Spacetime-Free Approach to Quantum Theory and Effective Spacetime Structure

TL;DR

This paper proposes a background-independent algebraic framework for quantum theory where spacetime geometry emerges from the relations between observables and states, aiming to understand the emergence of spacetime and gravity.

Contribution

It introduces a spacetime-free algebraic approach to quantum theory where effective spacetime structures arise from quantum states and observable relations without assuming background geometry.

Findings

Effective spacetime structures can emerge from quantum states.

Perturbations in quantum states lead to changes in the emergent spacetime geometry.

The framework links quantum statistical properties to gravitational phenomena.

Abstract

Motivated by hints of the effective emergent nature of spacetime structure, we formulate a spacetime-free algebraic framework for quantum theory, in which no a priori background geometric structure is required. Such a framework is necessary in order to study the emergence of effective spacetime structure in a consistent manner, without assuming a background geometry from the outset. Instead, the background geometry is conjectured to arise as an effective structure of the algebraic and dynamical relations between observables that are imposed by the background statistics of the system. Namely, we suggest that quantum reference states on an extended observable algebra, the free algebra generated by the observables, may give rise to effective spacetime structures. Accordingly, perturbations of the reference state lead to perturbations of the induced effective spacetime geometry. We initiate the study of these perturbations, and their relation to gravitational phenomena.