Periodic Reporting for period 4 - QUANTIVIOL (Quantifying Quantum Gravity Violations of Causality and the Equivalence Principle)
Reporting period: 2022-03-01 to 2023-08-31
Black holes provide a unique battleground where fundamental principles of physics clash. Hawking calculated 45 years ago that black holes permanently destroy information that falls into them, violating the principle of unitarity. In the decades since Hawking's calculation, strong evidence has emerged that quantum gravity effects neglected by Hawking rescue the principle of unitarity, allowing information to escape form black holes.
However, the price of restoring unitarity is steep: we must give up at least one of two other cherished principles. Either black holes must violate causality, allowing signals to travel faster than the speed of light. Or, they must violate the equivalence principle, the foundation of Einstein's theory of general relativity, and burn up infalling observers at their event horizon.
In this project, we will quantify, for the first time, the extent of this conflict. How large must the violations of causality or the equivalence principle be in order to rescue unitarity? And can these quantum gravity effects be measured observationally?
However, the price of restoring unitarity is steep: we must give up at least one of two other cherished principles. Either black holes must violate causality, allowing signals to travel faster than the speed of light. Or, they must violate the equivalence principle, the foundation of Einstein's theory of general relativity, and burn up infalling observers at their event horizon.
In this project, we will quantify, for the first time, the extent of this conflict. How large must the violations of causality or the equivalence principle be in order to rescue unitarity? And can these quantum gravity effects be measured observationally?
We have quantified the entanglement between the quantum fields inside and outside the event horizon. We have also worked to better understand wormholes, which play a key role in understanding how the information escapes from black holes. While wormholes were confined to the realm of science fiction just 5 years ago, it turns out that they are ubiquitous in quantum gravity. My team has played an important role in understanding these wormholes.
A key question is what types of spacetime geometries can exist in semi-classical gravity. My team has made substantial progress on this question, by establishing lower bounds on the energy density of quantum field theories, which then lead to constraints on exotic spacetime geometries. We have also shown how to make use of the novel negative energy available in quantum field theory to construct traversable wormholes.
Additionally, we have constrained the size of quantum gravity effects near black holes, calculating the extent to which correlation functions in pure states differ from the average. These calculations indicate the size of quantum gravity effects and constrain theories that postulate large quantum gravity corrections near black hole horizons.
Our results have been disseminated in journal articles, seminars, colloquia, and workshops. Other researchers in the field have exploited and built upon our results.
A key question is what types of spacetime geometries can exist in semi-classical gravity. My team has made substantial progress on this question, by establishing lower bounds on the energy density of quantum field theories, which then lead to constraints on exotic spacetime geometries. We have also shown how to make use of the novel negative energy available in quantum field theory to construct traversable wormholes.
Additionally, we have constrained the size of quantum gravity effects near black holes, calculating the extent to which correlation functions in pure states differ from the average. These calculations indicate the size of quantum gravity effects and constrain theories that postulate large quantum gravity corrections near black hole horizons.
Our results have been disseminated in journal articles, seminars, colloquia, and workshops. Other researchers in the field have exploited and built upon our results.
The project has now been completed. We developed new techniques for calculating, in the context of gravity, to what extent observables in a class of pure states differ from the average. We used these techniques to estimate the size of quantum gravity effects near black holes, giving robust predictions.
In addition, we developed techniques in quantum field theory to place lower bounds on the energy density. We made use of these lower bounds to derive singularity theorems which generalize the famous Penrose singularity theorem to the real quantum mechanical world.
In addition, we developed techniques in quantum field theory to place lower bounds on the energy density. We made use of these lower bounds to derive singularity theorems which generalize the famous Penrose singularity theorem to the real quantum mechanical world.