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PROFESSOR BIANCA DITTRICH

Quantum of gravity Professor Bianca Dittrich discusses her career in physics, delving into her innovative loop quantum gravity research and its potential to form the basis of a unified quantum gravity theory will give us a deeper understanding of the nature of space and time. As spacetime is the ‘stage’ on which all other physics happens, this new understanding is bound to influence how we understand the Universe and everything that happens within it quite heavily.

Why is the goal of unifying particle physics and general relativity so difficult to attain with current knowledge?

Can you begin by describing how you started researching quantum gravity?

The first research I conducted in quantum gravity was during my diploma (Master’s) thesis in Germany. I worked with Professor Renate Loll who developed the quantum gravity approach of causal dynamical triangulations, and we were looking into the question of how black holes can be described using this theory. I then undertook my PhD with Professor Thomas Thiemann, which focused on things that could be possible observables when working towards creating a theory of quantum gravity.

What does the theory of quantum gravity aim to achieve, and what benefits will this bring to our understanding of the Universe?

Quantum gravity aims to achieve a consistent theory of our Universe that would be valid over all scales. This is opposed to particle theory and general relativity, which we know are not valid at extremely high energy scales.

As examples, we hope that this could explain the origin of the Universe or the structure of black holes. More generally, quantum gravity

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Particle physics and general relativity are based on very different principles. They describe physics at very different scales; namely microscopic and macroscopic, respectively.

In particle physics, one has a fixed spacetime background, for instance flat space, whereas in general relativity spacetime itself is dynamical.

Thus, there are many extremely useful concepts and techniques of standard quantum field theory – such as the notion of a particle itself – that cannot be applied to a quantisation of general relativity. This means that we have to come up with new concepts, principles and techniques.

The difficult part is to discover the consequences of this theory for the tiniest length in the Universe – which is the Planck scale at 10-35 m – as well as for the largest scales, and everything in between. The new theory has to be consistent with what we know about physics at larger scales, but also solve some deep problems that arise at microscopic scales. Bridging many scales is a very hard problem in physics in general, and in this situation we have to bridge all the scales known to physics.

Can you provide insight into the basis of the loop quantum gravity approach to a quantum gravity theory? Why does it not require a fixed spacetime background?

Spacetime is described by geometry, and this geometry in loop quantum gravity characterises

the basic (quantum) objects as being in the form of quantum geometrical operators.

Thus, spacetime geometry is `fluctuating’: a state of this theory does not describe a fixed spacetime, but encodes the probabilities to measure different spacetime geometries. The consistent construction of such a picture was achieved by Ashtekar, Lewandowski, Smolin, Rovelli and others.

In standard quantum mechanics, a state describes the system at a given time and dynamics are encoded in how this state evolves in time. However, with spacetime being a unified object, a state in quantum gravity describes all of spacetime. The dynamics of the theory is now encoded in the fact that only states of a certain form (satisfying certain equations) are allowed. Constructing these particular states is the key problem, as this is needed to extract predictions of the theory at the different scales.

What are the key differences between string theory and loop quantum gravity theory in forming a unified quantum gravity theory?

The starting points of string theory and loop quantum gravity are quite different.

In string theory, quantum spacetime is tested indirectly. Properties of spacetime are encoded in how very small strings move and interact. Also, in holographic approaches, the properties of the bulk of spacetime are encoded into a boundary theory.

In loop quantum gravity (and other approaches of quantum gravity) one tries to directly construct quantum spacetime; for instance, such a construction could occur via quantum geometrical operators.

This means that one has to confront some problems head-on, but of course the hope is to gain a much more direct understanding of quantum spacetime.

PROFESSOR BIANCA DITTRICH

Unifying the Universe Experts from the Perimeter Institute for Theoretical Physics in Canada are using their extensive expertise in applied mathematics and physics to expand the reach of loop quantum gravity, with an ultimate goal of joining general relativity with quantum mechanics IN THE EARLY 20th Century, two theories revolutionised the way humanity understood the physical world: general relativity and quantum mechanics. The brainchild of Albert Einstein, general relativity maintains that space and time are interwoven, and that this union defines the dynamics of large bodies in our Universe.

Quantum mechanics, on the other hand, describes the motion and interaction of subatomic particles, incorporating counterintuitive concepts such as energy quantisation, wave-particle duality and the uncertainty principle.

The conflict between these two theories is not one of exactitude, but scale, as both general relativity and quantum mechanics are very successful when it comes to describing their own domains, but completely hopeless when describing one anothers’. With compelling and vast evidence suggesting neither theory is false, scientists are working hard to merge these macro and micro views of the workings of the cosmos. By doing so, they will be able to define quantum gravity and, in essence, create a theory of how the Universe works at every scale.

LOOP QUANTUM GRAVITY One specific theory researchers have proposed to bridge the gap between general relativity and quantum mechanics is loop quantum gravity (LQG). LQG takes an approach to the Universe that is similar to taking an integral in calculus. Just as an integral can generalise the area of a mathematical object made up of infinitely small, distinct parts, LQG shows that the continuity of space is built out of something that is granular and discrete. In fact, some have likened this picture of the Universe to a cloth that is made up of extremely fine threads of fabric.

Professor Bianca Dittrich – a researcher in the Perimeter Institute for Theoretical Physics, an independent research organisation in Canada committed to solving foundational issues in theoretical physics – is fascinated by this picture of spacetime in LQG. She has committed the bulk of her career to understanding why and showing how quantum gravity is discrete on the microscopic scale, but gives way to a continuum at larger scales.

CONSTRUCTING MODELS Extracting large-scale behaviour from microscopic building blocks is no easy task.

Dittrich has relied on several methods to achieve this goal. One method that has proven rather successful is coarse graining and Wilsonian renormalisation: “The idea is to construct a family of models at different scales where the model at the coarser scale takes into account the effect of the microscopic degrees of freedom,” explains Dittrich. It is an elegant task, which relies on a bottom-up approach: instead of aiming to describe the dynamics of the system all at once, Dittrich has used these methods to break the problem up into manageable parts, modelled them and then used these simulations to construct new models that are on a coarser scale.

The coarse graining of the models is implemented using tensor network renormalisation tools.

In essence, scientists can use these methods to represent quantum states in terms of networks of interconnected tensors. This is useful for defining the system’s entanglement properties and identifying the system’s most relevant degrees of freedom. “With the help of tensor networks, we can express the dynamics of LQG in a form where different numbers of fundamental building blocks have been summarised into ‘effective’ building blocks,” Dittrich expands.

“Also, these methods can be adapted to work in a background-independent context.” This is important to her research because LQG must be background-independent, meaning it must explain space and time instead of relying on a fixed spacetime background.

SPIN FOAMS Dittrich’s work with LQG has led her to explore models known as spin foams, which describe the time evolution of spin networks. Spin networks use nodes and edges to describe the quantum state of a space at any point in time in a 3D space. For example, six edges joining in a node can describe a cube and if one edge is connected to another node with a further five edges it can represent two cubes glued at a common square.

Spin foams describe the dynamics of LQG in the context of 4D spacetime, which arises as a time evolution of a spin network.

Recently, Dittrich has been working on creating lower dimensional models that mimic key construction principles of spin foams: “We successfully applied tensor network techniques to these models and extracted their large-scale behaviour,” she explains. “The results are very

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To understand and show how – from a microscopic theory which can be understood to describe fundamental building blocks – a continuum spacetime emerges at larger scales. The question of how to derive largescale properties of this emerging spacetime from microscopic background-independent dynamics can be considered the Holy Grail of quantum gravity research.

Since its beginning, LQG has been based on the Ashtekar-Lewandowski (AL) vacuum state, which describes a complete degenerate spatial geometry. Experts in the field were convinced that this was the only possible backgroundindependent vacuum state that could exist, due to the fact that it has been proven to be unique.

Dittrich has changed this picture by altering subtle assumptions of the uniqueness proof. Working with Dr Marc Geiller, she has shown that another representation exists. Upon examining the topological phases that grew out of her spin foam investigations, the team has turned standard thinking within the LQG physics community on its head with the new discovery.

KEY COLLABORATORS Dr Mercedes Martin-Benito, Radboud University Nijmegen, The Netherlands Dr Wojciech Kaminski, Perimeter Institute for Theoretical Physics, Canada Sebastien Steinhaus (dipl. phys.), Perimeter Institute for Theoretical Physics, Canada Dr Marc Geiller, Pennsylvania State University, USA

FUNDING This research was supported by the Perimeter Institute for Theoretical Physics.

Research at the Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. Further funding has been provided by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery grant and an Early Researcher Award from the Ontario Government.

CONTACT Professor Bianca Dittrich Faculty Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo, ON N2L 2Y5 Canada T +1 519 569 7600 x 7504 E bdittrich@perimeterinstitute.ca ww.perimeterinstitute.ca/people/biancadittrich PROFESSOR BIANCA DITTRICH studied Physics at the University of Potsdam and worked for her PhD at the Max Planck Institute for Gravitation Physics and the Perimeter Institute. After a postdoc at the Perimeter Institute and a Marie Curie Fellowship at Utrecht University she headed a Max Planck Research Group at the Max Planck Institute in Potsdam. She joined the Perimeter Institute as a faculty member in 2012.

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encouraging and indicate that spin foams yield rich dynamics and topological phases.”

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Their new vacuum is much closer to the spirit of spin foam quantisation as it describes geometries with zero curvature, which characterise the basic building blocks of spin foams. Excitations – that is, deviations from the vacuum – are then parameterised by curvature. This is in contrast to the AL vacuum which gives geometries with zero volume and excitations parameterised by nonvanishing volume. “The methods we applied to construct this new representation are sufficiently general to be applied to other topological phases,” Dittrich elaborates. “This allows us to expand the dynamics of LQG around different vacua.

Thus, from looking at the theory from different viewpoints, we will not only learn much more about the structure of the theory but also facilitate physical predictions in different regimes.”

Significantly, this new vacuum state parallels nicely with general relativity, and could make it much easier for scientists to make cosmological predictions and describe large-scale physics, such as the propagation of matter fields on (quantum) spacetime.

TO INFINITY AND BEYOND The future is bright for Dittrich’s research endeavours, and she already has two directions in which she wants to expand knowledge. First, she will extend her lower dimensional spin

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foam models to three and four dimensions, with the intention of describing their dynamics and discovering a large-scale limit for LQG. And second, she will explore the topological phases she has discovered further to see if she can find more alternative representations for LQG. Dittrich is optimistic about the effect her research – both past and upcoming – will have on the scientific community: “If this programme is successful, it will reveal how spacetime can emerge from a more fundamental quantum structure. Similar to the discovery of the atomicity of matter, such a viewpoint can revolutionise our understanding of physics”.