Inter-theory Relations in Quantum Gravity: Correspondence, Reduction, and Emergence

TL;DR

This paper explores the relationships between current theories and quantum gravity, emphasizing correspondence, reduction, and emergence, to clarify their roles in theory development and the criteria for identifying quantum gravity.

Contribution

It clarifies the roles of correspondence, reduction, and emergence in quantum gravity, proposing that reduction is a form of correspondence and discussing emergence's limited role.

Findings

Correspondence demonstrates compatibility between overlapping theories.

Reduction is a special case of correspondence and part of QG definition.

Emergence likely occurs between QG and general relativity but is not essential for QG development.

Abstract

Relationships between current theories, and relationships between current theories and the sought theory of quantum gravity (QG), play an essential role in motivating the need for QG, aiding the search for QG, and defining what would count as QG. Correspondence is the broad class of inter-theory relationships intended to demonstrate the necessary compatibility of two theories whose domains of validity overlap, in the overlap regions. The variety of roles that correspondence plays in the search for QG are illustrated, using examples from specific QG approaches. Reduction is argued to be a special case of correspondence, and to form part of the definition of QG. Finally, the appropriate account of emergence in the context of QG is presented, and compared to conceptions of emergence in the broader philosophy literature. It is argued that, while emergence is likely to hold between QG and general relativity, emergence is not part of the definition of QG, and nor can it serve usefully in the development and justification of the new theory.