter”. 00:08:36.000 --> 00:08:48.000 There is something in the galaxies which causes the stars to move faster than Newton's laws allow. 00:08:53.000 --> 00:09:00.000 I am now switching back to the transparencies. 00:09:06.000 --> 00:09:17.000 So as of 1970 we know that there must be much more in the galaxy than the visible stars. 00:09:17.000 --> 00:09:23.000 Now we switch to our time, where we have space telescopes such as Hubble. 00:09:23.000 --> 00:09:30.000 This picture has been combined from Hubble images and images from the Earth-based Magellan telescopes. 00:09:30.000 --> 00:09:34.000 This is state of the art. That's the kind of pictures we can create today. 00:09:34.000 --> 00:09:42.000 Here we see the cluster of galaxies “Abell 1689”. I hope that my pronunciation is not too wrong. 00:09:42.000 --> 00:09:48.000 Probably something like “able 1689”. 00:09:48.000 --> 00:09:55.000 This galaxy cluster consists, of course, of galaxies, which in turn consist of stars. 00:09:55.000 --> 00:10:00.000 Now we can do what Zwicky did in 1933. 00:10:00.000 --> 00:10:05.000 We look how bright these stars are. Then we can calculate their mass. 00:10:05.000 --> 00:10:16.000 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. 00:10:16.000 --> 00:10:24.000 That's 4.7 trillons, or 4.7 million millions, a 1 with 12 zeroes. So many suns are these. 00:10:24.000 --> 00:10:29.000 That's a lot. That's not peanuts. 00:10:29.000 --> 00:10:38.000 In fact what we can see in visible light is just a small fraction of what can be seen altogether. 00:10:38.000 --> 00:10:48.000 This is an X-ray image of the same galaxy cluster. We see some diffuse structure. What is that? 00:10:48.000 --> 00:11:00.000 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. 00:11:00.000 --> 00:11:10.000 Its size is several 100 kiloparsec, hundreds of thousands or millions of light years, one big gas cloud. 00:11:10.000 --> 00:11:17.000 It is not very dense. On Earth, we would consider this cloud a vacuum. There is nothing. 00:11:17.000 --> 00:11:26.000 In outer space, however, this is a gas cloud. Now we can calculate from the brightness how much gas there is. 00:11:26.000 --> 00:11:31.000 We find out that it is almost ten times as heavy as the stars are. 00:11:31.000 --> 00:11:37.000 The visible stars comprise not much more than one tenth of the total mass. 00:11:37.000 --> 00:11:42.000 Almost 90% of the total mass belongs to this gas cloud. 00:11:42.000 --> 00:11:50.000 So this whole thing is much heavier than what we can assume considering the stars it contains. 00:11:53.000 --> 00:12:00.000 But there is more, yet another method how to put this thing on a balance, the gravitational lensing effect. 00:12:00.000 --> 00:12:06.000 I am magnifying this image a little. 00:12:06.000 --> 00:12:11.000 When we look at this magnified image, we see some round structures. 00:12:11.000 --> 00:12:16.000 Here … and there … round streaks … 00:12:16.000 --> 00:12:23.000 This looks as if someone had put down a cup on this. Something is round here. 00:12:23.000 --> 00:12:31.000 These are distorted galaxies, the so-called gravitational lensing effect. I am zooming in. 00:12:31.000 --> 00:12:39.000 This weird streak is a galaxy located behind the galaxy cluster. 00:12:39.000 --> 00:12:44.000 The galaxy cluster bends the light around itself because it is so heavy. 00:12:44.000 --> 00:12:52.000 Like through a lens the light takes a way around the cluster, causing these weird streaks. 00:12:54.000 --> 00:13:01.000 Now astronomers can calculate how heavy the lens must be. 00:13:01.000 --> 00:13:08.000 How heavy must the stuff in the centre be, the stars and the gas, to create precisely this streak? 00:13:08.000 --> 00:13:17.000 Here we see the distribution of gravity. This blue glow shows where the biggest mass is. 00:13:17.000 --> 00:13:24.000 That fits well. Here are the stars and the gas. Then let's have a look how much it is. 00:13:25.000 --> 00:13:31.000 That's again more than ten times as much mass as we already have in the shape of stars and gas. 00:13:31.000 --> 00:13:41.000 Whatever there is, 90% of it we cannot see. What we can see, stars and gas, comprises not even 10%. 00:13:41.000 --> 00:13:45.000 Just a little more than 5%. 00:13:45.000 --> 00:13:51.000 So the universe in this galaxy cluster consists of dark matter by 93.7%. 00:13:51.000 --> 00:14:00.000 From the remaining parts, 5.6% are gas. The stars, 0.7%, do not really stand out. 00:14:00.000 --> 00:14:05.000 The stars are the lightest thing here. 00:14:06.000 --> 00:14:12.000 So we know: Something is there. Now we ask, of course: What is that? 00:14:12.000 --> 00:14:17.000 This question has already been asked in the time of Zwicky. 00:14:17.000 --> 00:14:24.000 I am now going to present the three most important answers to this. 00:14:24.000 --> 00:14:28.000 What approaches are there to explain dark matter? 00:14:28.000 --> 00:14:37.000 First, normal matter which just does not give light. Second, new elementary particles, previously unknown. 00:14:37.000 --> 00:14:43.000 There is also the possibility that there is a new law of gravity. 00:14:43.000 --> 00:14:48.000 These are the three most important approaches. 00:14:49.000 --> 00:14:54.000 Let'start with normal matter which just does not give light. What could it be? 00:14:54.000 --> 00:15:02.000 For instance a planet without a sun. When a planet does not get illuminated by a sun, we cannot see it. 00:15:02.000 --> 00:15:05.000 Then it is dark. Dark matter. 00:15:05.000 --> 00:15:15.000 Or, we have seen gas clouds using X-rays. They are emitting X-rays because they are hot. 00:15:15.000 --> 00:15:19.000 But when the gas cloud is cold, it does not give light. Then it is just dark. 00:15:19.000 --> 00:15:24.000 Then we would not see it, and it would be a candidate for dark matter. 00:15:24.000 --> 00:15:29.000 Then there are more exotic object such as neutron stars, or, fully extreme, black holes. 00:15:29.000 --> 00:15:35.000 I won't address in detail today what a black hole is. In any case it is black. We do not see it. 00:15:35.000 --> 00:15:41.000 It can get visible indirectly by matter falling into the black hole heating up in an accretion disk. 00:15:41.000 --> 00:15:47.000 But we cannot see the black hole itself, so it is another candidate for dark matter. 00:15:47.000 --> 00:15:57.000 Okay, but now we have one problem with this. As we have seen, in the galaxy cluster there are 93% dark matter. 00:15:57.000 --> 00:16:01.000 If all of this are planets without a sun, they would bustle about somewhere all the time. 00:16:01.000 --> 00:16:06.000 They would fly through our telescopes all the time. Even if they do not give light, they would obscure something. 00:16:06.000 --> 00:16:09.000 For instance if they pass by a star. 00:16:09.000 --> 00:16:13.000 If they are just a few we can say: Okay, we didn't discover them yet. 00:16:13.000 --> 00:16:21.000 However meanwhile we have very good telescopes such as the Hubble and James Webb space telescopes. 00:16:21.000 --> 00:16:26.000 With this kind of instruments we would have detected something if there was anything. 00:16:26.000 --> 00:16:31.000 But we did not find anything, so we are stuck with: There is nothing. 00:16:31.000 --> 00:16:36.000 All of these candidates certainly exist. We even know a few of them. 00:16:36.000 --> 00:16:43.000 However this is not suited to explain 93% of the total matter. 00:16:43.000 --> 00:16:48.000 More than 10 times what we can see … We would have detected something. 00:16:48.000 --> 00:16:51.000 This is not a good explanation. 00:16:51.000 --> 00:17:01.000 These so-called Massive Astrophysical Compact Halo Objects, MACHOs for short, are no working explanation for dark matter. 00:17:02.000 --> 00:17:04.000 Well, what else could it be? 00:17:04.000 --> 00:17:07.000 This leads us to quantum physics. 00:17:07.000 --> 00:17:12.000 What do we consist of? Of atoms. 00:17:12.000 --> 00:17:17.000 What do atoms consist of? Of nuclei and electrons orbiting them. 00:17:17.000 --> 00:17:22.000 What do atomic nuclei consist of? Of protons and neutrons. 00:17:22.000 --> 00:17:31.000 What do protons and neutrons consist of? Of up quarks and down quarks. This means: We are here. That's us. 00:17:31.000 --> 00:17:37.000 These are all existing particles, and all of them have been detected at the LHC and elsewhere. 00:17:37.000 --> 00:17:44.000 Only a small part of them is visible matter. What about the others? Maybe that's dark matter. 00:17:44.000 --> 00:17:51.000 There are, for instance, these candidates, the neutrinos. 00:17:51.000 --> 00:18:00.000 They are extremely difficult to detect. They are invisible. This makes them good candidates for dark matter. 00:18:00.000 --> 00:18:07.000 But they have some problems. They are very light. It is not even clear whether they have a mass at all. 00:18:07.000 --> 00:18:14.000 Again: If they comprise 90% of total matter, they must be extremely many. 00:18:14.000 --> 00:18:21.000 But they have yet another problem. They are so fast that they have traversed a galaxy cluster before noticing it. 00:18:21.000 --> 00:18:26.000 They practically move at lightspeed all the time. 00:18:26.000 --> 00:18:33.000 Because they are so fast, they cannot explain the rotational behaviour of galaxies. 00:18:33.000 --> 00:18:36.000 So neutrinos cannot explain rotation curves. 00:18:36.000 --> 00:18:43.000 What else could it be? All the other particles are unstable. They decay immediately. 00:18:43.000 --> 00:18:46.000 Not the electrons, but all these particles. 00:18:46.000 --> 00:18:51.000 These are interaction particles. Forces. They do not have anything to do with this. 00:18:51.000 --> 00:18:55.000 What about the Higgs boson. It decays, too, but … 00:18:55.000 --> 00:19:01.000 Maybe there are little brothers of the Higgs boson. There are some theories. So-called little Higgs particles. 00:19:01.000 --> 00:19:05.000 They would be candidates. 00:19:05.000 --> 00:19:15.000 Or there are big brothers of the neutrinos in yet another theory. To solve certain problems … 00:19:15.000 --> 00:19:23.000 … one has thought out certain new ideas and, er … stop. Okay … now. 00:19:23.000 --> 00:19:30.000 It might be possible to explain neutrino oscillations by assuming yet another kind of neutrinos. 00:19:30.000 --> 00:19:36.000 They are heavy. They are even more difficult to detect then normal neutrinos. They might be dark matter. 00:19:36.000 --> 00:19:40.000 We have searched for them. As of today, we found nothing. 00:19:40.000 --> 00:19:45.000 We have searched for little Higgs particles. We found nothing. 00:19:45.000 --> 00:19:49.000 Then there are axions as a theory. 00:19:49.000 --> 00:19:55.000 One tries to explain certain properties of the gluons by introducing new particles, so-called axions. 00:19:55.000 --> 00:20:00.000 We have searched for them. As of today, we found nothing. 00:20:00.000 --> 00:20:04.000 But now comes supersymmetry. It solves all problems. 00:20:04.000 --> 00:20:10.000 We try to unify general relativity with quantum field theory using a so-called supersymmetric theory. 00:20:10.000 --> 00:20:18.000 It cancels the non-renormalisable divergences of gravity. Neat. A great theory. 00:20:18.000 --> 00:20:24.000 Now we build the LHC and check it. We find: There is nothing. 00:20:24.000 --> 00:20:31.000 One was absolutely sure that one would find any of these at the LHC. 00:20:31.000 --> 00:20:35.000 But we didn't. There is nothing. 00:20:35.000 --> 00:20:43.000 As of today there are no sterile neutrinos, no axions, no little Higgs particles, and no supersymmetric partners. 00:20:43.000 --> 00:20:46.000 There is nothing. 00:20:46.000 --> 00:20:50.000 Probably this is not dark matter. 00:20:50.000 --> 00:20:53.000 Of course the jury is still out. 00:20:53.000 --> 00:20:57.000 It might be that the next particle collider will find something. 00:20:57.000 --> 00:21:02.000 But it is getting more and more unlikely that one of these theories is correct. 00:21:02.000 --> 00:21:07.000 Probably each of these is a nice idea, but wrong, unfortunately. 00:21:07.000 --> 00:21:12.000 So we still do not know what dark matter is. 00:21:12.000 --> 00:21:19.000 There is yet another idea. Maybe this is not a new kind of matter, but a new law of nature. 00:21:19.000 --> 00:21:27.000 To understand how a new law of nature can explain additional matter, I am now going a little far afield. 00:21:27.000 --> 00:21:32.000 This has been done before in the 19th century. 00:21:32.000 --> 00:21:37.000 In 1686, Newton established the law of universal gravitation. 00:21:37.000 --> 00:21:41.000 Those who have attended our physics lectures should know this law. 00:21:41.000 --> 00:21:52.000 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. 00:21:52.000 --> 00:21:59.000 A beautiful law. Newton discovered it in 1686. 00:21:59.000 --> 00:22:05.000 In 19th century very smart people did calculations using this law, in particular Le Verrier. 00:22:05.000 --> 00:22:14.000 He calculated very thorougly using Newton's law and investigated the orbit of Uranus around the Sun. 00:22:14.000 --> 00:22:23.000 Back then, Uranus had been discovered quite recently. Its orbit was surveyed. How does Uranus orbit the Sun? 00:22:23.000 --> 00:22:29.000 It was found: Sometimes it is somewhat too early on its orbit; sometimes it is too late. 00:22:29.000 --> 00:22:35.000 It might be that there is yet another planet out there which tugs at Uranus. 00:22:35.000 --> 00:22:39.000 Its gravity causes Uranus to behave somewhat wiredly. 00:22:39.000 --> 00:22:44.000 Le Verrier calculated this very thoroughly. 00:22:44.000 --> 00:22:53.000 In 1846 he made a prediction: Look at that place. There might be a new planet. 00:22:53.000 --> 00:22:59.000 Gottfried Galle did that. He looked at that place. 00:22:59.000 --> 00:23:05.000 Le Verrier said: There might be a new planet. And right beside it there was a new planet. 00:23:05.000 --> 00:23:11.000 He found it within half an hour. An incredible triumphe for physics. 00:23:11.000 --> 00:23:20.000 Just by calculating Le Verrier predicted: Look there. There is a new planet. Half an hour later the astronomer actually found it. 00:23:20.000 --> 00:23:24.000 Yes, we have a new planet. We call it Neptun. Great. 00:23:24.000 --> 00:23:31.000 Newton's laws are very good, and the people who can apply them are very good, too. 00:23:31.000 --> 00:23:38.000 Let's do this again. The innermost planet, Mercury, behaves weirdly, too. 00:23:38.000 --> 00:23:42.000 Sometimes it is early, sometimes late, and there is the so-called perihelion precession. 00:23:42.000 --> 00:23:46.000 This looks like a circle. In fact it is an ellipse. 00:23:46.000 --> 00:23:53.000 This ellipse slowly rotates around the sun. That's the so-called perihelion precession. 00:23:53.000 --> 00:24:00.000 Based on the perihelion precession, Le Verrier calculated that there must be yet another planet, orbiting. 00:24:00.000 --> 00:24:06.000 He was so sure about this that he already had a name for the new planet. 00:24:06.000 --> 00:24:09.000 The new planet was even mapped on celestial maps already. 00:24:09.000 --> 00:24:17.000 The planet Vulcan orbits the Sun closer than Mercury does. It is only a matter of time until we have found it. 00:24:17.000 --> 00:24:24.000 One has been searching for it. For 50 years. One found nothing. There is nothing. 00:24:24.000 --> 00:24:35.000 One found a few little rocks orbiting the Sun, but nothing which could explain the orbit of Mercury around the Sun. 00:24:35.000 --> 00:24:42.000 What now? What is the reason for it? This was found by Einstein. 00:24:42.000 --> 00:24:49.000 With his general relativity he established, in 1915, a new law of gravity. 00:24:49.000 --> 00:24:53.000 It is almost the same as Newton's one. 00:24:53.000 --> 00:25:01.000 Here I am showing the Scharzschild metric by approximation, showing what changes. 00:25:01.000 --> 00:25:06.000 This r² becomes r times r minus rₛ. 00:25:06.000 --> 00:25:17.000 Instead of taking the square of the distance between the Sun and Mercury, I take that distance and multiply it by itself minus rₛ. 00:25:17.000 --> 00:25:22.000 This rₛ is 3 kilometres. On the distance between the Sun and Mercury. 00:25:22.000 --> 00:25:30.000 The Earth is about 150 millions of kilometres away from the Sun. Adding 3 kilometres does not really matter. 00:25:30.000 --> 00:25:38.000 However these 3 kilometres cause Mercury to behave just a little different from what Newton predicted. 00:25:38.000 --> 00:25:44.000 This perfectly explains the orbit of Mercury. This explanation is valid until today. 00:25:44.000 --> 00:25:50.000 We are checking this again and again, using better and better telescopes and better and better calculation methods. 00:25:50.000 --> 00:25:56.000 Le Verrier used paper and pencil. Today these calculations are carried out by supercomputers. 00:25:56.000 --> 00:26:05.000 We always find: It's correct. Mercury behaves exactly as calculated by Einstein in 1915. 00:26:05.000 --> 00:26:18.000 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. 00:26:18.000 --> 00:26:27.000 In 1983, this gave Milgrom the idea: Maybe we can explain dark matter the same way? 00:26:27.000 --> 00:26:32.000 Maybe there is a deviating law of gravity, too. 00:26:32.000 --> 00:26:38.000 Not in the vicinity of the Sun, but far, far away, where we would not feel anything, normally. 00:26:38.000 --> 00:26:42.000 Maybe something changes there. 00:26:42.000 --> 00:26:47.000 I have written down his formula in a somewhat clumsy way to have the F on one side. 00:26:47.000 --> 00:27:00.000 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. 00:27:00.000 --> 00:27:10.000 When we assume this law of gravity which behaves a little different than Newton at far distances, … 00:27:10.000 --> 00:27:15.000 Could this explain dark matter? Let's try out. 00:27:15.000 --> 00:27:20.000 What do we need to test? The virial theorem. 00:27:20.000 --> 00:27:28.000 We repeat Zwicky's calculations of 1933 for the Coma Cluster. Maybe that works out. 00:27:28.000 --> 00:27:39.000 It does. Using modified gravity we can explain the behaviour of galaxy clusters, that the galaxies are flying about way too fast. 00:27:39.000 --> 00:27:47.000 When gravity behaves differently at far distances, the cluster stays together. Then it fits. 00:27:47.000 --> 00:27:54.000 So modified gravity explains the mystery of 1933. 00:27:54.000 --> 00:28:00.000 Next mystery. The stars in the galaxies are rotating much faster then they are supposed to. 00:28:00.000 --> 00:28:10.000 So there must be additional mass, or we have a modified law of gravity. Let's try it out. 00:28:10.000 --> 00:28:14.000 Wow. We get an excellent result. 00:28:14.000 --> 00:28:21.000 The explanation by modified gravity perfectly matches the observations, much better than dark matter does. 00:28:21.000 --> 00:28:30.000 So he did it. Milgrom is right. Let's give him a Nobel prize. He's still alive. He succeeded to explain dark matter. 00:28:30.000 --> 00:28:39.000 Now we jump to our time where we investigate galaxy clusters using the effect of gravitational lensing. 00:28:39.000 --> 00:28:46.000 We find that it does not work at all. It is not just a little wrong, but totally wrong. 00:28:46.000 --> 00:28:49.000 What is going totally wrong? 00:28:49.000 --> 00:28:53.000 For one thing, the calculated gravity is way too strong. 00:28:53.000 --> 00:29:01.000 We have seen that dark matter comprises about 93%. The remaining 7% are gas and stars. 00:29:01.000 --> 00:29:10.000 Using modified gravity we do not get 93%, but something like 99% of dark matter. 00:29:10.000 --> 00:29:14.000 Nice try, but overshot. It does not work. 00:29:14.000 --> 00:29:21.000 But there is something else which does not work. That's why this theory is rated as refuted as of 2006. 00:29:21.000 --> 00:29:34.000 The gravity is at the wrong place. What does that mean? This leads us to the so-called Bullet Cluster I mentioned initially. 00:29:38.000 --> 00:29:47.000 Here we see the so-called Bullet Cluster, which translates to “Geschoßhaufen” or “Gewehrkugelhaufen” in German. 00:29:47.000 --> 00:29:57.000 In fact these are two galaxy clusters which have collided some astronomically short time ago – 100 million years ago. 00:29:57.000 --> 00:30:02.000 One is here, and the other one is over there. 00:30:02.000 --> 00:30:07.000 This small cluster has fallen through the big one. 00:30:07.000 --> 00:30:12.000 It came from the left, and the other one came from the right, and then they passed through each other. 00:30:12.000 --> 00:30:19.000 What has this to do with dark matter? Let's have a look how heavy these clusters are. 00:30:19.000 --> 00:30:28.000 By counting the stars in the galaxies like Zwicky did, we arrive at 3.8·10¹³ solar masses. 00:30:28.000 --> 00:30:37.000 38 trillions, 38 millions of millions times our Sun. That many stars we see here. 00:30:37.000 --> 00:30:43.000 Again there are gas clouds. 00:30:43.000 --> 00:30:49.000 Something weird stands out. Here are stars, and the gas clouds are besides them. 00:30:49.000 --> 00:30:58.000 There are stars, and the gas clouds are besides them again, and they have a weird shape. Why? What happened there? 00:30:58.000 --> 00:31:04.000 Let's have a look at a small animation which shows what happened there. 00:31:07.000 --> 00:31:10.000 Just a moment … 00:31:22.000 --> 00:31:30.000 Here we see the galaxy clusters how they might have looked like before the collision. Now they are about to collide. 00:31:30.000 --> 00:31:39.000 These dots are galaxies with stars. The gas clouds are depicted in pink. 00:31:39.000 --> 00:31:45.000 The gas clouds drop behind the galaxies at the moment when they pass each other. 00:31:45.000 --> 00:31:48.000 They decelerate each other. 00:31:48.000 --> 00:31:59.000 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. 00:31:59.000 --> 00:32:03.000 The galaxies just move on, passing each other. 00:32:03.000 --> 00:32:10.000 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. 00:32:10.000 --> 00:32:18.000 The gas clouds do notice it. They heat up each other. Then they emit X-rays. That's why we can see them. 00:32:18.000 --> 00:32:22.000 They decelerate each other and drop behind the galaxies. 00:32:22.000 --> 00:32:28.000 Here are the stars, and the gas cloud which was between them initially, has dropped behind them. 00:32:28.000 --> 00:32:35.000 And the same here: Here are the stars, and the gas cloud has dropped behind them. 00:32:49.000 --> 00:33:00.000 The galaxies collided 100 million years ago. The gas clouds have heated up and decelerated each other. 00:33:00.000 --> 00:33:05.000 The galaxies did not even notice that there was something. 00:33:05.000 --> 00:33:09.000 This also explains this shape. 00:33:09.000 --> 00:33:15.000 This small galaxy cluster has passed the big one like a bullet from a shotgun. 00:33:15.000 --> 00:33:22.000 This looks like the shock wave of a bullet in the air. This photo was taken using a special camera. 00:33:22.000 --> 00:33:28.000 A bullet passes through the air at a supersonic speed, causing shock waves of this kind. 00:33:28.000 --> 00:33:33.000 It looks the same as this other shock wave because it was formed the same way. 00:33:33.000 --> 00:33:38.000 This small cloud passed the big one like a bullet passes the air. 00:33:38.000 --> 00:33:43.000 That's why it is called “Bullet Cluster”. 00:33:43.000 --> 00:33:47.000 Now what about dark matter? 00:33:47.000 --> 00:33:52.000 We can study it using the effect of gravitational lensing. 00:33:52.000 --> 00:34:01.000 In 2006, Clowe et al. – again I hope that I get the pronunciation right – published a groundbreaking work. 00:34:01.000 --> 00:34:05.000 They examined where the dark matter is. 00:34:05.000 --> 00:34:10.000 It is here, and it is there. 00:34:10.000 --> 00:34:20.000 The dark matter, the biggest source of gravity, is located where the stars are, and it is not where the gas is. 00:34:20.000 --> 00:34:28.000 We remember: The gas is much heavier than the stars are. Here it is a little less than 10 times as heavy. 00:34:28.000 --> 00:34:33.000 The biggest visible mass is here, where the gas clouds are. 00:34:33.000 --> 00:34:39.000 The biggest measured mass is here, close to the stars. 00:34:39.000 --> 00:34:48.000 This clearly proves that modified gravity is wrong, because then the biggest gravity would have to be with the gas clouds. 00:34:48.000 --> 00:34:55.000 Dark matter must exist. It moves together with the stars. It is collision-free, just like the stars. 00:34:55.000 --> 00:34:59.000 This means, they pass each other without even noticing. 00:34:59.000 --> 00:35:06.000 So as of 2006 it is clear that the theory of modified gravity has been refuted. 00:35:06.000 --> 00:35:12.000 The theory of dark matter has been confirmed again, even though we still do not know what it is. 00:35:15.000 --> 00:35:27.000 In 2007, Angus and McGough – again I hope that I am pronouncing them correctly – calculated the relative speed between both galaxy clusters. 00:35:27.000 --> 00:35:32.000 They passed each other – at what speed? 00:35:32.000 --> 00:35:37.000 We can read this off the shape of the shock wave, just like with a rifle bullet. There it works, too. 00:35:37.000 --> 00:35:42.000 They calculated 4700 kilometres per second. 00:35:42.000 --> 00:35:48.000 That's rather fast, even by astronomic measures. In fact it is too fast. 00:35:48.000 --> 00:35:52.000 They cannot be that fast. 00:35:52.000 --> 00:35:58.000 Someone must have accelerated them. We can calculate: How much matter is in the universe? Who tugs at whom? 00:35:58.000 --> 00:36:01.000 Something must have accelerated them towards each other. 00:36:01.000 --> 00:36:04.000 There is noone who could accelerate them that strongly. 00:36:04.000 --> 00:36:13.000 Assuming the theory of dark matter, even if there is a lot of dark matter, they can gain at most 2900 km/s. 00:36:13.000 --> 00:36:17.000 They are, however, significantly faster. 00:36:17.000 --> 00:36:28.000 Assuming the theory of modified gravity, gravity is different. At large distances it is stronger than one would otherwise assume. 00:36:28.000 --> 00:36:33.000 This explains that they have been accelerated towards each other over large distances. 00:36:33.000 --> 00:36:40.000 Then we can calculate thet they could have gained a relative speed of up to 4800 km/s. 00:36:40.000 --> 00:36:48.000 So the Bullet Cluster proves clearly that the theory of dark matter is wrong. There is no dark matter. 00:36:48.000 --> 00:36:54.000 It clearly proves that there is modified gravity. That's the only way to explain the Bullet Cluster. 00:36:54.000 --> 00:36:58.000 That's the current state of research. To summarise it to a signle word: 00:36:58.000 --> 00:37:02.000 Huh? We simply don't know. 00:37:02.000 --> 00:37:07.000 The Bullet Cluster proves that dark matter exists and that modified gravity is wrong. 00:37:07.000 --> 00:37:11.000 And the very same Bullet Cluster also proves the opposite. 00:37:11.000 --> 00:37:19.000 As of today, astrophysicists are at a loss. We have no idea what dark matter is, whether it exists at all, … 00:37:19.000 --> 00:37:29.000 or whether there is modified gravity instead. However both has in fact been refuted. We do not know anything. 00:37:29.000 --> 00:37:35.000 That's common in science, and that's what makes it interesting. There are actual unsolved mysteries. 00:37:35.000 --> 00:37:44.000 It is not that someone knows the solution and did not tell us yet, but the solution is actually unknown. 00:37:44.000 --> 00:37:53.000 Now here I could say: This is my answer to the question: What is dark matter? Nobody knows. 00:37:53.000 --> 00:37:58.000 But then something strange happened. I am now switching back to 2021. 00:37:58.000 --> 00:38:07.000 Back then I held another speech, titled: “6 · 9 = 42. My search for the Theory of Everything” 00:38:07.000 --> 00:38:12.000 That was during the pandemy. The speech was only online. 00:38:12.000 --> 00:38:16.000 Among other things, I showed this transparency. 00:38:16.000 --> 00:38:21.000 What did I find in my search for the Theory of Everything? 00:38:21.000 --> 00:38:26.000 I found this so-called noncommutative geometry. 00:38:26.000 --> 00:38:33.000 It was developed essentially by Alain Connes, a French mathematician. 00:38:33.000 --> 00:38:38.000 What is noncommutative geometry? 00:38:42.000 --> 00:38:45.000 We take not only the normal dimensions … 00:38:45.000 --> 00:38:52.000 Can you still hear me well? I just got some weird noises … Nothing changed? Okay. 00:38:52.000 --> 00:38:58.000 In normal geometry we work with three dimensions, length, width, and height. 00:38:58.000 --> 00:39:02.000 Or with just two dimensions. Then we have a sheet with length and width. 00:39:02.000 --> 00:39:07.000 Now I can crumple up the sheed, then it is bent. 00:39:07.000 --> 00:39:11.000 This sheet has its usual two dimensions. 00:39:11.000 --> 00:39:18.000 Now Connes gave it a noncommutative extension, a discrete extra-dimension. 00:39:18.000 --> 00:39:22.000 Not the usual third dimension, which would turn the sheet into a solid. 00:39:22.000 --> 00:39:26.000 Instead it gets a discrete extra-dimension. What does “discrete” mean? 00:39:26.000 --> 00:39:32.000 In length, width, and height, I can think of arbitrary lengths. 00:39:32.000 --> 00:39:39.000 When there are 10 cm, there are also 10.01 cm, or 10.275 cm, or whatever. 00:39:39.000 --> 00:39:44.000 In this discrete extra-dimension there are just only four points. 00:39:44.000 --> 00:39:50.000 A point in this extra-dimension can only be at one of four places. 00:39:50.000 --> 00:39:56.000 Taken together with the normal two dimensions, we get a universe consisting of four sheets. 00:39:56.000 --> 00:40:02.000 So this is a two-dimensional universe, consisting of four sheets. 00:40:02.000 --> 00:40:07.000 Well, what is it good for? 00:40:07.000 --> 00:40:12.000 Now we examine which kind of physics is admissable in this universe. 00:40:12.000 --> 00:40:17.000 This was achieved by Connes, Chamseddine, and others. 00:40:17.000 --> 00:40:24.000 I can recommend Mr. Schücker, who presented this in a way which can be understood well by physicists. 00:40:24.000 --> 00:40:31.000 Those who have studied physics have a chance to understand this. Oh – there is someone … 00:40:35.000 --> 00:40:45.000 Four-page world. A world consisting of four pages. The whole world consists of these four pages. 00:40:45.000 --> 00:40:53.000 Now we can examine what kind of physics is admissable on this world. What could happen there? 00:40:53.000 --> 00:41:00.000 The condition is: All forces are geometry. This is a generalisation of general relativity. 00:41:00.000 --> 00:41:05.000 On this world, essentially nothing happens, which is boring. 00:41:05.000 --> 00:41:09.000 Let's take this world. What is that? 00:41:09.000 --> 00:41:18.000 This M denotes Minkowski space. That's a four-dimensional world with length, width, height, and time. In other words, that's us. 00:41:18.000 --> 00:41:23.000 Now we attach additional sheets to this world. 00:41:23.000 --> 00:41:31.000 These are the 3×3 matrices over the complex numbers. These are the complex numbers themselves. 00:41:31.000 --> 00:41:38.000 And these are Hamilton's quaternions. Those who have attended my lecture “Algorithms and Data Structures“ might remember that I mentionend them briefly. 00:41:38.000 --> 00:41:45.000 So this is our world with additional sheets. Neat. 00:41:45.000 --> 00:41:52.000 Now when I do general relativity on this world, what kind of physics do I get? What is admissible? 00:41:52.000 --> 00:41:59.000 When I am lucky, I get general relativity again. Maybe we get something different. Let's see. 00:41:59.000 --> 00:42:03.000 We obtain a somewhat longer formula. 00:42:03.000 --> 00:42:07.000 It starts here and continues at the bottom. I am extracting it in isolation. 00:42:07.000 --> 00:42:12.000 So this is the admissible physics on this small formula we just saw. 00:42:12.000 --> 00:42:21.000 That small formula could be converted to this one. Neat. What does that do for us? What is that? 00:42:21.000 --> 00:42:26.000 This is the Standard Model of elementary particles, the Standard Model of quantum field theory. 00:42:26.000 --> 00:42:35.000 This tiny formula implies the whole Standard Model. When you deal with it for longer you can recognise it. 00:42:35.000 --> 00:42:47.000 Above there are quarks and leptons. These are the up quark, the down quark, and the electron. That's us. 00:42:47.000 --> 00:42:53.000 Then there are forces between them. This is the so-called electroweak interaction. 00:42:53.000 --> 00:43:01.000 That's both electromagnetism and the weak interaction in the atomic nuclei and even smaller elementary particles. 00:43:01.000 --> 00:43:05.000 This is the strong interaction which holds the atomic nuclei together. 00:43:05.000 --> 00:43:11.000 First, up and down quarks form protons and neutrons this way. 00:43:11.000 --> 00:43:15.000 Then it holds them together. So this is nuclear energy. 00:43:15.000 --> 00:43:24.000 And this is the Higgs mechanism, the Higgs boson and the mechanism which gives the particles mass. 00:43:24.000 --> 00:43:28.000 I consider this an extreme surprise. 00:43:28.000 --> 00:43:34.000 We take some tiny formula out of the air. We take a universe with some weird sheets. 00:43:34.000 --> 00:43:38.000 Then we get this formula, and it is perfectly correct. 00:43:38.000 --> 00:43:42.000 That's totally surprising. 00:43:42.000 --> 00:43:50.000 So from the third line on, this is the Standard Model of quantum field theory. 00:43:50.000 --> 00:43:56.000 Great. And what are the other lines? For instance what's that at the top? 00:43:56.000 --> 00:43:59.000 That's general relativity. 00:43:59.000 --> 00:44:08.000 In 1996, Connes and others have unified general relativity with quantum field theory. 00:44:08.000 --> 00:44:12.000 So this problem has been solved for a long time. 00:44:12.000 --> 00:44:16.000 Why is this unknown? Why didn't that guy get a Nobel Prize in Physics for that? 00:44:16.000 --> 00:44:22.000 Well, he got a Fields Medal, but for very different things. That's kind of a Nobel Prize in Mathematics. 00:44:22.000 --> 00:44:27.000 Why doesn't anybody know this theory? 00:44:27.000 --> 00:44:33.000 This theory has the same problem as general relativity itself has. It is said to be non-quantisable. 00:44:33.000 --> 00:44:43.000 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. 00:44:43.000 --> 00:44:48.000 Why is it unknown? Because it is non-quantisable. 00:44:48.000 --> 00:44:57.000 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. 00:44:57.000 --> 00:45:05.000 This is a so-called Feynman diagram, intended to depict how an electron and a muon exchange a graviton. 00:45:05.000 --> 00:45:14.000 This means: A tiny electron and an equally tiny muon interact via their gravity. 00:45:14.000 --> 00:45:23.000 This calculation method, using these diagrams, does not work as soon as general relativity comes into play. 00:45:23.000 --> 00:45:28.000 As it stands, noncommutative geometry does not change this. 00:45:28.000 --> 00:45:34.000 So he didn't solve a problem. He only wrote down something where it was clear already … 00:45:34.000 --> 00:45:39.000 Everyone can put a plus sign in between. Then why am I interested in this? 00:45:39.000 --> 00:45:46.000 In 2021 I developed, or completed, a different quantisation method. 00:45:46.000 --> 00:45:51.000 I have been researching this since 2009, and in 2021 I found: 00:45:51.000 --> 00:46:03.000 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. 00:46:03.000 --> 00:46:13.000 So I did not quantise gravity, but I gravitised non-gravity – or I geometrised it, or however you want to name it. 00:46:13.000 --> 00:46:19.000 This was a short version of my speech of 2021. 00:46:19.000 --> 00:46:24.000 Back then I stopped at the middle line. What is that? 00:46:24.000 --> 00:46:30.000 This is what I wrote on my transparency back then. This is new. Nobody knows what it is. 00:46:30.000 --> 00:46:41.000 But I found some hints in scientific articles that this might be dark matter in the form of modified gravity. 00:46:41.000 --> 00:46:50.000 I didn't pursue this. In 2021 I said that this should be addressed by someone who has already learned the ropes. 00:46:50.000 --> 00:46:56.000 Working my way into it would take way too long. I do not have that much time. 00:46:56.000 --> 00:47:02.000 Then I couldn't resist and read up the ropes, and I found: Yes, it is indeed dark matter. 00:47:02.000 --> 00:47:08.000 I'm sorry, but I accidentally solved this mystery on the side. 00:47:08.000 --> 00:47:16.000 What does all this mean? We have seen that the first line of that formula is general relativity. It looks like this. 00:47:16.000 --> 00:47:25.000 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. 00:47:25.000 --> 00:47:39.000 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. 00:47:39.000 --> 00:47:42.000 Now we must apply this to that. 00:47:42.000 --> 00:47:48.000 This was already done by Schwarzschild in 1915, and now we have a new formula. 00:47:48.000 --> 00:47:53.000 Now we must calculate the same again. Maybe we get a different force law. 00:47:53.000 --> 00:47:58.000 Fortunately I didn't have to do this by myself. This was done by … er … the names will appear soon … 00:47:58.000 --> 00:48:03.000 One is named Mannheim and the other one Kazanas or similar … 00:48:03.000 --> 00:48:11.000 “Kazanas” was correct. So a few years ago, Kazanas and Mannheim did that. 00:48:11.000 --> 00:48:16.000 They obtained this force law. 00:48:16.000 --> 00:48:24.000 It is really simple. If you look at this formula, and if you know what these R mean … they are really complicated … 00:48:24.000 --> 00:48:28.000 It is amazing that a force law this simple comes out. 00:48:28.000 --> 00:48:37.000 It is general relativity plus a constant force which does not depend on the distance. There is no r. 00:48:37.000 --> 00:48:45.000 This means that each of us – and our Sun – excerts a force on an object in the Andromeda galaxy. 00:48:45.000 --> 00:48:52.000 This does not sound very plausible, so the first thought is: Too bad. This theory must be wrong. 00:48:52.000 --> 00:48:56.000 In fact this constant force is extremely tiny. 00:48:56.000 --> 00:49:08.000 For our Sun I calculated a gravitational acceleration of 2.4·10⁻²² m/s². 00:49:08.000 --> 00:49:15.000 For comparison: The Earth has 9.81 m/s². That's much more powerful gravity. 00:49:15.000 --> 00:49:27.000 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. 00:49:27.000 --> 00:49:32.000 That's extremely extremely extremely tiny gravity. 00:49:32.000 --> 00:49:37.000 Then the second thought is: This might be correct, but who is interested in that? 00:49:37.000 --> 00:49:41.000 Such a tiny force does not cause anything. Nothing happens. 00:49:41.000 --> 00:49:47.000 Except: We consider something extremely big, like a galaxy cluster. 00:49:47.000 --> 00:49:57.000 In 1989, Kazanas and Mannheim calculated that this is a possible explanation for dark matter. 00:49:57.000 --> 00:50:02.000 This is one of the theories of modified gravity. 00:50:02.000 --> 00:50:08.000 So it has the same problems as all theories of modified gravity. 00:50:08.000 --> 00:50:19.000 The explanation of the virial theorem works with this kind of modified gravity. 00:50:19.000 --> 00:50:23.000 The rotation curves match perfectly. Excellent. 00:50:23.000 --> 00:50:31.000 Gravitational lenses do not match at all. We obtain utter rubbish. 00:50:31.000 --> 00:50:40.000 What kind of rubbish? The modified gravity is too strong and at the wrong place. 00:50:40.000 --> 00:50:49.000 Now we are back where we were. But something is different. My first thought when I saw this formula was … 00:50:49.000 --> 00:50:54.000 Okay, later. First, let me show why it is utter rubbish. The modified gravity is too strong. 00:50:54.000 --> 00:51:01.000 I have selected a paper by Dutta and Islam from 2018. 00:51:01.000 --> 00:51:14.000 They have calculated for the galaxy cluster Abell 1689, which I already presented, how big the calculated gravity must be. 00:51:14.000 --> 00:51:22.000 We calculate the gravity for this galaxy cluster. Depending on how we calculate we get one of these blue curves. 00:51:22.000 --> 00:51:29.000 They are about the same. Using two different models we find out that the curve goes like this. 00:51:29.000 --> 00:51:34.000 Now we compare it to the measured curve. 00:51:34.000 --> 00:51:43.000 When we evaluate gravitational lenses, look for circles on Hubble images and calculate how strong the gravity must be, 00:51:43.000 --> 00:51:53.000 then we obtain this curve. These are two workgroups, one around Limousin and one around Umetsu, French and Japanese astronomers. 00:51:53.000 --> 00:51:57.000 There are many more curves. I will show some later. 00:51:57.000 --> 00:52:05.000 They measured this curve. Well, that's not exactly a good match. 00:52:05.000 --> 00:52:10.000 Even with a lot of phantasy one would not claim that this calculation was correct. 00:52:10.000 --> 00:52:18.000 It goes really, really wrong. The gravity is way to strong, as we see here. 00:52:18.000 --> 00:52:24.000 The curve is going up. It should go down. What is going wrong here? 00:52:24.000 --> 00:52:35.000 Now comes my thought. This L, this Lagrange density contains an R. This other one contains an R². 00:52:35.000 --> 00:52:43.000 And this and that are kind of R², too. So this L contains kind of R² three times. 00:52:43.000 --> 00:52:51.000 This R denotes gravity. It is the Ricci scalar of curvature. 00:52:51.000 --> 00:53:00.000 This is the Riemann tensor, and this is the Ricci tensor. All these R denote gravity, curvature of space. 00:53:00.000 --> 00:53:07.000 How curved is our space? When I look around, I do not really perceive it as curved, but mostly straight. 00:53:07.000 --> 00:53:12.000 This means that this R is tiny. 00:53:12.000 --> 00:53:17.000 Space curvature means that when I step to the right, and suddenly the time is different. 00:53:17.000 --> 00:53:23.000 Or I go two metres forward and end up behind myself or something like that. We do not have such effects. 00:53:23.000 --> 00:53:29.000 When we calculate this R we get a really tiny number. 00:53:29.000 --> 00:53:34.000 Now this contains R², which then is even much smaller. 00:53:34.000 --> 00:53:44.000 For instance if R is 1/1000, then R² is 1/1000000. In fact it is even much smaller than that. 00:53:44.000 --> 00:53:53.000 From this I conclude that this so-called conformal gravity, this new formula for gravity, is only relevant when the gravity is very strong. 00:53:53.000 --> 00:54:00.000 When is gravity strong? For instance when we approach the Sun. 00:54:00.000 --> 00:54:06.000 On Earth we can still say: Something fell on my head. So gravity is strong. 00:54:06.000 --> 00:54:11.000 In an intergalactic gas cloud, gravity is not strong, but rather weak. 00:54:11.000 --> 00:54:16.000 This means, my first conclusion when I saw this formula was: 00:54:16.000 --> 00:54:21.000 Conformal gravity holds for stars, but not for gas clouds. They do not take part. 00:54:21.000 --> 00:54:26.000 They are too light – per volume. They are not dense enough. 00:54:26.000 --> 00:54:34.000 In several papers I read that there is no real difference between stars and gas clouds. Both are masses. 00:54:34.000 --> 00:54:39.000 Those who say there is no difference should try to fly across them. 00:54:39.000 --> 00:54:45.000 When you fly across a gas cloud, you do not feel it. It is too tenuous. 00:54:45.000 --> 00:54:52.000 When you try to fly across a star, you do feel it. Better don't do that. 00:54:52.000 --> 00:54:56.000 Using this, we can explain the remaining parts. 00:54:56.000 --> 00:55:03.000 We can explain the graviational lensing effect being too strong, and we can even explain the Bullet Cluster. 00:55:03.000 --> 00:55:07.000 I will show you. 00:55:07.000 --> 00:55:12.000 This is Abell 1689 again and a lot of measured curves. 00:55:12.000 --> 00:55:20.000 This time I took the surface mass density rather than gravitational acceleration. 00:55:20.000 --> 00:55:27.000 There are more data for this. One is by … oh, now I must speak Dutch … Nieuwenhuizen. 00:55:27.000 --> 00:55:37.000 Alamo-Martínez et al., Umetsu, Broadhurst, … there are many measured curves. 00:55:37.000 --> 00:55:42.000 The red curve was calculated by myself. 00:55:42.000 --> 00:55:50.000 I do not claim that it matches the data perfectly, but it is not worse than the other curves. It blends in quite well. 00:55:50.000 --> 00:55:56.000 The curves do not really agree. Some are lower, some are higher. 00:55:56.000 --> 00:56:02.000 It is not perfect, but it matches quite well. Much worse curves have been praised in the news: 00:56:02.000 --> 00:56:08.000 “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. 00:56:08.000 --> 00:56:18.000 It is quite good. I calculated it for two more galaxy clusters, too, and it looks quite similar. It really fits. 00:56:18.000 --> 00:56:27.000 I calculated it for three galaxy clusters. Each time I obtained a curve which fits the data quite well. So this might be correct. 00:56:27.000 --> 00:56:36.000 Now let's take the Bullet Cluster. Above we see again the image by Clowe et al. from 2006. 00:56:36.000 --> 00:56:47.000 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. 00:56:47.000 --> 00:56:56.000 Now I used my formula to calculate where the biggest gravity is. It is here and there. 00:56:56.000 --> 00:57:06.000 The images do not match perfectly, but I can say with an easy conscience that there is some similarity between them. 00:57:06.000 --> 00:57:14.000 So the Bullet Cluster, too, can be explained using modified gravity, using so-called conformal gravity, 00:57:14.000 --> 00:57:20.000 which emerges as a side product from noncommutative geometry. 00:57:20.000 --> 00:57:26.000 We are virtually perfectly on schedule. This is what I wanted to tell you. 00:57:26.000 --> 00:57:37.000 I accidentally found a new explanation for dark matter because of my interest in noncommutative geometry. 00:57:37.000 --> 00:57:42.000 So far my results suggest that this explanation is correct. 00:57:42.000 --> 00:57:48.000 This is of course not the end of this story. I will verify this further. 00:57:48.000 --> 00:57:53.000 For instance that image of the Bullet Cluster is not similar enough for my taste. Something is still wrong. 00:57:53.000 --> 00:58:00.000 Probably I am overlooking some small thing. For instance there is one problem … 00:58:00.000 --> 00:58:08.000 I am calculating the gravity from the stars. For this we must know where the stars are. 00:58:08.000 --> 00:58:19.000 For instance when I look at that point, is that a big galaxis farther away or a small galaxis which is closer? 00:58:19.000 --> 00:58:24.000 That's not really clear. Now when I consult literature … 00:58:24.000 --> 00:58:33.000 Well, gravitational lensing … gas clouds … okay, stars exist, too, but the gravitational lens is much more interesting. 00:58:33.000 --> 00:58:37.000 You do not find anything about stars. I have the impression that astronomers do not like stars. 00:58:37.000 --> 00:58:44.000 They like gas clouds, black holes, gravitational lenses, neutron stars. But plain stars bustling about … 00:58:44.000 --> 00:58:50.000 It is really difficult to find out which of them belong to the galaxy cluster and which ones do not. 00:58:50.000 --> 00:58:54.000 In any case I have to check this further. 00:58:54.000 --> 00:58:58.000 I am, however, somewhat confident about this. 00:58:58.000 --> 00:59:07.000 First, I must build up my understanding how to check which stars belong to the cluster and which ones do not. 00:59:07.000 --> 00:59:13.000 The more I learn about this, the better my results get. So it looks good so far. 00:59:13.000 --> 00:59:21.000 One day, I will have something I can write down and publish. Then it will appear in the journals. 00:59:21.000 --> 00:59:27.000 So far this has not been published anyware. This speech was the first time I went public with this. 00:59:27.000 --> 00:59:37.000 With this I thank you for your attendance. I am now available for your questions. Thank you.