Entanglement and smooth geometry in 4-spacetime

Abstract

We try to understand quantum entanglement by geometric relations of spatially separated regions of 4-spacetime. The relations become detectable by working in the Euclidean smoothness structure underlying the Lorentzian structure. There are 5-dimensional bridges, i.e. 5-dimensional nontrivial smooth hcobordisms connecting spatially separated 4-regions of spacetime. These connections are nonlocal in spacetime. At the quantum regime spacetime is reduced to its smooth atlases of charts which are related by automorphisms of the maksimal Boolean algebra in the quantum lattice of projections. Quantum entanglement in 4-spacetime can be represented by exotic smoothness structures on R4, which are determined by the h-cobordisms due to the results in particular by Casson, Akbulut, Freedman, Donaldson or Gompf. The involutions of corks correspond to the phases between the Boolean ZFC-models and to the change of the exotic R4 inW5. This work is more a description of the ongoing project than a detailed presentation of the results. The discussion focuses on certain general contexts and even philosophical features.