Spacetime-Free Approach to Quantum Theory and Effective Spacetime Structure

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.

References in corpus (8)

• Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
• Universality of Gravity from Entanglement
• Relational physics with real rods and clocks and the measurement problem of quantum mechanics
• Algebraic Quantum Field Theory
• Emergent General Relativity
• Modular Theory, Non-Commutative Geometry and Quantum Gravity
• The quantum geometric limit
• Unspeakables and the Epistemological path towards Quantum Gravity

Cited by in corpus (5)

• Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
• Reality and super-reality: properties of a mathematical multiverse
• Local Lorentz covariance in finite-dimensional Local Quantum Physics
• Spacetime granularity from finite-dimensionality of local observable algebras
• Thermal Time and Kepler's Second Law