Quantum Histories and Quantum Gravity

Abstract

This paper reviews the histories approach to quantum mechanics. This discussion is then applied to theories of quantum gravity. It is argued that some of the quantum histories must approximate (in a suitable sense) to classical histories, if the correct classical regime is to be recovered. This observation has significance for the formulation of new theories (such as quantum gravity theories) as it puts a constraint on the kinematics, if the quantum/classical correspondence principle is to be preserved. Consequences for quantum gravity, particularly for Lorentz symmetry and the idea of "emergent geometry", are discussed.

35 pages (29 pages main body), two figures

References in corpus (27)

• Analogue Gravity
• Nonstandard optics from quantum spacetime
• Reconstructing the Universe
• Quantum Mechanics as Quantum Measure Theory
• Lorentz violation at high energy: concepts, phenomena and astrophysical constraints
• Lorentz invariance and quantum gravity: an additional fine-tuning problem?
• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• Decoherence, Chaos, and the Correspondence Principle
• Forks in the Road, on the Way to Quantum Gravity
• Classical world arising out of quantum physics under the restriction of coarse-grained measurements
• Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
• Robust Limits on Lorentz Violation from Gamma-Ray Bursts
• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• Quantum Gravity Phenomenology, Lorentz Invariance and Discreteness
• Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
• On Loop Quantum Gravity Phenomenology and the Issue of Lorentz Invariance
• Towards the QFT on Curved Spacetime Limit of QGR. I: A General Scheme
• Disordered locality in loop quantum gravity states
• Towards the QFT on Curved Spacetime Limit of QGR. II: A Concrete Implementation
• Semiclassical States for Constrained Systems
• On Recovering Continuum Topology from a Causal Set
• Manifold dimension of a causal set: Tests in conformally flat spacetimes
• Quantum Histories
• Quantum Geometry and Diffusion
• Geometry, pregeometry and beyond
• Modelling Planck-scale Lorentz violation via analogue models
• Perspectives on Quantum Gravity Phenomenology

Cited by in corpus (7)

• Causal Sets: Quantum gravity from a fundamentally discrete spacetime
• Chaos, decoherence and quantum cosmology
• A Dynamics for Discrete Quantum Gravity
• The Universe as a Quantum Computer
• Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty )$-QGR
• Models for Discrete Quantum Gravity
• An Isometric Dynamics for a Causal Set Approach to Discrete Quantum Gravity