Clock-dependent spacetime

TL;DR

This paper explores a quantum gravity framework where spacetime properties like dimension and topology depend on the choice of local clocks, challenging the fixed background assumptions of classical relativity.

Contribution

It introduces a theory of quantum gravity without a preferred Hilbert space partition, showing spacetime features depend on local clock choices.

Findings

Spacetime properties vary with local clock selections.

The theory does not assume a fixed spacetime background.

Spacetime topology and geometry are emergent from clock choices.

Abstract

Einstein's theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local kinematic Hilbert spaces. In this paper, we consider a theory of quantum gravity that does not come with a preferred partitioning of the kinematic Hilbert space. It is pointed out that, in such a theory, dimension, signature, topology and geometry of spacetime depend on how a collection of local clocks is chosen within the kinematic Hilbert space.