Understanding the Big Bang and how our universe came into being is perhaps the greatest challenge of modern physics -- it will require a new theory reconciling quantum theory and general relativity.
Professor Nicolai. “However, string theorists haven’t been able to establish a compelling connection with the standard model of particle physics. We need to go beyond string theory to find a unifying or basic principle.” The different groups of researchers could benefit greatly from sharing their ideas, insights and experience with each other. However, Professor Nicolai says they tend to exist as separate communities. “These communities don’t really talk to each other, they live in parallel universes,” he says. Professor Nicolai and his colleagues are taking a different approach, aiming to maintain an open dialogue with researchers from different areas. “We need to be open, and to listen to other ideas,” he stresses. “As members of the supergravity and superstring community we remain in contact with researchers in other approaches and try to keep up to date with their research.” The origins of Professor Nicolai’s work in this area can be traced back to earlier research by the physicists Vladimir Belinski, Isaak Khalatnikov and Evgeny Lifshitz (BKL). Their work represents a key discovery in mathematical and theoretical cosmology. “They studied the Einstein equations very close to the singularity and discovered that as you approach the singularity in four dimensions, chaotic behaviour sets in. These are the so-called BKL oscillations,” explains Professor Nicolai. These oscillations have
been known about for around 50 years, but further and much more recent analysis has led to deeper insights. “It turns out that there is an extremely interesting mathematical pattern here which is indicative of a huge infinite-dimensional symmetry,” continues Professor Nicolai. This symmetry is the Kac-Moody E10 symmetry, which is vastly bigger than anything that has been considered so far in physics. Symmetries like this are an important
The E10 symmetry is now the focus of intense attention in the eQG group, with the aim of developing a unified theory of quantum gravity and the other fundamental interactions that is entirely defined by symmetry principles. E10 is a unique mathematical object, says Professor Nicolai. “It is an infinite prolongation of the known symmetries that have been used in physics so far,” he says. The E10 symmetry is also known to have an extremely complicated structure. “The existence of this particular structure has
Once you enter a black hole, you invariably run into a gravitational singularity, where spacetime essentially breaks down. It’s completely clear that at that point another theory is needed. organising principle in physics. “The standard model of particle physics is based on a symmetry. Once you have this symmetry, then with a little extra information you can write down all the equations for the standard model,” outlines Professor Nicolai. The idea Professor Nicolai is exploring is that the true symmetry of gravity, of what comes after Einstein’s general theory of relativity, is only revealed as you push further towards a singularity. “A singularity needs extremely short distances – or extremely high energies. These two things are reciprocal,” he continues.
been known about in mathematics for more than 50 years, but there hasn’t been much progress in terms of understanding it,” outlines Professor Nicolai. “Not many mathematicians are currently working on it, because of its extreme complexity.” An impression of this complexity is conveyed by the `pychedelic’ picture on the following page which represents a slice through the root lattice of the E10 algebra. There is also a theory in physics which cannot be extended further, namely 11-dimensional supergravity, which is often mentioned in connection with M-theory.
A view of the M87 supermassive black hole in polarised light produced by the Horizon Telescope (EHT) collaboration. However, this picture shows only the “outside” of the black hole. The singularity inside the black hole, whose properties research efforts like eQG are trying to explore and understand, hides behind an event horizon from which no information can escape.
The search for a unified theory Einstein’s general theory of relativity is one of the pillars of modern physics, yet it doesn’t explain what happens when spacetime breaks down at a gravitational singularity. Researchers in the eQG Group are working to develop a new theory of quantum gravity, bringing together general relativity and quantum mechanics, as Professor Hermann Nicolai explains.
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The General Theory of Relativity
Exceptional Quantum Gravity
was published over a century ago and it works beautifully to this day, with even modern observations of gravitational waves conforming to Einstein’s field equations. Einstein’s field equations also predict the existence of black holes, which is where the theory starts to break down. “Once you enter a black hole, you invariably run into a gravitational singularity, where spacetime essentially breaks down. It’s completely clear that at that point another theory is needed, because general relativity doesn’t tell you what happens at that singularity,” explains Professor Hermann Nicolai, Director Emeritus of the Max Planck Institute for Gravitational Physics.
A new description is required to deal with this problem, a topic at the core of Professor Nicolai’s work. As the head of the Exceptional Quantum Gravity (eQG) Research Group, Professor Nicolai and his colleagues are addressing one of the greatest challenges in modern physics. “We aim to unify general relativity and quantum mechanics,” he says. A new theory of quantum gravity would represent an important step towards resolving singularities; an analogy can be drawn here with the example of the hydrogen atom. “With the hydrogen atom you have a singularity of the Coulomb potential that would destroy the atom within fractions of a second, but
quantum mechanics helps resolve it,” outlines Professor Nicolai. “We aim to bring together general relativity and quantum mechanics in a way that likewise eliminates all singularities.” The basic building blocks of such a theory have not been identified however, and a wide variety of different approaches to the problem have been put forward. These include approaches based on loop quantum gravity, spin-foam quantum gravity and string theory, the idea that the basic constituents of matter are not point-like particles but rather one-dimensional extended objects, or strings. “The idea is that these strings vibrate, and their vibration modes is what makes up elementary particles,” explains
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