Unimodular conformal and projective relativity

• Main Author: Bradonjić, Kaća
• Language: en_US
• Published: Boston University 2018
• Online Access: https://hdl.handle.net/2144/31513

Thesis (Ph.D.)--Boston University === PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at [e-mail]. Thank you. === Existing approaches to quantum gravity fail to fully reconcile the background independence of general relativity and the role of the quantum of action in quantum-mechanical theories. They disagree as to which classical space-time quantities (or observables) should be quantized, and use quantization techniques without taking into consideration the role of measurability analysis in assuring consistency between the definability of these observables and their individual measurability and joint co-measurability by some idealized process. This thesis outlines the framework of a new approach, called Unimodular Conformal and Projective Relativity (UCPR), discusses the classical measurability of all of its basic observables, and examines the problem of extending this analysis to a physically motivated theory of quantum gravity. We consider the unimodular group of transformations (i.e., those with the unit determinant), rather than the full diffeomorphism group, as the basic symmetry group of the theory. This reduction leads to a natural decomposition of the linear affine connection into a projective connection and an affine one-form, and of the Riemannian pseudo-metric into a conformal metric and a volume-element. The geometric representation of all four structures is motivated by their physical interpretation. The projective connection and affine one-form are motivated by the law of inertia; the first determines the paths traversed by massive particles moving only under the combined influence of inertia and gravitation, while the second assures that these particles move at constant speed. The conformal metric determines constant-phase wave-fronts of zero rest-mass fields, while the volume-element permits the averaging of physical fields independently of other space-time structures. Using the UCPR framework, we decompose the usual general-relativistic Lagrangian, and derive the homogenous and inhomogenous field equations and compatibility conditions for the four fundamental fields. The application of this formalism to systems including only zero rest-mass fields is presented. Finally, we outline some approaches to classical measurability analysis of all the relevant structures, and their possible extension to phenomena in which the quantum of action plays a significant role. === 2031-01-01