Structure, Individuality and Quantum Gravity

TL;DR

This paper explores the conceptual foundations of quantum gravity, emphasizing the importance of relations and the principle of maximal permutability, and reviews various candidate theories including string theory and causal set theory.

Contribution

It introduces a novel criterion, the principle of maximal permutability, for identifying fundamental entities in quantum gravity theories, integrating structural realism with quantum and relativistic concepts.

Findings

Relations between things and things between relations are both fundamental.

Processes should be fundamental over states in quantum gravity.

Survey of current quantum gravity approaches and new perspectives on space-time quantization.

Abstract

After reviewing various interpretations of structural realism, I adopt here a definition that allows both relations between things that are already individuated (which I call ``relations between things'') and relations that individuate previously un-individuated entities ("things between relations"). Since both space-time points in general relativity and elementary particles in quantum theory fall into the latter category, I propose a principle of maximal permutability as a criterion for the fundamental entities of any future theory of ``quantum gravity''; i.e., a theory yielding both general relativity and quantum field theory in appropriate limits. Then I review of a number of current candidates for such a theory. First I look at the effective field theory and asymptotic quantization approaches to general relativity, and then at string theory. Then a discussion of some issues common to all approaches to quantum gravity based on the full general theory of relativity argues that processes, rather than states should be taken as fundamental in any such theory. A brief discussion of the canonical approach is followed by a survey of causal set theory, and a new approach to the question of which space-time structures should be quantized ends the paper.