The Chrono'Geometrical Structure of Special and General Relativity: Towards a Background-Independent Description of the Gravitational Field and Elementary Particles

TL;DR

This paper proposes a background-independent, Hamiltonian framework for describing gravity and matter in a way that unifies special and general relativity, addressing foundational interpretational issues and suggesting a new quantization scheme.

Contribution

It reformulates relativistic physics to incorporate the chrono-geometrical structure and proposes a background-independent approach to gravity and matter quantization.

Findings

Background-independent description of gravitational field and matter

Resolution of interpretational issues like point-events and simultaneity

Proposal of a new background-independent quantization scheme

Abstract

Since the main open problem of contemporary physics is to find a unified description of the four interactions, we present a possible scenario which, till now only at the classical level, is able to englobe experiments ranging from experimental space gravitation to atomic and particle physics. After a reformulation of special relativistic physics in a form taking into account the non-dynamical chrono-geometrical structure of Minkowski space-time (parametrized Minkowski theories and rest-frame instant form) and in particular the conventionality of simultaneity (re-phrased as a gauge freedom), a model of canonical metric and tetrad gravity is proposed in a class of space-times where the deparametrization to Minkowski space-time is possible. In them it is possible to give a post-Minkowskian background-independent description of the gravitational field and of matter. The study of the dynamical chrono-geometrical structure of these space-times allows to face interpretational problems like the physical identification of point-events (the Hole Argument), the distinction between inertial (gauge) and tidal (Dirac observables) effects, the dynamical nature of simultaneity in general relativity and to find background-independent gravitational waves. These developments are possible at the Hamiltonian level due to a systematic use of Dirac-Bergmann theory of constraints. Finally there is a proposal for a new coordinate- and background-independent quantization scheme for gravity.