Grant: Discovery Grants Program - Individual

The physics of the small, on the scale of atomic and nuclear phenomena, is described by quantum theory. There are now broadly successful quantum theories describing three of the four observed fundamental forces in nature, the electromagnetic, and the weak and strong nuclear interactions. On the other hand the physics of large scales, such as solar systems, galaxies and cosmology as a whole, are described by a gravitational theory, the most successful of which is Einstein's general relativity. This theory envisions gravity not as a force but as a manifestation of the curvature of the geometry of space and time, welded together as one entity: spacetime. General relativity has passed every experimental test to which it has been subjected, the most recent being the direct detection of gravitational waves. Quantum theory is expected to be important in gravitational phenomena involving very strong gravitational fields of highly compact objects, such as near the center of black holes and in the very early stages of the Universe; these are regimes of large spacetime curvature. In these regimes, general relativity predicts curvature singularities, which are taken as a sign of the breakdown of the theory. As in atomic physics, it is expected that quantum theory will come to the rescue and "resolve" the singularity. For these reasons, combining gravitation with quantum theory is widely considered to be the frontier problem in theoretical physics. It would reveal what is a quantum geometry with quantum matter. The purpose of this research program is to explore the possible physics of quantum gravity using two distinct approaches. One of these falls under the broad area referred to in the literature as "semiclassical" gravity, where gravity is viewed as classical and matter as quantum; the goal is to study the full interacting dynamics of classical geometry with quantum matter---how does a quantum state affect spacetime geometry, and how in turn does geometry affect the quantum state? This has not been previously explored from a Hamiltonian perspective that might be called "semiclassical geometrodynamics." The second problem is the exploration of gravitational collapse with potential quantum gravity effects included; two important effects are the discreteness of spacetime on sufficiently small scales and quantum fluctuations of geometry. Classical gravitational collapse leads to a black hole;  the goal is to find how quantum effects modify the collapse process and what is the ultimate result of quantum evolution. The ideas and methods to be employed in this research program will provide new ways for studying coupled quantum-classical dynamics and new insights into quantum gravity. Students working on the associated projects will develop deep critical thinking and computer programing skills of wide applicability to society.