Some Remarks on the Logic of Quantum Gravity

TL;DR

The paper argues that a realist interpretation is essential for quantum gravity theories and suggests that the topos approach offers a promising formalism that avoids the instrumentalist limitations of Hilbert space.

Contribution

It introduces the topos approach as a promising framework for quantum gravity that supports a realist interpretation, contrasting it with the Hilbert space formalism.

Findings

Topos approach provides a natural neo-realist interpretation.

Hilbert space formalism tends to enforce instrumentalist views.

The relation between system logic and metalogic is discussed.

Abstract

We discuss some conceptual issues that any approach to quantum gravity has to confront. In particular, it is argued that one has to find a theory that can be interpreted in a realist manner, because theories with an instrumentalist interpretation are problematic for several well-known reasons. Since the Hilbert space formalism almost inevitably forces an instrumentalist interpretation on us, we suggest that a theory of quantum gravity should not be based on the Hilbert space formalism. We briefly sketch the topos approach, which makes use of the internal logic of a topos associated with a quantum system and comes with a natural (neo-)realist interpretation. Finally, we make some remarks on the relation between system logic and metalogic.