2021/09/30 by Ding Jia
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Causal sets #Classical mechanics #Context (archaeology) #Cosmology and Gravitation Theories #Duality (order theory) #Geometry #Gravitation #Loop quantum gravity #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Path integral formulation #Physics #Pure mathematics #Quantum #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Spacetime #Spin foam #Symmetry (geometry) #Theoretical physics #gr-qc #hep-lat #hep-th #quant-ph
paper · pdf · open access · doi:10.1088/1361-6382/ac4615
published in Classical and Quantum Gravity 39(3), 035016 (IOP Publishing) · matches well published version
openalex publication_date 2021/12/23 · arxiv created 2022/03/01 · arxiv updated 2022/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
An important task faced by all approaches of quantum gravity is to incorporate superpositions and quantify quantum uncertainties of spacetime causal relations. We address this task in 2D. By identifying a global Z2 symmetry of 1+1D quantum gravity, we show that gravitational path integral configurations come in equal amplitude pairs with timelike and spacelike relations exchanged. As a consequence, any two points are equally probable to be timelike and spacelike separated in a universe without boundary conditions. In the context of simplicial quantum gravity we identify a local symmetry of the action which shows that even with boundary conditions causal uncertainties are generically present. Depending on the boundary conditions, causal uncertainties can still be large and even maximal.