Statistical Geometry of Weaves in Quantum Gravity

University Of Mississippi, University MS

Investigators

Abstract

This project is part of an ongoing effort by a large number of researchers to develop a quantum gravity theory, which fully incorporates quantum principles into general relativity and gravitation. Many approaches have been proposed over the years; currently, the two that are widely regarded as the most promising ones are superstring theory, which emphasizes the relation of other forces with gravitation, and quantum geometry, which emphasizes the need to understand the fundamental structure of space and time. These two approaches may be related to each other and lead to complementary views of the same theory, but at present they are being independently pursued. This project will contribute to the quantum geometry approach, which uses the Ashtekar variables for general relativity and "weaves" or networks of points to replace smooth space. The goal is to use statistical techniques and computer simulations to study in detail (i) which combinations of such networks are the ones we ordinarily observe as smooth space, and (ii) how large the uncertainties or fluctuations of space are as a result. While calculations by other researchers have given approximate, preliminary results on the first part, the techniques that will be used in this project are unique in enabling us to address the second one. From the point of view of our basic understanding of nature, the quantum gravity program is often listed as one of the top outstanding problems today. Both quantum theory and general relativity are supposedly applicable to all physical phenomena, and this can only be true if they are compatible with each other. We have reason to believe that, once we understand their connection well, quantum gravity will have applications in many different areas, similarly to what happened with quantum theory almost 100 years ago. The suggestion has been made, for example, that quantum gravity sets the ultimate limits for information storage and computation capabilities. For the time being, however, we need to test the theory with simpler predictions that can be verified, such as the effect of these fluctuating "weaves" on particles and radiation that reach us from distant galaxies across billions of light years. Successfully predicting effects such as this one will lead to progress in quantum gravity, and will also give us a new tool for the analysis of information from the most distant parts of the universe. This project at the University of Mississippi will contribute by helping develop a reliable working model for the fluctuating weaves that make up space, as well as using the excellent computational facilities of the University and helping train students in the use of computational techniques.