Grant: Discovery Grants Program - Individual

"What is the nature of space and time?" This is a question that has advanced the development of physics through the centuries. Physics was revolutionized at the beginning of the 20th century by three separate paradigm shifts. Firstly, Einstein's special relativity, that is the realization that space and time are unified to a so-called Lorentzian spacetime. Secondly, Einstein's general relativity, that is the vision of Lorentzian spacetimes as dynamical objects that describe the gravitational force. And thirdly, the invention of quantum theory that prescribes an inherent fuzziness to fundamental matter. By the end of the 20th century, it became clear that general relativity and quantum theory, taken separately, predict their own demise: Einstein's theory predicts the collapse of matter to black holes, that crash more and more matter into a spacetime singularity. Quantum theory, describing the fundamental matter interactions, leads to infinities and therefore inconsistencies at very small distances. We need therefore a theory of quantum gravity that replaces smooth spacetime, on which 20th century physics is based, with a truly quantum spacetime. A theory that designates spacetime itself as a fuzzy object would mark a fourth revolution in our understanding of space and time. Currently, we have a number of approaches to a quantum theory of gravity. Most of these approaches are based on the so-called Wick rotation, which replaces real time with imaginary time. This allows the application of powerful simulation techniques, but this process also compromises the Lorentzian nature of spacetime. The Wick rotation technique, although being widely applied in physics, is therefore highly problematic in quantum gravity. In particular it prevents a proper understanding of Lorentzian quantum spacetimes and quantum notions of causal structures. The main aim of this research program will be the development of Lorentzian quantum gravity. This will include methods and tools for computing physical processes within Lorentzian quantum gravity and the investigation of quantum causal structures. The methods and insights will be applied to cosmology and black holes. Understanding their quantization will lead to a resolution of the singularities of the classical theory and their associated paradoxes. By providing a Lorentzian framework and computational tools, this research will be transformative for quantum gravity. A proper understanding of quantum causal structures and quantum time will be only possibly within such a Lorentzian framework and will have a deep impact on physics and philosophy. Quantum gravity research provides an opportunity to work at the true cutting edge of physics. This attracts excellent students, and provides opportunities to engage the public through outreach. These factors will increase student engagement in STEM subjects, which in turn will enable Canada to keep and expand its advantage in the research and development sector.