Protected: Maxim Hoekmeijer

This summary is intended for non-experts. I first explain something about fundamental physics, what it is and how far we have come. Based on that, I will motivate why I conducted my research and briefly explain what that research entails.

Fundamental Physics

Children always ask many questions. These questions are usually formulated briefly and concisely and are simply 'why?'. Answering those questions, although quite simple at first, can become quite difficult after a while. This is mainly because children can actually keep asking questions indefinitely. See an example below. Why do trees grow? Trees grow so they can get bigger and catch more light. Why? Because they need light to survive. Why? Without light, plants cannot make food for themselves. Why? Light provides the energy needed to create food. Why? The food the tree needs costs energy to make. Why? Because the chemical energy needed for the composition of glucose, the food, is more than the chemical energy in water and carbon dioxide. Why?

Most parents have had enough by this point. They will kindly or unkindly request the child to stop asking those annoying questions. But suppose a very smart mother or father continues to answer the child. Where would it end? Let's assume this parent has been able to take in all the knowledge that we as humanity possess. Even then, at some point, this knowledgeable parent will be able to do nothing but admit they no longer know the answer to the question.

Finding the answer to this final 'why' question is precisely the task of fundamental physics. The deeper we go, the more fundamental it becomes. Conversely, fundamental physics is at the base. You start with fundamental physics and end with the answer to the question of why trees grow.

By now, we are at a point in fundamental physics where we can answer quite a few deep 'why' questions. This has taught us many lessons about how our world works. Take, for example, electricity and magnetism. We know that matter can have an electrical charge and thus creates an electrical field. We also know that when an electrical charge moves, or in other words, a current is present, a magnetic field is created. These two different principles are more intertwined than they seem at first sight. It turns out that a changing magnetic field also creates an electrical field. Conversely, the same applies: a changing electrical field also creates a magnetic field. This feels reasonably plausible, as one is caused by charge and the other by moving charge. Yet this has a special consequence. Suppose we are in a situation where there is no charge (and no moving charge). Then you would expect that no electrical and also no magnetic fields are present. However, the equations describing electrical and magnetic fields as a result of (moving) electrical charge say something else. In this situation, it is possible for these fields to be present, in the form of an electromagnetic wave. These waves are a mix of changing electrical and magnetic fields that maintain each other. A requirement that these waves must meet according to the equations is that they must always travel through space at the same speed. This speed can be calculated, and the result is: the speed of light. This is no coincidence. It turns out to be correct: light is nothing more than an electromagnetic wave. The light that now hits your eye from the paper, the light that comes from the sun to the earth, and the light that gives trees the energy to grow, are all electromagnetic waves. This realization has allowed people to explain all kinds of phenomena regarding light, both quantitatively and qualitatively. Think, for example, of the refraction or reflection of light. This is quite special. You start by describing how electrical and magnetic forces work, and you end by explaining what light is.

As always, this new explanation gives rise to a new 'why' question. Why does light always travel at the same speed? If a truck on the highway overtakes another truck, it usually takes a long time. One drives 80 km/h and the other 81 km/h. The reason it takes so long is simple: their relative speed is only one km/h, which is quite slow. With light, it works differently. Your relative speed with respect to light is always the same. Light always overtakes you with the speed of light, regardless of how fast you drive yourself. Similarly, if light hits you, it always does so with the speed of light, regardless of how fast you move towards that light. This might be hard to believe, but the equations and especially experiments (!) confirm this. How is this possible?

It was Albert Einstein who was the first to realize all this. He showed, using the constant speed of light, that space and time are relative for everyone. When thinking of time, people think of a clock that ticks per second and shows how much time has passed between one moment and the next. Intuitively, the elapsed time between these two moments is fixed. However, this is not the case. Suppose we stand next to each other and have two clocks. I take one with me in my car and drive a lap on the highway while you stay and wait. When I return, our clocks are no longer the same: mine is behind yours. This is not because one of the two clocks is faulty, but because fundamentally less time has passed for me than for you. Normally we don't notice this. The reason for this is that our speeds on the highway are (hopefully) quite low. Low compared to the speed of light, which is extremely high. If we were to design a spaceship that could travel at nearly the speed of light, the difference in elapsed time would be noticeable. Suppose Bob and Alice are twins and Bob receives a spaceship as a present on his 18th birthday, with which he may explore space at almost the speed of light. He travels into empty space for half a year and then returns to earth because it gradually gets boring in that spaceship. Bob is back just in time to celebrate his 19th birthday. Alice, his twin sister, is now elderly, however. For Bob, a year has passed, while Alice's whole life has passed by in the meantime. This is the so-called twin paradox, and although it seems ridiculous, fundamental physics has full confidence that our world works this way.

It could just be that your child later asks you 'Why do I sometimes feel a shock when I touch you?' and that you explain half an hour later that time is relative for everyone.

Of course, it doesn't stop here, and many more deep 'why' questions have been asked and answered. For example, the next 'why' question led Einstein to describe gravity. He showed that gravity is nothing more than curved space and time—the same space and time that are relative for everyone. In a completely different field, the microscopic world of atoms and molecules, deep insights have also been gained into the fundamental properties of matter. This went completely against our everyday intuition. It turns out that not everything is certain in our universe. By this, I don't mean that we as humanity don't know everything for certain, but that it is fundamentally impossible to know certain things for certain. Where it seems natural to us that matter is in a certain place in space, this is not the case at all. For example, it is often said that a small particle, such as an electron in an atom, can be in two places at once. More specifically: no precise position can be assigned to the electron, even though it exists. Many other insights followed this, too many to list here.

Ultimately, we have arrived in fundamental physics at two fundamental theories which, each in their own domain, describe the universe and everything in it as well as we can. The first is Albert Einstein's theory of general relativity. This describes how gravity works, that it is nothing but curved space and time, and how this space and time are relative for everyone. This theory is used to describe the large scale of our universe. Think of our solar system, the GPS systems we use to navigate, how galaxies form, and how black holes can arise. The other theory goes by the name the standard model. This describes the other three forces we know, including the electromagnetic force we talked about above. It shows what all the matter we know is fundamentally made of, what interactions are possible, and how matter behaves on an extremely small scale. In short: general relativity describes everything that is large, and the standard model describes everything that is small. Every experiment performed to date to test one of these two theories has passed with flying colors.

Quantum Gravity

What then is the deepest 'why' question that has not yet been answered? This question was already asked about eighty years ago, and physicists have not yet succeeded in answering it. It's roughly like this. We know what matter is made of, and what all the properties of these building blocks are. These properties are all 'quantum'. By this, I mean that fundamental uncertainties are associated with them, and that, for example, no precise position can be assigned. On the other hand, we know how gravity works, and for example that the closer two massive objects are to each other, the stronger they attract each other. But if the position of the matter cannot be fundamentally determined, how can we know how strong the gravity between the two objects is? Or, rather, how does the universe know that?

The same problem occurs with the electromagnetic force. Positive and negative charges attract each other, and how strong this attraction is depends on how close the two charges are to each other. How this can be reconciled with the quantum properties of matter has been solved in the standard model. How this works exactly is somewhat complicated. The core of the solution is that the electrical and magnetic fields themselves must also have quantum properties. With gravity, the expectation is that it must work the same way. Except with gravity, electrical and magnetic fields are not the entities responsible for the creation of this force, but space and time themselves. This means that space and time are expected to have quantum properties. That is to say, uncertainties are associated with space and time, and that, for example, the distance between two points is fundamentally uncertain. How all this works exactly, no one knows. The reason is that the standard method used in the standard model does not work for gravity. If one tries to apply it, it results in all kinds of conflicts, such as probabilities higher than 100% – something that by definition should not be possible.

The 'why' question can therefore be formulated as follows: Why can't we reconcile gravity with the standard model? In other words, what makes gravity so different from the other forces we know in our universe that it cannot be reconciled with the quantum properties of matter?

Another 'why' question you can ask is: why does it matter? We can describe all contemporary experiments, and for all the technology we want to develop in the foreseeable future, we don't need the answer to the deepest 'why' question anyway. The first reason we would like an answer to this problem is childlike curiosity. A child wants to know why trees grow purely because the child wants to know, not because they want to plant a forest. In addition, one can make the argument that new fundamental insights could certainly be used in the distant future. However, this is not my personal motivation. I hope to gain other insights with the answer to this 'why' question. A theory of quantum gravity will, hopefully, describe what happened during the Big Bang. In other words, it will provide an answer to the question of how our universe was created. This will undoubtedly lead to new 'why' questions and it may be that the explanation is disappointing. But every bit of extra information about how we all came to be will always be enough to amaze.

For people in fundamental physics, there is in any case enough motivation to solve this problem. It is also not the case that physicists have not tried to find the answer to this question in the last eighty years. On the contrary, many attempts have been made to solve this problem, leading to a range of ideas about how space and time can have quantum properties. Making these ideas concrete and formulating them in a mathematically consistent theory is difficult. Yet this is not the biggest obstacle. What makes it extremely difficult is that gravity is much weaker than the other forces. This might seem contradictory, because gravity dominates the universe on a large scale. You can also turn this around, however. It costs you no effort to pick up this booklet. The entire gigantic earth pulls this booklet down, and you don't even stop to think that you are easily winning the battle for the booklet from the earth. The reason that gravity dominates on a large scale is also because it doesn't have to compete with any of the other forces. The electromagnetic force is absent because large objects, such as planets, are electrically neutral. The other two forces are also absent on a large scale. Because gravity is so extremely weak, it is difficult to create an experiment in which the quantum properties of gravity - or of space and time - become relevant. Quantum properties are only visible on a small scale (this is because of a phenomenon called 'decoherence'). But on a small scale, the masses and energies responsible for creating gravity are extremely small. With such a small mass/energy, and an extremely weak force, this produces very small effects that are not experimentally detectable.

The result is that it is totally unclear in which direction we should look. We have many ideas about how quantum gravity works and everyone has their own judgment about which idea is most promising. However, no one knows, and it is not possible at this time to test who is close. In short, due to the lack of experiments, we have a total lack of hints that can steer us in the right direction.

Einstein sometimes wondered if God had a choice when he created the universe. By this, he meant that he wondered if there was only one way to design the universe in a consistent way. If this were the case, it would in principle be possible to answer the deepest 'why' question with theory alone. I think, however, that this is not the case. I think we will never get there with theory alone, either because multiple ways are possible, or because we will never be good enough to work out all possible options theoretically. I am convinced that we need experimental input, which we have also always had in the past to answer other difficult 'why' questions. The experimental input is needed to eventually test our ideas, but in the first instance also primarily to think in the right direction. The search for observational hints, despite all the obstacles associated with it, is therefore the motivation behind the research I did during my PhD.

My Research

To bring quantum gravity into contact with experiment, we must choose a certain experimental context. There are various possibilities for this, but during my PhD, I looked at black holes. The reason for this is that there has been substantial experimental progress in this field in recent years. For example, gravitational waves from two merging black holes were detected for the first time, and the first photo of a black hole was taken, see Fig. 3.1. I focus on the latter for the pragmatic reason that a single black hole is much easier to describe compared to two black holes rotating around each other. Summarizing everything so far, I don't study black holes because they are incredibly cool (although they are), but because I ultimately want to know how our universe was created.

Black holes are black. The reason for this is that every black hole has an event horizon. This event horizon is not something you can grab onto, but is the boundary from which, once crossed, there is no returning. Even light can no longer escape from inside the event horizon. As said before, light always travels at the same speed. But gravity is nothing but the curvature of space and time, so light is also under the influence of gravity, as light follows the path of a 'straight line' in a curved space. To better understand what I mean by this, you can imagine standing on the North Pole of the earth. You then just walk straight forward. Eventually, you end up back at the North Pole. You have only walked in a straight line, except this straight line is a circle because the surface of the earth is a curved space. Unlike the earth, the space in the vicinity of black holes is so curved that even the speed of light is not enough to escape that curved space. Furthermore, it appears from Albert Einstein's theory that nothing can go faster than light, and so nothing can escape the black hole. Everything that falls into the event horizon can never get out again.

The photo taken of a black hole, see Fig. 3.1, shows that there is a dark part in the center. This part is often called the shadow of a black hole. That shadow is there (among other things) because of the event horizon. But the size of the shadow does not correspond one-to-one with the event horizon. The size of the shadow has to do with the location where light can orbit the black hole. This location is outside the event horizon. If you are there yourself, you can see the back of your own head by looking forward. Albert Einstein's theory of general relativity predicts that black holes exist and have an event horizon, and predicts the location where light can orbit the black hole. In other words, this theory predicts that when you take a photo of a black hole, you see a shadow and how large this shadow is. This prediction, made almost a hundred years ago, perfectly matches the observations made.

What we are looking for is what this photo can tell us about quantum gravity. How this works is actually quite simple. The photo taken of the black hole is what it is. Furthermore, we don't know exactly how quantum gravity works, but there are all kinds of ideas about it. These ideas adapt Albert Einstein's theory of general relativity. A different description of gravity can have consequences for the existence of the event horizon and for the location where light can orbit. We then look in these alternative descriptions of gravity at what the photo should look like and whether this could agree with the photo taken. If not, we know that the underlying idea cannot be correct and we have learned something. I'm not trying to find things that are correct, but things that are not correct. Determining how these alternative descriptions describe black holes is easier said than done, and forms the majority of the research conducted over the past four years.

There is only one problem. The black holes that people have been able to photograph are gigantic. They go by the name supermassive black holes and are located in the center of our own galaxy and the galaxy closest to us. Because the black holes are so large, the effects of quantum gravity are very small. Very small changes mean a small impact on the photo, and therefore that we don't learn much from it. It is therefore only meaningful if the small (microscopic) changes lead to large (macroscopic) effects, hence the subtitle. Contrary to my expectations, this turns out to be the case under certain circumstances. In Chapter 9, we discover and describe a mechanism where very small changes have the consequence that the event horizon ceases to exist. In Chapter 10, we show that this (under certain assumptions) has the consequence that a shadow is no longer visible in the resulting images. For me personally, finding this mechanism ('the magnifying mechanism') is the main result of this thesis. Explaining the origin and working of this mechanism in simple words is, however, something I haven't succeeded in yet.