THE SEARCH FOR A THEORY OF EVERYTHING
“Spacetime is dynamical, so it has a life of its own. It is governed by laws of physics”
The two main theories of physics are at odds with one another. Einstein’s General Relativity explains gravity, but it contradicts quantum theory: how we understand matter, atoms and particles. Theoretical physicist Fay Dowker tells Amy Barrett why the theories are incompatible, and how she intends to bring them together…
WHAT CHALLENGE DO PHYSICISTS FACE TODAY?
I am working on the problem of quantum gravity. We don’t have a theory of quantum gravity yet. The challenge is to find one. It’s a problem because our current two best fundamental theories in physics [General Relativity and quantum theory] are not compatible with each other. It’s a strong statement to say they are contradictory, but I’m not afraid of saying that. Science advances by looking at contradictions between different pieces of our understanding, and it focuses on those contradictions in order to make progress.
Science tolerates contradictions, but not forever.
WHAT ARE THE CONTRADICTIONS INVOLVED IN THE PROBLEM OF QUANTUM GRAVITY?
Our best theory of gravity, currently, is General Relativity. Largely formulated by Albert Einstein, according to this theory, gravitational phenomena – such as the motions of the planets around the Sun, black holes, the motions of galaxies in the Universe – are manifestations of the geometry of a fabric that we call space-time.
Space-time is four-dimensional, and it’s dynamical, so it has a life of its own. It is governed by laws of physics. It bends and it warps, and it ripples, and it carries energy. It is a physical entity in our current understanding of gravity.
The way that it bends and warps is governed by the matter in the Universe. Depending on what matter there is, then space-time responds to it. If two black holes, for example, are in orbit around each other, spiralling in towards each other, then that will predictably create ripples in this space-time fabric called gravitational waves.
But the contradiction arises because our best and most fundamental understanding of matter is quantum mechanical. One of the essential features of quantum mechanics is that quantum mechanical events are inherently unpredictable. When a quantum mechanical event happens, we don’t know in advance what the outcome will be. We know what the possibilities are, but we won’t know which one will happen. Like if you go to a horse race, you know that one of the horses will win, but you don’t know which one in advance. That quantum mechanical feature of matter is ignored by General Relativity. There’s the contradiction: quantum mechanics says that matter behaves in a stochastic or random way, but General Relativity assumes that matter behaves in a predictable way.
SO HOW DO WE FIND A RESOLUTION TO THIS CONTRADICTION?
There’s a global community of people working on quantum gravity. It’s a strange situation at the
moment, in which the experimental evidence pointing us in one direction or another in quantum gravity research is very, very scarce. It’s hard to be guided by actual observations. For example, at the time of the Big Bang, roughly 13.7 billion years ago, when the matter in the Universe was in a hot, dense state… that realm is where both gravitational and quantum effects will be important. But it’s very far from us in time. So, it’s difficult for us to probe that era to get experimental evidence of what quantum gravity should be like.
CAN WE LOOK OUT INTO SPACE AND SEE THIS HAPPENING?
We can. So, cosmology – which is the study of the Universe at the largest scales that we can observe – is probably the most promising area that we can look to for evidence for different approaches to quantum gravity. I am hopeful that more and more cosmological data will, in the not so distant future, start to distinguish between different approaches, and we’ll be able to be guided by that cosmological data in our research in quantum gravity.
WHAT ARE THE DIFFERENT APPROACHES?
I could divide them roughly into two… I mean, there’s overlap between them, and there are scientists who work on more than one approach, but roughly speaking, they can be divided into two camps. There’s one approach which comes from a tradition of particle physics, called string theory. These are physicists who have been focused on trying to understand matter at the most fundamental level, the standard model of particle physics. In string theory, the fundamental particles are conjectured to be different modes of vibration of a fundamental substance, which is one-dimensional. That’s why it’s called string theory; string is one-dimensional.
The other tradition takes the four-dimensional fabric of space-time as the starting point and to think about it as having a quantum mechanical nature. That stems from physicists working on General Relativity and gravitational physics, from which arises approaches that are more focused on space-time than they are on matter.
FOUR-DIMENSIONAL SPACE-TIME IS QUITE HARD TO GET YOUR HEAD ROUND.
Yes, yes, it is. It’s a new worldview, a new way of thinking about the Universe. How do you get your head around three dimensions?
THREE DIMENSIONS IS SOMETHING THAT WE’RE ALL FAMILIAR WITH, RIGHT?
Yes, good. But what does it mean exactly? Well, what it means is that you can think of a thing, let me say… my teacup. To tell you where it is, I have to give you three numbers, three coordinates. How high it is above the floor, how far it is from the front wall, and how far it is from the side wall. That’s what we mean by space being threedimensional. If you want to pinpoint your position in Bristol right now on a map, you only need to give two numbers: the two coordinates of the coordinate grid on the map. So, the map of Bristol is two-dimensional, the space in this room around my teacup is three-dimensional.
The idea of four-dimensional space-time is that you need four numbers to pin down not just where you are but when you are. And what I mean by ‘when you are’ is not you, because you persist for many moments of time, but a particular instance of you. I mean, you now.
So, to say where that event is of you, you need to give four numbers. Three where you are in space, roughly speaking, and one of what time it is at that moment. Four-dimensional space-time is the collection of all these events.
HOW DOES THAT RELATE TO QUANTUM GRAVITY?
Well, first of all it relates to gravity. Space-time is the fundamental way that we understand gravity.
If you take all of the events in the Universe, then they form this four-dimensional fabric. The structure of that four-dimensional fabric manifests itself as gravitational phenomena. It explains gravity. It tells us why the planets orbit the Sun and why the galaxies behave as they do, why black holes exist, so this four-dimensional fabric of space-time is gravity.
Now, to understand quantum gravity, we have to understand quantum space-time. In General
“The idea of four-dimensional space-time is that you need four numbers to pin down not just where you are but when you are … a particular instance of you. I mean, you now”
Relativity, space-time is smooth and continuous. But in the approach to quantum gravity that I work on, called causal set theory, the conjecture is that this smooth fabric is just an approximation to something which is fundamentally granular, bitty, pixelated. Fundamentally atomic. The word ‘atom’ means uncuttable. It’s something you can’t divide up any more. It’s conjectured to be made of fundamental events that are the smallest possible events, and you can’t cut them up any more.
Causal set is just the name we give to the mathematical, discrete, atomic object. The originator of causal set theory is my close colleague, a physicist called Rafael Sorkin.
HOW WILL THINKING ABOUT SPACE-TIME AS GRANULAR HELP SOLVE THE PROBLEM?
It relates to our understanding of the nature of the quantum world. There’s no consensus on how to understand quantum theory, and but one approach is called ‘the sum over histories’. It’s associated very closely with the particle physicist Richard Feynman.
In this approach, you think about a quantum system in terms of things that can happen, events, and then histories, which are very detailed ways in which that event can happen. Feynman’s sum over histories gives you a way of making predictions about those events, rules about how to calculate the probability of an event happening.
My colleagues and I are trying to base an understanding of the quantum physical world, on this sum over histories.
PROF STEPHEN HAWKING WAS YOUR PHD SUPERVISOR. WHAT WAS HE LIKE?
It was an amazing experience being his student. Stephen was a generous supervisor. He involved me in the work that he was doing, he gave me a great problem to work on, and he was approachable. I was a shy person and not good at putting myself forward, but he was not standoffish at all. He always made time for me. Even though I would often have to wait for a long time before seeing him because he was so busy, he always made it clear that science and his work and his research was a priority.
That was an important part of my PhD. The things that he taught me are still part of the way that I think about physics. The opportunities that I got from being his student also helped me enormously in my subsequent career. He just expected us to be involved in whatever he was doing at the time. I think that’s very, very encouraging for a young scientist, to feel that they’re part of something bigger.