International Research Fellowship Program: Computational Investigation of the Semiclassical Limit of Loop Quantum Gravity

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0401966WillisThe International Research Fellowship Program enables U.S. scientists and engineers to conduct three to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad.This award will support a twenty-two-month research fellowship by Dr. Joshua L. Willis to work with Dr. J. Daniel Christensen at the University of Western Ontario.Reconciling Einstein's theory of gravity (general relativity) with quantum theory is a central, fundamental problem in theoretical physics, and loop quantum gravity is presently the only rigorously well defined candidate quantum theory of gravity. Establishing whether or not it has the correct classical limit is the key open question for this approach to quantum gravity. What this work seeks to understand is whether the theory, which gives a description of space and time at the smallest scales where it is essential to treat the gravitational force quantum mechanically, is also able to describe the large scales already successfully described by Einstein's general theory of relativity. Thus, it is an important consistency check on the theory: it must agree with the classical theory where the latter is valid. In this project, the PI seeks to investigate the semiclassical limit of the full theory. Specically, he proposes to continue existing work at the host institution as well as to begin other work, each of which seeks to computationally investigate whether or not the description of space arising in loop quantum gravity - an interconnected network or lattice of "edges" joined together at vertices - can look on a large enough scale like the smooth continuum of space that we see around us. We do this by calculating, numerically, whether certain characteristic properties of the continuum picture, such as the areas of surfaces, have values coming from the quantum theory that are very close to those coming from the classical theory. The results from simpler models have so far been encouraging, but firm conclusions cannot be drawn until the full theory is investigated. UWO provides a unique opportunity to do this as Dr. Christensen's group there is perhaps the only one in the world where such a computational approach to quantum gravity is being carried out. Even though the field of quantum gravity as a whole can be rather abstract and involve mathematics not accessible to many undergraduates, the computational aspects of the work are accessible and allow a "hands-on" approach to learning both computational techniques and also the physics of the model to which those techniques are applied. By its nature, this work must draw on different disciplines, from pure mathematics, to physics, to computational methods, and thus involves interaction between researchers and students in these fields.