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Paper   IPM / Astronomy / 14574
School of Astronomy
  Title:   SpaceTime from Hilbert Space: Decompositions of Hilbert Space as Instances of Time
  Author(s):  M. Noorbala
  Status:   Submitted
  Journal: arXiv
  Year:  2016
  Supported by:            ipm IPM
There has been recent interest in identifying entanglement as the fundamental concept from which space may emerge. We note that the particular way that a Hilbert space is decomposed into tensor factors is important in what the resulting geometry looks like. We then propose that time may be regarded as a variable that parameterizes a family of such decompositions, thus giving rise to a family of spatial geometries. As a proof of concept, this idea is demonstrated in two toy models based on Kitaev's toric code, which feature a dynamical change of dimension and topology.

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