WEBVTT Kind: captions Language: en 00:00:39.000 --> 00:00:44.000 6 · 9 = 42 My Search for the Theory of Everything Prof. Dr. rer. nat. Peter Gerwinski 10 May 2021 00:00:45.000 --> 00:00:54.000 Good evening. Welcome to my speech about: 6 · 9 = 42. My Search for the Theory of Everything. 00:00:54.000 --> 00:01:00.000 That's a weird title. I'll start by explaining where it comes from. 00:01:00.000 --> 00:01:09.000 That's a quote from the novel The Hitchhiker's Guide to the Galaxy by Douglas Adams, a science fiction parody. 00:01:09.000 --> 00:01:19.000 There, philophers ask a computer: “What's the answer to the ultimate question of life, the universe, and everything.” 00:01:19.000 --> 00:01:25.000 The computer calculates for 7½ million years and then answers: “42.” 00:01:25.000 --> 00:01:31.000 The philosophers aren't really enthusiastic about this. Then the computer explains: 00:01:31.000 --> 00:01:35.000 “I think the problem is that you've never actually known what the question is.” 00:01:35.000 --> 00:01:41.000 Then the philosophers build an even bigger computer, and … 00:01:41.000 --> 00:01:47.000 Okay, now I'm spoilering the contents of the novel and of the movies. 00:01:47.000 --> 00:01:52.000 At the end of the second book the question appears, and it reads: “What is 6 times 9?” 00:01:52.000 --> 00:01:59.000 After that the leading character says: “I always thought something was fundamentally wrong with the universe.” 00:01:59.000 --> 00:02:03.000 Thus ends volume 2 of the 5-volume trilogy. 00:02:03.000 --> 00:02:16.000 This is about physics. My question is somewhat more humble: “What are the laws of nature?” That's what physics deals with. 00:02:16.000 --> 00:02:22.000 The current state of research reads: One theory explains everything which is big. 00:02:22.000 --> 00:02:30.000 That's general relativity. It explains the universe as a whole, black holes and things of comparable size. 00:02:30.000 --> 00:02:37.000 And we have quantum field theory, which explains the smallest parts of the universe. 00:02:37.000 --> 00:02:42.000 Quarks, leptons, and the Higgs boson fall within this scope. 00:02:42.000 --> 00:02:46.000 Both theories describe medium-sized objects. 00:02:46.000 --> 00:02:51.000 A microbe or a planet – seen from both theories they are about medium-sized. 00:02:51.000 --> 00:02:59.000 You can choose one of both theories to describe medium-sized things. 00:02:59.000 --> 00:03:03.000 Both contain so-called classical physics. 00:03:03.000 --> 00:03:09.000 This raises the question why we cannot use both theories together. 00:03:09.000 --> 00:03:13.000 As everyone knows, noone has yet succeeded on this. 00:03:13.000 --> 00:03:16.000 You cannot combine these theories. 00:03:16.000 --> 00:03:20.000 When you ask an expert why not you get the answer: 00:03:20.000 --> 00:03:25.000 “Quantisation of gravity leads to non-renormaliseable divergences.” 00:03:25.000 --> 00:03:29.000 Uh-huh. What is this supposed to mean? 00:03:29.000 --> 00:03:34.000 Where precisely lies the insurmountable contradiction? 00:03:34.000 --> 00:03:41.000 I studied physics, and I asked this question to several people, but I didn't get a satisfying answer. 00:03:41.000 --> 00:03:46.000 In the year when I turned 42 I decided that I want to find out by myself. 00:03:46.000 --> 00:03:52.000 I want to actually know what the problem is. What is the question? 00:03:52.000 --> 00:03:58.000 My approach: I try to unify both theories. 00:03:58.000 --> 00:04:03.000 Then I'll see where I run into a dead end. 00:04:03.000 --> 00:04:09.000 And what I found out thereby is what I want to speak about today. 00:04:09.000 --> 00:04:16.000 This implies that I must summarise all of physics in this speech. 00:04:16.000 --> 00:04:18.000 It is scheduled for about 1 hour. 00:04:18.000 --> 00:04:30.000 I'll explain all of physics today, classical physics, special and general relativity, and quantum physics, up to quantum field theory. 00:04:30.000 --> 00:04:37.000 After that we can address the question: What is quantum gravity? Where's the problem? 00:04:37.000 --> 00:04:44.000 And then I can tell what I found out and how my research might continue after this. 00:04:44.000 --> 00:04:49.000 Okay. We start in ancient Greece. 00:04:49.000 --> 00:04:59.000 Back then, Aristotle was one of the first who asked how things move. 00:04:59.000 --> 00:05:06.000 Why do things fall down, but fire goes up, air goes up, water and earth go down. 00:05:06.000 --> 00:05:10.000 His explanation: These are the four elements everything consists of. 00:05:10.000 --> 00:05:18.000 Birds can fly because their feathers contain a high amount of the element air. 00:05:18.000 --> 00:05:23.000 This theory explains, more or less, how things move on Earth. 00:05:23.000 --> 00:05:34.000 But when you look at the sky you see things orbiting around the Earth: the stars, the Sun, and the Moon. 00:05:34.000 --> 00:05:39.000 Aristotle's explanation: This is something entirely different. 00:05:39.000 --> 00:05:47.000 Sky objects don't consist of fire, water, earth, and air. 00:05:47.000 --> 00:05:56.000 They consist of a fifth element, quintessence, or aether. Things consisting of aether move in circles. 00:05:56.000 --> 00:06:08.000 It took over 2000 years until somone succeeded to resolve this contradiction that sky objects move entirely differently than objects on Earth. 00:06:08.000 --> 00:06:21.000 In 1686, Newton described in his Mathematical Principles of Natural Philosophy that both is in fact the same. 00:06:21.000 --> 00:06:31.000 The fall of a thing on the Earth and the orbit of the Moon around the Earth are in fact the same thing, caused by gravity. 00:06:31.000 --> 00:06:39.000 Here we see Newton's law of gravity. Don't worry, you don't need to understand and to memorise all these formulas, … 00:06:39.000 --> 00:06:42.000 … except if you are studying at our university. 00:06:42.000 --> 00:06:50.000 Gravity depends on the distance between the two things which attract each other, … 00:06:50.000 --> 00:06:57.000 … and from the two masses. This G is the gravitational constant. The important thing is that it depends on the distance. 00:06:57.000 --> 00:07:06.000 On the left we see a force. Using this, Newton calculated how things move. 00:07:06.000 --> 00:07:11.000 For this purpose he developed a new calculation method, the so-called differential equation. 00:07:11.000 --> 00:07:19.000 “Differential equation” means: How it is now tells us how it changes. 00:07:19.000 --> 00:07:27.000 Here we see an important special case of Newton's equation of motion: force = mass · acceleration. 00:07:27.000 --> 00:07:31.000 Acceleration tells us how the velocity changes. Velocity tells us how the position changes. 00:07:31.000 --> 00:07:36.000 How it is now, the force, tells us, how it changes. 00:07:36.000 --> 00:07:44.000 Newton had great difficulties to solve this differential equation using pen and paper. Of course. He had just invented this. 00:07:44.000 --> 00:07:50.000 Today this is much easier. I can simply ask my computer to solve this differential equation for me. 00:07:50.000 --> 00:07:54.000 That's what I'm doing now. 00:07:54.000 --> 00:08:01.000 Here we see the simulation of a ball lying on top of a tower. 00:08:01.000 --> 00:08:12.000 When I poke it, it flies to the side in a characteristic curve, a so-called parabola, the ballistic trajectory. 00:08:12.000 --> 00:08:20.000 The computer has calculated this using the differential equation we just have seen. 00:08:20.000 --> 00:08:28.000 Now I can make the tower higher, so the Earth's curvature comes into play. 00:08:28.000 --> 00:08:36.000 Again the ball falls down, essentially describing a parabola – not entirely, but very similar. 00:08:36.000 --> 00:08:39.000 I can make the tower even higher. 00:08:39.000 --> 00:08:50.000 When I poke the ball with sufficient thrust, I can reach regions behind the horizon. In some sense, I can throw the ball around the earth. 00:08:50.000 --> 00:09:03.000 When I go even further, I can literally throw the ball around the Earth. Now the ball describes an elliptic orbit around the Earth. 00:09:03.000 --> 00:09:10.000 It precisely returns to the point where I threw it, and it will orbit around the Earth forever. 00:09:10.000 --> 00:09:22.000 When I do this in the right distance and with the right velocity I get a circular orbit of an object, for instance the Moon, around the Earth. 00:09:22.000 --> 00:09:31.000 This way Newton has shown that both is indeed the same: motion on Earth and motion in the sky. 00:09:34.000 --> 00:09:42.000 What else is part of classical physics? A very important thing is the principle of relativity, established by Galilei in 1632. 00:09:42.000 --> 00:09:53.000 Imagine you are in a train. Someone is walking inside the train – in hurry, at 10 km/h, in the direction of travel. 00:09:53.000 --> 00:09:58.000 Sitting in the train I can say: He's walking at 10 km/h, rather fast. 00:09:58.000 --> 00:10:04.000 Now the train is moving as well, at 100 km/h. 00:10:04.000 --> 00:10:13.000 Then an observer at the station can say: He's passing the station at 110 km/h. 00:10:13.000 --> 00:10:22.000 And the walking person can say: When I look outside I can see the ground departing backwards at 110 km/h. 00:10:22.000 --> 00:10:29.000 And all three of them are right. That's the principle of relativity: Everything is relative. 00:10:29.000 --> 00:10:37.000 That's quite simple, but there is a problem. Light doesn't act that way. 00:10:37.000 --> 00:10:42.000 In 1810 Arago was the first to measure that … 00:10:42.000 --> 00:10:47.000 When I depart from a star, its light should reach me more slowly. 00:10:47.000 --> 00:10:55.000 Or when a star approaches me, or the Earth is approaching the star along its way around the Sun, the light should be faster. 00:10:55.000 --> 00:10:59.000 He measured, however, that the light has always the same speed, whatever I do. 00:10:59.000 --> 00:11:06.000 In 1887, Michelson and Morley ascertained this extremely precisely in their famous experiment. 00:11:06.000 --> 00:11:13.000 It is really like this: The light has always the same speed, whatever I do, however I try to accelerate it. 00:11:13.000 --> 00:11:20.000 The light in the vacuum. It's slower in glass, but I cannot make it faster, whatever I do. 00:11:20.000 --> 00:11:24.000 This contradicts Galilei's theory of relativity. 00:11:24.000 --> 00:11:34.000 An explanation was found by Einstein in 1905. He said: Our measurements weren't wrong. 00:11:34.000 --> 00:11:39.000 Instead our perceptions of space and time are wrong. 00:11:39.000 --> 00:11:47.000 Space and time depend on the observer. In particular: When you move, your time goes slower. 00:11:47.000 --> 00:11:55.000 This sounds incredible at first, but it fits the measurements. And later it has been checked directly. 00:11:55.000 --> 00:11:59.000 In 1971 there was the Hafele-Keating experiment. 00:11:59.000 --> 00:12:10.000 They put an atomic clock into an aircraft and let it fly around the whole earth, both clockwise and counterclockwise. 00:12:10.000 --> 00:12:16.000 After that they compared the time shown by this atomic clock to the time shown by another atomic clock which had remained on the ground. 00:12:16.000 --> 00:12:27.000 The atomic clocks showed that the time passed in the aircraft was one tenth of a millionth part of a second shorter than the time passed on ground. 00:12:27.000 --> 00:12:34.000 This sounds incredible. That's a very short time. Probably their measurement was errorneous … nope. Atomic clocks are this precise. 00:12:34.000 --> 00:12:37.000 In fact, seen from today, this is a quite normal time interval. 00:12:37.000 --> 00:12:42.000 Today's computers are calculating in the range of some gigahertz. 00:12:42.000 --> 00:12:52.000 A gigahertz corresponds to 1 billionth of a second. This means that within a tenth of a millionth of a second, a computer can do 100 things. 00:12:52.000 --> 00:12:56.000 This is clearly measurable. 00:12:56.000 --> 00:13:03.000 In the International Space Station which circles around the Earth every 90 minutes, this effect is much bigger. 00:13:03.000 --> 00:13:10.000 There you can measure it using an ordinary stop watch. Over there, 1/100th second per year passes less than on Earth. 00:13:10.000 --> 00:13:19.000 So it seems to be correct what Einstein came up with to explain the weird behaviour of the light. 00:13:19.000 --> 00:13:32.000 Now you can carry on calculating. When you move, your time passes slower. And when you move with the speed of light, your time comes to a hold. 00:13:32.000 --> 00:13:39.000 And when you move even faster than light, your time passes backwards. 00:13:39.000 --> 00:13:52.000 This can be a problem. From “Back to the Future” we know what can happen when you travel to the past and disrupt the romance of your own parents. 00:13:52.000 --> 00:14:02.000 This can reduce the probability of your own birth. A time travel to the past can lead to paradoxa. 00:14:02.000 --> 00:14:08.000 Travelling faster than light is the same as travelling to the past. 00:14:08.000 --> 00:14:15.000 When you travel faster than light you end up in the past, which can lead to problems. 00:14:15.000 --> 00:14:21.000 The same holds when it is not a human travelling faster than light, but just information. 00:14:21.000 --> 00:14:29.000 For instance if I send a message to my father telling “Keep the hands off that woman!” this might lead to problems. 00:14:29.000 --> 00:14:36.000 Information and objects may travel at most with the speed of light, otherwise we end up in the past and run into problems. 00:14:36.000 --> 00:14:48.000 But what happens if I'm in a train which already moves with 75% of the speed of light, and I run forward with another 75% of the speed of light? 00:14:48.000 --> 00:14:54.000 Then I should have, seen from the station, 150% of the speed of light. 00:14:54.000 --> 00:15:00.000 I don't. We can measure it. We can calculate it and measure it. 00:15:00.000 --> 00:15:12.000 Seen from the station you “only” run with 96% of the speed of light. In no event you can surpass the speed of light. 00:15:12.000 --> 00:15:15.000 This can be measured. 00:15:15.000 --> 00:15:27.000 That's how nature is like, whether we understand it or not. Of course our brains are not made for understanding such things, but we can calculate it. 00:15:27.000 --> 00:15:37.000 But now we have a problem with Newton. The gravitational force, for instance that of the Sun, only depends on the distance. 00:15:37.000 --> 00:15:46.000 If the Sun jumps by 1m, its gravity which affects me must change without any delay. 00:15:46.000 --> 00:15:51.000 But that mustn't be. Then it would move faster than light. 00:15:51.000 --> 00:16:04.000 So we need a new theory of gravity. That's general relativity, developed by Einstein as well. 00:16:04.000 --> 00:16:12.000 Special relativity plus gravity yields general relativity. How to approach this? 00:16:12.000 --> 00:16:20.000 Einstein used the equivalence principle, which says that inertial and gravitational mass are the same. 00:16:20.000 --> 00:16:24.000 What does that mean? 00:16:24.000 --> 00:16:32.000 When an aircraft takes off you feel like pressed into your seat due to the acceleration. 00:16:32.000 --> 00:16:38.000 “Inertial and gravitational mass are the same.” means: “Acceleration feels like gravity.” 00:16:38.000 --> 00:16:42.000 This is taken advantage of in, for instance, flight simulators. 00:16:42.000 --> 00:16:51.000 When I tilt the simulator, raising its nose, I feel like being pressed into my seat, so I feel that the aircraft is accelerating. 00:16:51.000 --> 00:16:58.000 Now Einstein says: This doesn't just feel alike. This is indeed the same. 00:16:58.000 --> 00:17:04.000 This is the so-called equivalence principle, and it has enourmous consequences. 00:17:04.000 --> 00:17:16.000 When I move without forces, for instance when I go by car straight ahead, then I feel that I'm not following a bend. I would feel the bend. 00:17:16.000 --> 00:17:23.000 Moving straight ahead means to move without forces, and moving without forces means to move straight ahead. 00:17:23.000 --> 00:17:35.000 But we have orbits. There is zero gravity. That's without forces. This should imply that you move straight ahead. 00:17:35.000 --> 00:17:49.000 Yes, that's what you do. An orbit is straight ahead. Not in normal space, but in a four-dimensional, curved space-time. 00:17:49.000 --> 00:17:59.000 The curvature of four-dimensional space-time is a gemetrical effect, but we perceive it as a force, gravity. 00:17:59.000 --> 00:18:05.000 How can we imagine this? 00:18:10.000 --> 00:18:20.000 Imagine you are on the surface of a big sphere, and you cannot depart from that surface just like that. 00:18:20.000 --> 00:18:28.000 Now we start two aircrafts from the equator precisely heading south. 00:18:28.000 --> 00:18:40.000 Both take care that they don't fly any bends. Then they will, of course, meet at the south pole. 00:18:40.000 --> 00:18:51.000 Then the two pilots can communicate: “Did you fly a bend?” “No. Did you?” “No. Then maybe there is an attracting force between our aircrafts.” 00:18:51.000 --> 00:18:58.000 But we know better. This is not an attractive force. It's a geometric effect. This is geometry on the surface of a sphere. 00:18:58.000 --> 00:19:08.000 That's how gravity works. It's just not the two-dimensional curved surface of a sphere, but four-dimensional, curved space-time. 00:19:08.000 --> 00:19:17.000 This can easily overcharge our brains, but we can calculate everything, and the results are amazingly correct. 00:19:17.000 --> 00:19:22.000 Here we see again Newton's formulas. What did Einstein improve? 00:19:22.000 --> 00:19:30.000 The problem is this “normal” equation. The differential equation is okay, for it contains the time. 00:19:30.000 --> 00:19:34.000 How it is tells us how it changes. A change implies time. 00:19:34.000 --> 00:19:40.000 This equation says: How it is tells us how it is. So we must replace this equation by a differential equation. 00:19:40.000 --> 00:19:46.000 That's what Einstein did. The equations he found we are now calling Einstein's field equations. 00:19:46.000 --> 00:19:56.000 This is “force = mass · acceleration”. This didn't change much. However this second equation looks totally different. 00:19:56.000 --> 00:20:03.000 For the experts: This is a differential equation because these terms contain the derivatives of g. 00:20:03.000 --> 00:20:12.000 You don't need to memorise now how these equations look like or what they mean. Just remember: I like differential equations. 00:20:12.000 --> 00:20:20.000 In particular you can use this equation to calculate gravity without getting into trouble with the speed of light. 00:20:20.000 --> 00:20:31.000 So this works. We can describe it mathematically using an equation. Now, what can we do with it? Can we use it to calculate something? 00:20:31.000 --> 00:20:43.000 Yes, we can. One year later, Schwarzschild was the first to solve Einstein's field equations. He found out how gravity around a star works. 00:20:43.000 --> 00:20:55.000 Good news: When the star is not too strong, for instance our Sun is too small for that, everything is essentially the same as with Newton. 00:20:55.000 --> 00:20:59.000 There are small deviations. We can measure them, and they are correct. 00:20:59.000 --> 00:21:09.000 That's good news. But what happens when the star is much heavier than our Sun? Then very strange things happen. 00:21:09.000 --> 00:21:19.000 When you approach the star to its so-called Schwarzschild radius, then space and time interchange their meanings. 00:21:19.000 --> 00:21:28.000 You fall on the star, and when you have passed the Schwarzschild radius, then the direction of the fall is the new direction of time. 00:21:28.000 --> 00:21:38.000 The fall into the black hole, that's how this kind of stars is called, becomes the new time. What used to be time, becomes normal space. 00:21:38.000 --> 00:21:46.000 Now you could travel to the future and to the past just like that, but you don't get anything out of it since you are inevitably falling into the black hole. 00:21:46.000 --> 00:21:52.000 You cannot escape because for that you would have to travel backwards in time. 00:21:52.000 --> 00:21:58.000 So you reach the centre of the black hole, and there is a so-called singularity in the equations. 00:21:58.000 --> 00:22:02.000 The formulas yield infinity. You cannot reasonably calculate with this. 00:22:02.000 --> 00:22:08.000 This is where the validity of general relativity ends. 00:22:08.000 --> 00:22:12.000 If we want to calculate further, we need a new theory. 00:22:12.000 --> 00:22:21.000 People looked at these results and concluded: We must have miscalculated. This cannot be. 00:22:21.000 --> 00:22:28.000 So we are searching for errors in our calculations. We are searching for errors in general relativity. 00:22:28.000 --> 00:22:34.000 Instead we found – black holes. 00:22:49.000 --> 00:22:55.000 In 1973 this object got discovered. We call it Cygnus X-1. 00:22:55.000 --> 00:23:04.000 It is the invisible companion of a blue giant star, and it absorbs that star. 00:23:04.000 --> 00:23:11.000 It's extremely massive. It weights 21 times as much as our Sun. 00:23:11.000 --> 00:23:25.000 But it's scarily small. We can calculate its Schwarzschild radius as 50km. Within this radius of 50km there is 21 times the mass of our Sun. 00:23:25.000 --> 00:23:30.000 There is no other choice. This cannot be anything else but a black hole. 00:23:30.000 --> 00:23:43.000 Meanwhile we know of more black holes. A very big one is in the centre of the Milky Way. We call it Sagittarius A-star. 00:23:43.000 --> 00:23:50.000 In 2002 one has cleared the last doubts that this is a black hole. 00:23:50.000 --> 00:24:01.000 One has measured the orbit of a star named S2 and found that it made a U-turn within just a few months. 00:24:01.000 --> 00:24:10.000 S2 is much heavier than our Sun, but it got tossed around like a ping pong ball by something in the centre, which is invisible. 00:24:10.000 --> 00:24:14.000 Since it is that mighty, it can be nothing else than a black hole. 00:24:14.000 --> 00:24:19.000 It has 4.3 million times the mass of our Sun. 00:24:19.000 --> 00:24:26.000 It's also bigger than 50km. It has a Schwarzschild radius of 22 millions of km. 00:24:26.000 --> 00:24:34.000 For comparison: The orbit of the Earth around the Sun has a distance of about 150 millions of km between the Earth and the Sun. 00:24:34.000 --> 00:24:39.000 But there are even much bigger ones, for instance this one. 00:24:39.000 --> 00:24:48.000 This black hole got photographed in 2019. We call it M87-star. 00:24:48.000 --> 00:24:58.000 This black hole got photographed in 2019. Why this one? Why not Sgr A*? That would be just next door. Or Cygnus X-1, which is even much closer. 00:24:58.000 --> 00:25:04.000 This thing is 1000 times as far as Sgr A*, but it is also 1000 times as big. 00:25:04.000 --> 00:25:08.000 Its mass is 6.5 billion times the mass of our Sun. 00:25:08.000 --> 00:25:18.000 Its Scharzschild radius is 120 astronomical units, 120 times the diameter of the orbit of the Earth around the Sun, bigger than the orbit of Pluto. 00:25:18.000 --> 00:25:25.000 One has interconnected the whole Earth to form one big radio telescope in order to take this photo. 00:25:25.000 --> 00:25:43.000 It is so big that it appears from Earth at the same size as Sgr A* in our own galaxy, although it is located in the far galaxy M87. Thus we call it M87*. 00:25:43.000 --> 00:25:49.000 What else can we calculate using Einstein's field equations? 00:25:49.000 --> 00:26:03.000 We can calculate backwards in time. How did everything around us come into existence? This leads us to the so-called Big Bang. 00:26:03.000 --> 00:26:12.000 When you calculate back far enough into the past, you reach, again, a so-called singularity. Then the equations yield infinity. 00:26:12.000 --> 00:26:22.000 This means that there was a second 0. From that point you cannot calculate backwards any further. At that point, time begins. 00:26:22.000 --> 00:26:30.000 At least we cannot use general relativity to calculate further into the past. That's when our universe emerged. 00:26:30.000 --> 00:26:37.000 The state just 1 thousandth of a second after the Big Bang can be calculated very well using general relativity. 00:26:37.000 --> 00:26:45.000 We can use general relativity to calculate how our universe came into existence. 00:26:47.000 --> 00:26:52.000 However there are also things we cannot yet calculate using general relativity. 00:26:52.000 --> 00:27:03.000 One of our unsolved mysteries is the so-called dark matter. I'm now trying to show you a film. Let's hope that you can see it in a moment … 00:27:18.000 --> 00:27:25.000 Okay, now you should at least see the two galaxise on my desktop, as still images. 00:27:25.000 --> 00:27:32.000 Now you can see two galaxies. They look alike because they don't move. 00:27:32.000 --> 00:27:43.000 The left image has been calculated using general relativity. The core is rotating fast. I'm trying to visualise this using my cursor. 00:27:43.000 --> 00:27:51.000 The outer stars are moving slowly. They are going round gently. 00:27:51.000 --> 00:27:57.000 This is also visualised as a curve. In the middle the stars are fast, in the outer regions they are slow. 00:27:57.000 --> 00:28:04.000 This was calculated using general relativity. However what we actually measure is an entirely different behaviour. 00:28:04.000 --> 00:28:10.000 The core is rotating fast, and the outer stars are moving as fast as the core. 00:28:10.000 --> 00:28:18.000 The velocity of the outer stars is the same as that of the inner ones. This contradicts general relativity. 00:28:18.000 --> 00:28:26.000 Here we have a mystery of our time, which we cannot yet explain. There must be something. 00:28:26.000 --> 00:28:30.000 We don't know what it is, but we call it dark matter. 00:28:30.000 --> 00:28:44.000 It might be actual matter. According to some other theories there are corrections to general relativity. In any case it is an unsolved mystery of our time. 00:28:44.000 --> 00:28:52.000 Thus we have reached the end of the first part of my speech, about general relativity. 00:28:52.000 --> 00:28:58.000 It says: Gravity is curvature of the four-dimensional space-time, and thus geometry. 00:28:58.000 --> 00:29:04.000 We have seen the limits of the theory. One is the emergence of the universe, the Big Bang. 00:29:04.000 --> 00:29:14.000 Another one is the centre of a black hole, where space and time simply end. Here the theory yields infinity, and we cannot calculate any further. 00:29:14.000 --> 00:29:19.000 And one of the unsolved mysteries is dark matter. 00:29:19.000 --> 00:29:29.000 Are there any comprehension questions so far, before we proceed to dealing with the smallest parts of the universe? 00:29:29.000 --> 00:29:33.000 You may ask questions now. 00:29:42.000 --> 00:29:45.000 This doesn't sound like any need of questions. 00:29:45.000 --> 00:29:51.000 So I suppose that you have grasped general relativity. 00:29:51.000 --> 00:29:57.000 We now leave the biggest things in the universe and proceed to the smallest ones. 00:29:57.000 --> 00:30:03.000 Again we start in ancient Greece, with Democritus. 00:30:03.000 --> 00:30:11.000 In about 420 BC, Democritus observed that when things decay, always something remains. 00:30:11.000 --> 00:30:18.000 For instance when an animal dies, it decays to earth, out of which plants can grow. 00:30:18.000 --> 00:30:26.000 From this Democritus concluded that there is something which cannot be devided any further, of which everything consists of. 00:30:26.000 --> 00:30:37.000 He named it “átomos” in his language, which means “indivisible”. That's why we still refer to the smallest parts of matter as “atoms”. 00:30:37.000 --> 00:30:50.000 Democritus: “By convention sweet is sweet, bitter is bitter, hot is hot, cold is cold, color is color; but in truth there are only atoms and the void.” 00:30:50.000 --> 00:30:58.000 It took over 2000 years until evidence was found that these atoms actually exist. 00:30:58.000 --> 00:31:04.000 In 1803 Dalton investigated the ratios of quantities in chemical reactions. 00:31:04.000 --> 00:31:10.000 For instance, when I let oxygen and hydrogen react, how much water do I get? 00:31:10.000 --> 00:31:15.000 When I take too much oxygen, that oxygen will be left over. 00:31:15.000 --> 00:31:21.000 I can implement chemical reactions only with the same ratios of quantities. 00:31:21.000 --> 00:31:29.000 Dalton took this as an evidence that these “atoms” actually exist. 00:31:29.000 --> 00:31:37.000 He found out that a carbon atom can bond with either one or two oxygen atoms. 00:31:37.000 --> 00:31:42.000 He found out there there are carbon monoxide and carbon dioxide. 00:31:42.000 --> 00:31:58.000 So there are specific rules how these atoms relate to each other, how they can react with each other, and what are the reaction products. 00:31:58.000 --> 00:32:04.000 During the next decades these rules have been investigated further. 00:32:04.000 --> 00:32:15.000 In the 1860s, various scientists found several relations and rules for the atoms. 00:32:15.000 --> 00:32:24.000 This culminated in the periodic table of elements, which is valid until today. It is depicted here in its modern form. 00:32:24.000 --> 00:32:32.000 Today we know 118 atoms and the rules how they relate to each other and which ones bond with which ones. 00:32:32.000 --> 00:32:39.000 On the right there are the inert gases. They are inert and essentially don't do anything, chemically. 00:32:39.000 --> 00:32:47.000 On their left there are the halogens. They are rather aggressive and can be used to make, for instance, bleach. 00:32:47.000 --> 00:33:03.000 There is a system behind this, from which scientists concluded even back then, that our “atoms” in fact consist of even smaller parts. 00:33:03.000 --> 00:33:10.000 The first pointers to these constituents of atoms have also been found in 19th century. 00:33:10.000 --> 00:33:18.000 In 1897, Thomson found out that the so-called cathod rays consist of particles. 00:33:18.000 --> 00:33:29.000 Those of us who, like me, had contact to CRT televisions know that it contains a glass tube, essentially with vacuum inside. 00:33:29.000 --> 00:33:38.000 One can place this metal cross inside and connect the tube to high voltage. Then there are these characteristic rays. 00:33:38.000 --> 00:33:45.000 Then this metal cross casts a shadow. Thomson concluded that something inside is moving on straight lines. 00:33:45.000 --> 00:33:52.000 Thomson found out: When we place a magnet close to the tube, the shadow moves. 00:33:52.000 --> 00:33:56.000 Then the particles move differently, on a curved path. 00:33:56.000 --> 00:34:02.000 When I remove the magnet, the shadow goes up again. When I put it back, the shadow goes down. 00:34:02.000 --> 00:34:13.000 Whatever it is, it flies straight ahead, it reacts to magnetic fields, and it casts a shadow. 00:34:13.000 --> 00:34:19.000 From this, Thomson concluded that these are particles, which we now call electrons. 00:34:19.000 --> 00:34:23.000 But where do the electrons come from? We just did connect it to a voltage. 00:34:23.000 --> 00:34:27.000 They must have been already inside the wires. 00:34:27.000 --> 00:34:34.000 Thus Thomson has identified the electrons as one ingredient of the atoms. 00:34:34.000 --> 00:34:43.000 From this Thomson made the first atomic model, also called the plum pudding model. 00:34:43.000 --> 00:34:52.000 An atom is a big cloud of electrons. For instance you need about 1800 electrons to balance a hydrogen atom. 00:34:52.000 --> 00:34:57.000 They are in kind of a bag, a massless background charge. 00:34:57.000 --> 00:35:03.000 The electrons are negatively charged, the background charge is positive. This holds everything together. 00:35:03.000 --> 00:35:10.000 Thomson was aware that this is just a rudimentary model, but we can already use it to explain several thigns. 00:35:10.000 --> 00:35:21.000 For instance, atoms can gather energy. The electrons in the “plum pudding” can vibrate. When they don't there is no energy. 00:35:21.000 --> 00:35:34.000 This got investigated further. In 1909, Rutherford, to put it simply, collided atoms. 00:35:34.000 --> 00:35:38.000 He found out that in most cases they simply passed each other. 00:35:38.000 --> 00:35:46.000 Only if the hit was precisely central something got reflected, but then in a very hard way. 00:35:46.000 --> 00:35:57.000 So an atom mostly consists of empty space, with a small core in the centre, the nucleus, which essentially contains all of the atom's mass. 00:35:57.000 --> 00:36:07.000 From this Rutherford created a new atomic mode. The nucleus is positively charged, the electrons negatively, thus they attract each other. 00:36:07.000 --> 00:36:15.000 Then the electrons can orbit the nucleus in a similar way as the planets are orbiting the Sun. 00:36:15.000 --> 00:36:26.000 This is a very nice atomic model. It has one further advantage: It also explains how atoms can gather energy. 00:36:26.000 --> 00:36:34.000 There are orbits with different heights. On this higher orbit the electron has more energy than on this lower one. 00:36:34.000 --> 00:36:42.000 When an electron jumps from a higher orbit to a lower one, the atom emits energy in the form of light. 00:36:42.000 --> 00:36:46.000 The height of the fall determins the colour. 00:36:46.000 --> 00:36:52.000 When the electron falls down a small height, the light is red. When it falls further down, it is violet. 00:36:52.000 --> 00:37:00.000 When it falls down even further, we get UV or X-rays. When it falls down by a very small height, we get IR or radio waves. 00:37:00.000 --> 00:37:06.000 That's a nice explanation, but there is one thing we cannot explain this way. 00:37:06.000 --> 00:37:11.000 Why does the electron stop falling? Why doesn't it fall down to the nucleus? 00:37:11.000 --> 00:37:23.000 Why aren't all fall heights allowed? If they were, every object could emit light of every colour. 00:37:23.000 --> 00:37:29.000 Then everything would contain every colour. Everything would be white. But that's not the case. 00:37:29.000 --> 00:37:36.000 Thus something is missing, which we need to explain everything. 00:37:36.000 --> 00:37:44.000 In 1913 Bohr found sort of an explanation. 00:37:44.000 --> 00:37:51.000 He just postulated that only specific orbits are allowed. “That's how it is like.” 00:37:51.000 --> 00:37:57.000 He set up mathematical formulas which orbits are allowed and which are not. 00:37:57.000 --> 00:38:03.000 This made it possible to explain the actual colours of the atoms. 00:38:03.000 --> 00:38:11.000 By the way, this is one of many meanings of the term “quantisation”. The orbits of the electrons around the nucleus are “quantised”. 00:38:11.000 --> 00:38:14.000 This means: Only specific orbits are allowed. 00:38:14.000 --> 00:38:21.000 What he couldn't explain: Why? Why are only specific orbits allowed? What's up there? 00:38:21.000 --> 00:38:28.000 An explanation for this was found later with the emerge of quantum theory. 00:38:28.000 --> 00:38:34.000 In 1926, Schrödinger set up an equation named after him. 00:38:34.000 --> 00:38:44.000 This equation describes the “orbits” of the electrons around the nucleus in a better way than ellipses do: as waves engulfing the nucleus. 00:38:44.000 --> 00:38:50.000 On the right we see an electron resting comfortably around a nucleus as a spherical cloud. 00:38:50.000 --> 00:38:56.000 On the left we see a wave consisting of two anti-nodes and two nodes. 00:38:56.000 --> 00:39:04.000 Down we see a wave consisting of four anti-nodes and four nodes, which, in some sense, orbits the nucleus. 00:39:04.000 --> 00:39:08.000 In fact there can be much more complicated structures. 00:39:08.000 --> 00:39:16.000 Now this thing has little energy and this other thing has more energy. When it changes from this state to the other one, light emerges. 00:39:16.000 --> 00:39:21.000 Now the question why the orbits are quantised does not even arise. 00:39:21.000 --> 00:39:27.000 Of course there is nothing between these two states, except if we can calculate it using the equation. 00:39:27.000 --> 00:39:35.000 The Schrödinger equation made it possible to comprehend the properties of the atoms very precisely. 00:39:35.000 --> 00:39:45.000 One could explain things already measured, and one could predict new things, measure them, and they turned out correct. That's a big success. 00:39:45.000 --> 00:39:53.000 Here we see the mathematical description of the waves. It is again a differential equation. I like differential equations. 00:39:53.000 --> 00:39:59.000 The left-hand side says how it changes. That depends on how it currently is. 00:39:59.000 --> 00:40:05.000 The Schrödinger equation is a differential equation, too, and it describes these waves. 00:40:05.000 --> 00:40:10.000 We can solve this equation. Then we get results which coincide with experiments. 00:40:10.000 --> 00:40:20.000 But the Schrödinger equation has one problem. It allows a wave, for instance an electron, to move with infinite speed. 00:40:20.000 --> 00:40:28.000 Now we have a problem with special relativity, which says that the speed of light is an upper bound. 00:40:28.000 --> 00:40:37.000 So the Schrödinger equation, and thus quantum mechanics, contradicts special relativity. How to deal with this contradiction? 00:40:37.000 --> 00:40:45.000 Two years later, Dirac solved this contradiction and set up the Dirac equation, named after him. 00:40:45.000 --> 00:40:51.000 It is a differential equation, too: How it is tells us how it changes. 00:40:51.000 --> 00:40:59.000 This equation harmonises with special relativity. It has the speed of light as an upper bound. 00:40:59.000 --> 00:41:05.000 Now we can precalculate how atoms behave even more precisely, and measure that. 00:41:05.000 --> 00:41:11.000 One thing which now could be explained that way is the so-called hyperfine structure. 00:41:11.000 --> 00:41:17.000 When you measure spectral lines very precisely, each of them splits into two lines. 00:41:17.000 --> 00:41:27.000 He predicted even more. The Dirac equation has four solutions, two of which have negative kinetic energy. 00:41:27.000 --> 00:41:30.000 What does that mean? 00:41:30.000 --> 00:41:34.000 To imagine kinetic energy, I sit down, in my thoughts, in my electric car. 00:41:34.000 --> 00:41:39.000 I operate … well, not the gas pedal, but the electricity button. 00:41:39.000 --> 00:41:49.000 I accelerate as fast as I can, and after that the battery is empty, because I had to extract the kinetic energy from the battery. 00:41:49.000 --> 00:41:58.000 If kinetic energy is negative, that implies that I accelerate my electric car, and the battery gets fuller and fuller. 00:41:58.000 --> 00:42:04.000 That would be nice, but this doesn't coincide with reality. So something is wrong with this equation. 00:42:04.000 --> 00:42:09.000 Now Dirac could say: Okay, I miscalculated. 00:42:09.000 --> 00:42:15.000 Instead he said: This is something new. This is so-called antimatter. 00:42:15.000 --> 00:42:24.000 These solutions with negative kinetic energy must be interpreted as “holes” of particles with positive kinetic energy. 00:42:24.000 --> 00:42:31.000 They whoosh around as holes, and they behave in every respect like normal matter, but somehow reversed. 00:42:31.000 --> 00:42:39.000 For instance an electron has negative charge, so an anti-electron should have positive charge. 00:42:39.000 --> 00:42:43.000 Well, four years later this got actually discovered. 00:42:43.000 --> 00:42:51.000 Anderson discovered a particle in the cosmic rays. This is the first-ever photo of a so-called positron. 00:42:51.000 --> 00:42:58.000 It behaves in every respect like an electron, but it doesn't carry a negative charge, but a positive one. 00:42:58.000 --> 00:43:09.000 This was a big triumph for physics. Anderson discovered it. Dirac had predicted it. That's perfect. What else cold we ask for? 00:43:09.000 --> 00:43:25.000 Now we can explain the whole world. We consist of atoms, which consist of a nucleus and electrons orbiting it, somehow, as waves. 00:43:25.000 --> 00:43:36.000 I didn't address that the nucleus consists of protons and neutrons. This was also discovered at the beginning of the 20th century. 00:43:36.000 --> 00:43:47.000 And there is the positron, discovered in 1932 by Anderson. But that's enough. Now we can explain the whole world. 00:43:47.000 --> 00:43:55.000 Well, we still need some “glue” for the nucleus to make the protons and the neutrons stick together. 00:43:55.000 --> 00:43:58.000 We call this the pion. Now we search for the pion. 00:43:58.000 --> 00:44:07.000 Instead we find – the muon, discovered in 1936, again by Anderson and again in the cosmic rays. 00:44:07.000 --> 00:44:16.000 The muon is like an electron, but it is much heavier, and it decays after 2.2 microseconds. 00:44:16.000 --> 00:44:20.000 The muon is not stable like the electron, but it decays, just by itself. 00:44:20.000 --> 00:44:25.000 This was unexpected. This doesn't fit into the picture. 00:44:25.000 --> 00:44:29.000 But actually we were looking for the pion. And we find it. 00:44:29.000 --> 00:44:39.000 But we also find the neutrino, and the kaon, and the sigma hyperon, and the lambda hyperon, and several mesons, and so on. 00:44:39.000 --> 00:44:48.000 Until the 1960s over 100 of these so-called elementary particles had been found, the so-called particle zoo. 00:44:48.000 --> 00:44:54.000 That's more than we wanted. Actually we just needed atoms. 00:44:54.000 --> 00:44:59.000 Instead we found a whole particle zoo. What do we do with it? 00:44:59.000 --> 00:45:05.000 First of all, let's examine how they relate to each other. Maybe they react with each other and form new particles, or similar. 00:45:05.000 --> 00:45:17.000 Yes, they are some rules how they relate. This already suggests that they might consist of something even smaller. 00:45:17.000 --> 00:45:23.000 This was actually found in the 1960s. One of the protagonists was Gell-Mann. 00:45:23.000 --> 00:45:27.000 In 1964 he set up the so-called quark hypothesis. 00:45:27.000 --> 00:45:33.000 Here we see, in some sense, the successor of the periodic table of elements. 00:45:33.000 --> 00:45:43.000 These are the smallest parts of the universe, quarks, leptons, and interaction particles, including the Higgs boson. 00:45:43.000 --> 00:45:50.000 We have found all of them, and there are no signs that there could be something even smaller. 00:45:50.000 --> 00:46:00.000 We are looking for smaller things, which is good, but up to now all indications are that these are indeed the smallest parts of the universe. 00:46:00.000 --> 00:46:06.000 This has been the case for over 40 years. Back then when the atoms got discovered it was clear very soon that they must have some ingredients. 00:46:06.000 --> 00:46:13.000 In this case it is clear, at least as of today, that these are indeed the smallest things. 00:46:13.000 --> 00:46:19.000 Now we can build the other elementary particles out of them. 00:46:19.000 --> 00:46:25.000 For instance we can build protons and neutrons out of up quarks and down quarks. 00:46:25.000 --> 00:46:31.000 When we take 1 quark of one type and 2 of the other type, we get either one or the other. 00:46:31.000 --> 00:46:34.000 The electron is one of the leptons. 00:46:34.000 --> 00:46:39.000 This means that we consist only of these three particles. 00:46:39.000 --> 00:46:48.000 Everyhing else we can only find in cosmic rays, in particle colliders, and in the centre of the Sun, but not in our everyday life. 00:46:48.000 --> 00:47:00.000 Just this corner dominates our lives. Everything else is, well, very interesting, but it doesn't affect our lives. 00:47:00.000 --> 00:47:08.000 Now we have the Standard Model of elementary particles, the Standard Model of quantum field theory, in front of us. 00:47:08.000 --> 00:47:14.000 As a theoretical physicist I want to know the details. How to do calculations with it? 00:47:14.000 --> 00:47:21.000 Can we use this to calculate what combines with what to form other things, how that behaves, and so on? 00:47:21.000 --> 00:47:31.000 Now we wish for a differential equation. We'll get one in some sense, but it's going to be very long. 00:47:31.000 --> 00:47:38.000 When we describe all of this using a differential equation, it gets very, very long. That's why we use an abbreviation. 00:47:38.000 --> 00:47:46.000 The Lagrangian density is, to put it simply, an extreme abbreviation for a differential equation. 00:47:46.000 --> 00:47:55.000 And when I abbreviate all of this massively, I get this nice, little formula. 00:47:55.000 --> 00:48:06.000 This formula describes the smallest parts of the universe, quarks, leptons, …, everything is in there, for instance the Higgs boson down here. 00:48:06.000 --> 00:48:12.000 It's good that the Higgs boson is there because if it weren't there, this formula would continue, than it would be about twice as long. 00:48:12.000 --> 00:48:23.000 This was a very great discovery. In 2012 at LHC the Higgs boson was discovered. That's good. The formula is long enough as it stands. 00:48:23.000 --> 00:48:32.000 Now what can we do with this? How can we apply this to calculate how the smallest particles behave? 00:48:32.000 --> 00:48:40.000 It is, of course, possible to convert this to a differential equation, for which it is an abbreviation. 00:48:40.000 --> 00:48:45.000 As an example I brought in yet another Lagrangian density, the one of general relativity. 00:48:45.000 --> 00:48:50.000 Then I can calculate Einstein's field equations from the Lagrangian density. 00:48:50.000 --> 00:48:55.000 That's what Lagrangian densities are for. We can convert them to differential equations. 00:48:55.000 --> 00:49:03.000 Of course for this Lagrangian density, it will become very long and confusing. And in fact that's not done usually. 00:49:03.000 --> 00:49:11.000 What to do instead? Instead we use time-ordered perturbation theory. 00:49:11.000 --> 00:49:19.000 This approximative method allows us to calculate something reasonable from this monstrous formula. 00:49:19.000 --> 00:49:28.000 “Approximative” sounds as if it was imprecise. No, just the opposite. This is in fact the most precise theory we ever had. 00:49:28.000 --> 00:49:36.000 We can use this to calculate how electrons behave in magnetic fields up to 11 decimals. 00:49:36.000 --> 00:49:41.000 When we measure it, the result coincides precisely with these 11 decimals. 00:49:41.000 --> 00:49:51.000 If we predicted a time 3000 years in advance, this accuracy would be below 1 second. That's extremely accurate. 00:49:51.000 --> 00:49:58.000 To calculate that precisely I need so-called Feynman diagrams. I decide in advance how precisely I want to know it. 00:49:58.000 --> 00:50:05.000 For a rough result I can do with just two of these so-called Feynman diagrams. 00:50:05.000 --> 00:50:11.000 This looks like colliding particls. Actually it is a mathematical abbreviation for integrals. 00:50:11.000 --> 00:50:20.000 Using two of these diagrams I can rudimentarily describe what happens when two electrons collide, or one electron and a positron. 00:50:20.000 --> 00:50:27.000 The positron is an anti-particle, thus it travels backwards with respect to this arrow. 00:50:27.000 --> 00:50:34.000 The electron moves this way. They collide. They annihilate each other. A gamma quantum emerges, gamma rays. 00:50:34.000 --> 00:50:43.000 Out of this gamma quantum emerges, for example, a pair of a muon and an anti-muon, which again moves backwards with respect to the arrow. 00:50:43.000 --> 00:50:50.000 This is just an illustrative interpretation of the Feynman diagram. Actually, it stands for an integral. 00:50:50.000 --> 00:51:01.000 If you don't apply 2, but 15000 Feynman diagrams you can calculate up to 11 decimals how electrons – or muons – behave in a magnetic field. 00:51:01.000 --> 00:51:09.000 Recently there were interesting experiments with muons which are currently being examined. 00:51:09.000 --> 00:51:13.000 This is the most successful physical theory we ever had. 00:51:13.000 --> 00:51:17.000 We can use this to describe the universe in microcosm perfectly. 00:51:17.000 --> 00:51:24.000 Up to now there is not a single experiment, maybe except the ongoing muon experiment, which would contradict all of this. 00:51:24.000 --> 00:51:29.000 That's a giant triumph for theoretical physics. 00:51:29.000 --> 00:51:36.000 Now we have reached the point where we can try to reconcile all this with gravity. 00:51:36.000 --> 00:51:41.000 For one thing we have the Standard Model of elementary particles, of quantum field theory. 00:51:41.000 --> 00:51:47.000 That's a very long Lagrangian density, which could fill all of this slide just by itself. 00:51:47.000 --> 00:51:56.000 On the other side we have general relativity with Einstein's field equations, a differential equation. How can we get this together? 00:51:56.000 --> 00:52:04.000 In fact that's very easy. I now describe general relativity using a Lagrangian density. 00:52:04.000 --> 00:52:10.000 Lagrangian densities have a pleasant property: I may just add them. 00:52:10.000 --> 00:52:16.000 Here it is, the Lagrangian density of quantum gravity. It's rather long. In particular these three dots are very long. 00:52:16.000 --> 00:52:22.000 However, general relativity + quantum field theory = quantum gravity. 00:52:22.000 --> 00:52:30.000 This has been well-known since the 1960s. So where is the problem of quantum gravity? 00:52:30.000 --> 00:52:40.000 The problem: When I try to apply time-ordered perturbation theory, Feynman diagrams, to this combined formula, … 00:52:40.000 --> 00:52:47.000 … then this works excellently for this part, but it doesn't work at all for that part. There it yields infinity. 00:52:47.000 --> 00:52:53.000 Well, this part also yields infinity, but there is a mathematical trick how we can, in some sense, reel in that infinity. 00:52:53.000 --> 00:52:57.000 That's the so-called renormalisation. However it doesn't work for this part. Here we still get infinity. 00:52:57.000 --> 00:53:02.000 These are the non-renormaliseable divergences you always hear about when you ask: 00:53:02.000 --> 00:53:11.000 Where is the problem of combining quantum field theory and general relativity. 00:53:11.000 --> 00:53:21.000 It is not possible to describe gravity using Feynman diagrams, using so-called gravitons, particles, which convey gravity. 00:53:21.000 --> 00:53:25.000 These are the non-renormaliseable divergences. 00:53:25.000 --> 00:53:28.000 As a theoretical physicist I always want to know the details. 00:53:28.000 --> 00:53:38.000 So I ask: It doesn't work. Is that just a technical problem, or is there a fundamental contradiction, causing that it doesn't work? 00:53:38.000 --> 00:53:43.000 I want to fathom that fundamental contradiction. 00:53:43.000 --> 00:53:49.000 What if we don't use Feynman diagrams, but instead we convert everything to a differential equation? 00:53:49.000 --> 00:53:55.000 Of course it will become extremely long. However, 15000 Feynman diagrams aren't exactly short, either. 00:53:55.000 --> 00:53:59.000 Let's just try. This leads us to the next problem. 00:53:59.000 --> 00:54:10.000 Describing pair annihilation and creation only works, so far, using Feynman diagrams or other methods using time-ordered perturbation theory. 00:54:10.000 --> 00:54:18.000 You need time-ordered perturbation theory, and as soon as you apply that to gravity, it yields infinity. 00:54:18.000 --> 00:54:26.000 What's this supposed to mean – “only works so far”? I want to have a very close look at this. 00:54:26.000 --> 00:54:33.000 What exactly goes wrong? Is this just a technical problem, or is there a fundamental contradiction? 00:54:33.000 --> 00:54:38.000 Now I can phrase my research question, my question about the question. 00:54:38.000 --> 00:54:48.000 Why isn't it possible to describe pair annihilation and creation using a differential equation? 00:54:48.000 --> 00:54:55.000 Now we have arrived at the results of my own research. 00:54:55.000 --> 00:55:10.000 To pursue this question I just try to describe pair annihilation and creation using a differential equation. 00:55:10.000 --> 00:55:17.000 Then I'll see what goes wrong. I write that down. This will answer my question about the question. 00:55:17.000 --> 00:55:25.000 I want to try that out. The first thing I encounter are mathematical obstacles. So I must do a lot of mathematical exercises. 00:55:25.000 --> 00:55:35.000 That's what I did, and I claim that I have understood the mathematical structures, which show up when I set up that differential equation. 00:55:35.000 --> 00:55:42.000 In fact it wouldn't be necessary to understand these structures for applying Feynman diagrams, for you can use them just as a recipe. 00:55:42.000 --> 00:55:49.000 But I want to do something different than Feynman diagrams, so I had a very, very close look on those mathematical structures. 00:55:49.000 --> 00:55:58.000 Then I tried to set up the differential equation. Now the big question reads: What precisely didn't work out? 00:56:00.000 --> 00:56:08.000 On 5 May 2018 at 22:39h I saw the differential equation in front of me. 00:56:08.000 --> 00:56:13.000 My attempt to find out why it is not possible to set up that differential equation has failed. I failed to fail. 00:56:13.000 --> 00:56:18.000 I succeeded to set up the differential equation. That was unexpected. 00:56:18.000 --> 00:56:24.000 Okay, this part seems to work. Then it must be something else which goes wrong. 00:56:24.000 --> 00:56:33.000 So probably it's not possible to solve the differential equation. It might yield zero or infinity or something else, which is useless. 00:56:33.000 --> 00:56:37.000 So let's see why the computer fails to solve it. 00:56:37.000 --> 00:56:48.000 I'm afraid it will actually fail right now. I'll now try again to show you a film of what my computer made out of this differential equation. 00:57:16.000 --> 00:57:27.000 Too bad. Perfect. I'll now switch to my slides and try to convey the film by some other means. We'll find a way. 00:57:27.000 --> 00:57:33.000 So it won't be a film, but a sequence of still pictures. 00:57:55.000 --> 00:58:07.000 Here we see the still picture again. 00:58:07.000 --> 00:58:12.000 I'll now go a little to the future. 00:58:12.000 --> 00:58:18.000 Now I let these particles approach each other. 00:58:18.000 --> 00:58:25.000 On the left we see, to put it simply, an electron. Actually it is a many-particle wave function. And on the right we see, so to say, a positron. 00:58:25.000 --> 00:58:35.000 Now I let them collide. Now they overlap. At first we don't see very much. 00:58:35.000 --> 00:58:42.000 This movie isn't linked yet, I'll do that soon, so you can download it. We can do that. 00:58:42.000 --> 00:58:50.000 The electron and the positron have touched. Now they permeate. 00:58:50.000 --> 00:58:55.000 We can still identify them, but we also see some blue glow. 00:58:55.000 --> 00:59:05.000 This blue glow are gamma quanta, which got produced because the two things have permeated each other. But there is more to happen. 00:59:05.000 --> 00:59:13.000 There is not much left of the electron and the positron. This cyan and rose are gamma quanta. 00:59:13.000 --> 00:59:20.000 From the electron and the positron there are only small remainders left, over here, and over there. 00:59:20.000 --> 00:59:31.000 Most of them has annihilated. This is the so-called pair annihilation. I just removed the gamma quanta from the image. 00:59:31.000 --> 00:59:40.000 This was a simulation of pair annihilation, calculated by solving a differential equation of quantum field theory. 00:59:40.000 --> 00:59:48.000 This was pair annihilation. What about pair creation? 01:00:16.000 --> 01:00:26.000 Here we see two gamma quanta which we let loose on each other. Two light rays. 01:00:26.000 --> 01:00:34.000 Or rather light waves. I can imagine this as two stones dropped into water. 01:00:34.000 --> 01:00:40.000 Waves emerge and spread. After some time they will overlap. 01:00:42.000 --> 01:00:48.000 Now the waves overlap, and we see a small glow in the middle. 01:00:48.000 --> 01:00:54.000 This glow are newly generated electrons and positrons. 01:00:54.000 --> 01:01:09.000 Here we see a simulation of pair creation, simulated by solving a differential equation of quantum field theory. 01:01:21.000 --> 01:01:27.000 So I tried to fail setting up and solving a differential equation, but I failed. 01:01:27.000 --> 01:01:36.000 It doesn't fail. It works. We can describe pair annihilation and creation by a differential equation. 01:01:36.000 --> 01:01:43.000 This is, at least from my point of view a huge sensation, which I announce today in public for the first time. 01:01:43.000 --> 01:01:47.000 What does this imply? What is it good for? 01:01:47.000 --> 01:01:57.000 This is a new method to calculate many-particle quantum wave functions. This is one of the many meanings of the word “quantisation”. 01:01:57.000 --> 01:02:06.000 So I accidentally found a new method of quantisation, an alternative to Feynman diagrams. 01:02:06.000 --> 01:02:10.000 Well, it isn't really an alternative to Feynman diagrams. Not yet. 01:02:10.000 --> 01:02:15.000 Yes, I'm calculating without Feynman diagrams, and it works. 01:02:15.000 --> 01:02:20.000 However the precision is far apart from what is possible using Feynman diagrams. 01:02:20.000 --> 01:02:23.000 11 decimals … I would be glad if I had just one. 01:02:23.000 --> 01:02:30.000 So far I have qualitative statements, that particles are annihilated and created. 01:02:30.000 --> 01:02:35.000 But my statements how much is happening there are yet very rudimentary. 01:02:35.000 --> 01:02:43.000 Anyway it is possible to describe many-particle quantum effects using a differential equation. 01:02:43.000 --> 01:02:50.000 But what is it good for? We already have the Feynman diagrams, and they work perfectly. Yes, but not for gravity. 01:02:50.000 --> 01:02:55.000 My method will still work when we include gravity. 01:02:55.000 --> 01:03:01.000 How do we describe gravity? Via Einstein's field equations. That's a differential equation. 01:03:01.000 --> 01:03:08.000 That we can describe general relativity via a differential equation is entirely clear. 01:03:08.000 --> 01:03:13.000 That this also works for pair annihilation and creation was not clear. 01:03:13.000 --> 01:03:20.000 I successfully implemented that and I accidentally developed a new quantisation method. 01:03:20.000 --> 01:03:26.000 And it is compatible with general relativity. 01:03:26.000 --> 01:03:30.000 And even more: It is also compatible with … Ah – sorry. One less. 01:03:32.000 --> 01:03:36.000 I found a method how to investigate quantum gravity. 01:03:36.000 --> 01:03:43.000 But I'm working without Feynman diagrams, so I won't be able to calculate gravitons. 01:03:43.000 --> 01:03:54.000 “Graviton” means, in the language of time-ordered perturbation theory, that I describe gravity by mediating particles, which I call gravitons. 01:03:54.000 --> 01:04:00.000 I can describe gravitons by Feynman diagrams, but that's precisely what I'm not doing. My simulation won't be able to show gravitons. 01:04:00.000 --> 01:04:08.000 Maybe I get something similar which even behaves like gravitons and even can be, one day, described by Feynman diagrams. 01:04:08.000 --> 01:04:11.000 However for now, my method is without gravitons. 01:04:11.000 --> 01:04:21.000 Instead I can add general relativity. I don't think that anything can go wrong here. 01:04:21.000 --> 01:04:31.000 But I can do even more. I can, for example, combine this with noncommutative geometry. Again, what is that? 01:04:32.000 --> 01:04:36.000 Well that is, in a way, the theory of everything. 01:04:36.000 --> 01:04:44.000 Noncommutative geometry was largely developed by Alain Connes, a French mathematician. 01:04:44.000 --> 01:04:50.000 It is a logical advancement of general relativity. 01:04:50.000 --> 01:04:59.000 General relativity says: Gravity is geometry. Noncommutative geometry says: All forces are geometry. 01:04:59.000 --> 01:05:05.000 Not only gravity, but also electromagnetic, weak and strong interaction. 01:05:05.000 --> 01:05:17.000 It's all geometry, but not on a curved space-time, but we have additional dimensions, so-called discrete extra-dimensions. 01:05:17.000 --> 01:05:25.000 How to imagine this? Our well-known dimensions length, width, height, and time are continuous. 01:05:25.000 --> 01:05:33.000 There I can measure not only 1, 2, 3, but also 1.5, 1.7, 1.72, … 01:05:33.000 --> 01:05:38.000 That's continuous. A discrete dimension has only a few points. 01:05:38.000 --> 01:05:49.000 For instance a discrete dimension of four points means that a particle can only be located at one of four positions. 01:05:49.000 --> 01:05:55.000 When we consider this togethher with a “normal” universe it looks about like this. 01:05:55.000 --> 01:06:05.000 Here we have a two-dimensional curved universe with a discrete extra dimension, which consists of four points. 01:06:05.000 --> 01:06:09.000 Well, what is this good for? 01:06:09.000 --> 01:06:15.000 In 1996 Chamseddine and Connes set up a formula which looks like this. 01:06:15.000 --> 01:06:23.000 It describes a universe with a four-dimensional curved space-time and 11 discrete extra-dimensions. 01:06:23.000 --> 01:06:28.000 For the experts: Here we see the 3x3 matrices over the complex numbers. 01:06:28.000 --> 01:06:33.000 However they don't provide 9 extra-dimensions, but only 8. 01:06:33.000 --> 01:06:40.000 These are Hamilton's quaternions, essentially vectors of two complex numbers, and these are the complex numbers themselves. 01:06:40.000 --> 01:06:46.000 So here we see a normal curved space-time with 11 extra-dimensions. 01:06:46.000 --> 01:06:53.000 Okay, so what? From this we can calculate a Lagrangian density. This one. 01:06:53.000 --> 01:06:56.000 But we recognise it. 01:06:56.000 --> 01:07:10.000 This is the Lagrangian of general relativity, and that, including the dots, is precisely the Lagrangian of the Standard Model of elementary particles. 01:07:10.000 --> 01:07:20.000 This tiny formula implies both, general relativity and the Standard Model of quantum field theory. 01:07:20.000 --> 01:07:26.000 They are together in one formula. So this formula describes quantum gravity. 01:07:26.000 --> 01:07:34.000 But there is something leftover, this weird stuff. What's that? We don't know what that is. 01:07:34.000 --> 01:07:40.000 I thought about this. This might be an explanation for dark matter. 01:07:40.000 --> 01:07:47.000 There are advanced theories, advanced versions of MOND theory – modified Newtonian dynamics. 01:07:47.000 --> 01:07:53.000 There are general-relativistic advancements, which can even explain the Bullet cluster. 01:07:53.000 --> 01:08:06.000 I think it's worth a try to look at these terms, whether they can explain dark matter. That would be the next sensation. 01:08:06.000 --> 01:08:13.000 So this formula is extremely powerful, and it has been known for 25 years. 01:08:13.000 --> 01:08:20.000 Why didn't Connes and his co-workers get the Nobel price? They wrote down quantum gravity. 01:08:20.000 --> 01:08:26.000 Yes, but this cannot be quantised. What does that mean? 01:08:26.000 --> 01:08:32.000 This Lagrangian density has been known since the 1960s, but we cannot do calculations with it. 01:08:32.000 --> 01:08:40.000 This can be calculated only with Feynman diagrams, and that cannot be calculated with Feynman diagrams. 01:08:40.000 --> 01:08:43.000 It is not possible to calculate both parts together using the same method. 01:08:43.000 --> 01:08:53.000 There is no calculation method for many-particle quantum wave functions which could be applied to investigate this Lagrangian density. 01:08:53.000 --> 01:09:04.000 Now it exists. Using my method I see no obstacles to “quantise” this Lagrangian density with these extra terms. 01:09:04.000 --> 01:09:09.000 We can calculate it using a many-particle quantum wave function. 01:09:09.000 --> 01:09:15.000 I have reached the end of my speech. What did we see? 01:09:15.000 --> 01:09:23.000 For the first time we can describe pair annihilation and creation using a differential equation. 01:09:23.000 --> 01:09:32.000 This is a new method to handle many-particle quantum wave functions. I developed a new quantisation method. 01:09:32.000 --> 01:09:39.000 It works without using Feynman diagrams. I'm not using time-ordered perturbation theory. Instead I directly solve the differential equation. 01:09:39.000 --> 01:09:45.000 This implies that I won't see any gravitons as mediating particles. 01:09:45.000 --> 01:09:49.000 But maybe we see something similar. We can investigate this now. 01:09:49.000 --> 01:09:58.000 My new quantisation method is compatible with general relativity and with noncommutative geometry. 01:09:58.000 --> 01:10:03.000 Thus this formula is a hot candidate for the theory of everything. 01:10:03.000 --> 01:10:10.000 While trying to find out why there is no theory of everything I accidentally found it, and it is 25 years old. 01:10:10.000 --> 01:10:16.000 I quantised it. That way I proved that it really is the theory of everything. 01:10:16.000 --> 01:10:33.000 Well, I can tell you a lot at this place. Just a moment, I'll upload it … We can spare that second … 01:10:33.000 --> 01:10:43.000 When you reload this URL now, you can look up all this in two scientific publications. 01:10:43.000 --> 01:10:47.000 One has 6 pages, the other one 110. Both in English, of course. 01:10:47.000 --> 01:10:55.000 When you have studied physics and you understood nonrelativistic quantum theory and special relativity, … 01:10:55.000 --> 01:11:01.000 … you are well-placed to understand at least the longer one of both papers. 01:11:01.000 --> 01:11:05.000 Okay, what comes next? How can we proceed from here? 01:11:05.000 --> 01:11:11.000 First of all, using what I have developed you can do much more. 01:11:11.000 --> 01:11:16.000 My objective was the combination with general relativity. 01:11:16.000 --> 01:11:22.000 In fact this is a method to calculate electrons and positrons rather precisely. 01:11:22.000 --> 01:11:30.000 This can be valuable for solid-state physics for examining new materials numerically. 01:11:30.000 --> 01:11:40.000 For instance: How must I change this material to obtain specific electrical properties? Then we can, for example, build faster computers. 01:11:40.000 --> 01:11:48.000 Then I have, at least as far as I can see, developed a new method to solve a partial differential equation. 01:11:48.000 --> 01:11:52.000 This has applications inside mathematics. 01:11:52.000 --> 01:12:01.000 Using this new method to solve differential equations we can do many things I cannot even guess right now. 01:12:01.000 --> 01:12:07.000 This might become valuable in constructing machines and buildings. 01:12:07.000 --> 01:12:12.000 For me as a theoretical physicists other things are more interesting. 01:12:12.000 --> 01:12:21.000 I said several times that we can combine this with general relativity. Yes, that's possible, but one has to do it, and that's a lot of work. 01:12:21.000 --> 01:12:28.000 I don't doubt that it will work out, because I developed this method in such a way that this will work out. 01:12:28.000 --> 01:12:37.000 I take something of which I know that it works for general relativity and apply it to quantum theory, and I look how far I get. 01:12:37.000 --> 01:12:46.000 Result: I get through. It should be feasible to combine this with general relativity, but it's a lot of work. 01:12:46.000 --> 01:12:52.000 I'm somewhat more scared of the extension to the full Standard Model. 01:12:52.000 --> 01:12:58.000 For one thing because it is huge. I must convert the Lagrangian density into a differential equation. It will be very long. 01:12:58.000 --> 01:13:02.000 For another thing I only calculated electrons and positrons so far. 01:13:02.000 --> 01:13:10.000 I'd like to calculate muons, and quarks, and Higgs bosons, and so on. There are many things which can go wrong. 01:13:10.000 --> 01:13:13.000 Here again I only expect just a lot of work. 01:13:13.000 --> 01:13:19.000 However it might be that it will become so much work for the computer that it cannot be calculated using today's computers. 01:13:19.000 --> 01:13:29.000 That's the worst thing which can happen. But I don't see anything which could go wrong concerning the concepts. 01:13:29.000 --> 01:13:36.000 I'm worrying mostly about the Higgs boson. Maybe this will require new algorithms, or we overwhelm everything by calculation power. 01:13:36.000 --> 01:13:39.000 Than it can happen that the calculation power does not suffice. 01:13:39.000 --> 01:13:51.000 What else can we do? We can apply everything to noncommutative geometry and look what kind of quantum gravity emerges. 01:13:51.000 --> 01:14:00.000 Maybe this approach provides an explanation for one of our last big mysteries, dark matter. 01:14:00.000 --> 01:14:05.000 This was my speech. I apologise for the technical problems. 01:14:05.000 --> 01:14:11.000 I hope you could hear me and see my slides. The movies didn't work out. Next time. 01:14:11.000 --> 01:14:19.000 Thank you for participating in this load test for our online learning platform. 01:14:19.000 --> 01:14:29.000 I thank you for your interest, for listening, for coming, and I'm now available for questions. Many thanks.