STATISTICAL GEOMETRY: A STUDY ON CLASSICAL AND QUANTUM CASES

• Main Author: ARI WAHYOEDI (NIM : 30211008) , SERAMIKA
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/24270
• Institution: Institut Teknologi Bandung

A fixed theory of gravity is far from being complete. The most promising theory of gravity in this century is general relativity (GR), which is still plagued by several problems. The problems we highlight in this thesis are the thermodynamical aspects and the quantization of gravity. Attempts to understand the thermodynamical aspect of GR have already been studied through the thermodynamics of black holes, while the theory of quantum gravity has already had several candidates, one of them being the canonical loop quantum gravity (LQG), which is the base theory in our work. The correct quantum gravity theory should give a correct and consistent classical limit, which is expected to be general relativity. There exists three theories of gravity which seems to converge towards loop quantum gravity: general relativity, discrete geometry, and (continuous) quantum gravity. These theory are predicted <br /> <br /> <br /> to be effective theories which emerge from LQG for specific asymptotical limits, parametrized by two variables: n and j, respectively, the number and the size of quanta of space. Large j limit gives semi-classical or mesoscopic limit, which is expected to be discrete geometry, large n limit gives the continuous quantum gravity, while both large j and n gives the classical ’continuum’ limit: general relativity. The problem to understand the thermodynamics of GR and to obtain the correct classical limit of discrete geometry and LQG, are related to each other by the language of statistical mechanics, a study of system with large degrees of freedom, where they are described using coarse-grained variables. Coarse-graining is a procedure to describe physical system with a smaller number of variables, which capture only useful information on the system under a lower resolutions. A procedure to coarse-grain a set of quanta of space which leads to the construction of statistical geometry is important, in particular, because it could provide a first step to clarify the problems. We study the statistical aspects of the quanta of space in both classical discrete and quantum pictures. To describe a complex system using fewer degrees of freedom, one requires a coarse-graining procedure. In this thesis, we proposed a coarse-graining method and then applied the method to gravity, both for the classical and quantum case, which leads to the construction of statistical discrete geometry and statistical spin-networks, respectively.