On the emergence of the structure of physics

Abstract

We consider Hilbert's problem of the axioms of physics at a qualitative or conceptual level. This is more pressing than ever as we seek to understand how both general relativity and quantum theory could emerge from some deeper theory of quantum gravity, and in this regard I have previously proposed a or as a key structure. Here, I outline some of my recent work around the idea of quantum space-time as motivated by this non-standard philosophy, including a new toy model of gravity on a space-time consisting of four points forming a square.This article is part of the theme issue 'Hilbert's sixth problem'.

Quantum gravity on a square graph

“…Here we recall briefly some elements the constructive 'bottom up' approach to quantum Riemannian geometry particularly as used in [5,6,7,8,21,27] that we will use. An introduction to the formalism is in [22] and for discrete sets in [21], with the square mainly from [23].…”

“…Note also that there are potentially two such square-lengths for every edge but we restrict to the 'edge-symmetric' case where the two weights are required to be the same. The quantum Riemannian geometry of a quadrilateral or 'square graph' in this context was recently solved in [23] and is recalled in Section 2.3 along with a small extension (Case 2) from [9]. We adapt these directly for a 'Lorentzian square graph' where horizontal edge weights will be taken negative.…”

Robot Consciousness

“…NL also includes histories that describe the development of NLnat (defined below), the controversy regarding scientific paradigms [185] in that history, and the philosophical questions that have arisen with respect to interpretation of the evolution of science. Examples of the latter are the topics mentioned in the Introduction [Section 1 A, B]: metamathematics and computation theory, metaphysics, the limits of scientific knowledge, and the relative realism [115], [186]-[188] of scientific theories. An essay such as the one that you are reading would be classified as an NL product.…”

Hilbert’s sixth problem: the endless road to rigour

“…F. Golse [32] develops a bridge between the quantum and classical parts of Hilbert's Sixth Problem: he studies the semiclassical mean-field limit for the quantum N-body problem and finds a convergence rate for the mean-field limit. This work is closely related to the analysis of "the limiting processes, there merely indicated, which lead from the atomistic view to the laws of motion of continua", requested by Hilbert. S. Majid in his opinion piece [33] goes beyond the commonly accepted quantum theories. The mission of his approach is to be a step towards understanding "how both General Relativity and Quantum Theory could emerge from some deeper theory of quantum gravity".…”