Schroedinger's cat and the clock: Lessons for quantum gravity

TL;DR

This paper explores how the role of classical clocks and the observer's integrity influence quantum gravity, proposing a topological quantum field theory framework that emphasizes boundary amplitudes and measurement implications.

Contribution

It introduces a novel formulation of quantum mechanics for gravity based on the observer's classical domain and boundary amplitudes, differing from existing approaches.

Findings

Quantum measurement principles imply the observer must be part of a classical domain.

Formulation of quantum mechanics as a topological quantum field theory.

Implications include in-out duality, wave function delocalization, and locality considerations.

Abstract

I review basic principles of the quantum mechanical measurement process in view of their implications for a quantum theory of general relativity. It turns out that a clock as an external classical device associated with the observer plays an essential role. This leads me to postulate a ``principle of the integrity of the observer''. It essentially requires the observer to be part of a classical domain connected throughout the measurement process. Mathematically this naturally leads to a formulation of quantum mechanics as a kind of topological quantum field theory. Significantly, quantities with a direct interpretation in terms of a measurement process are associated only with amplitudes for connected boundaries of compact regions of space-time. I discuss some implications of my proposal such as in-out duality for states, delocalization of the ``collapse of the wave function'' and locality of the description. Differences to existing approaches to quantum gravity are also highlighted.