LEAPS-MPS: Investigating Emergent Gravity in Combinatorial Quantum Systems

San Jose State University Foundation, San Jose CA

Investigators

Abstract

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). This award funds the research activities of Professor Kassahun Betre at San Jose State University. Space and time are perhaps the most fundamental aspects of physical reality. However, a deeper explanation of their nature is still a mystery. Many possible approaches toward addressing this issue have been pursued in recent years; these are usually grouped under names such as String Theory, Loop Quantum Gravity, and Causal Dynamical Triangulation. As part of this project, Professor Betre will pursue a complementary approach called Emergent Background-Independent Quantum Gravity (EBIQG). This approach posits that the building blocks of space and time are certain quantum-mechanical relationships that can be expressed in the form of graphs. Within such an approach, space and time emerge only as macroscopic averages. Professor Betre will build numerical tools that simulate the statistical and thermodynamic properties of the graph-theoretic quantum systems, and construct a model for the emergence of dimension and geometry in a two-dimensional quantum gravity. This project is also envisioned to have significant broader impacts. San Jose State University is a minority-serving institution, and undergraduate and masters students participating in this research project will develop not only analytical research skills but also practical skills in conducting numerical simulations. This project will also provide these students the experience and confidence to succeed in STEM fields. More technically, this research will bring two important new directions to the field of EBIQG. First, it highlights the emergence of the uniform dimension of space itself as a starting point. A graph-theoretic generalization of the dimension of Euclidean space called inductive dimension is used as a dynamical quantity of the graph microstates that course-grains into the emergent dimension of smooth manifolds. Second, this research project models discretized space using all geometric graphs --- graph-theoretic analogues of triangulations of surfaces --- rather than just regular lattices and regular graphs. With this approach, the emergence of quantum gravity from the graph models appears as a degenerate zero- temperature ground state. Such research will therefore help to pave the way towards a concrete model for emergent integer dimension and geometry from a non-geometric graph-theoretic Hilbert space. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.