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07 February 2025
 
  » arxiv » 1109.0118

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Emergence of Space-Time from Topologically Homogeneous Causal Networks
Giacomo Mauro D'Ariano ; Alessandro Tosini ;
Date 1 Sep 2011
AbstractIn this paper we study the emergence of Minkowski space-time from a causal network. Differently from previous approaches, we require the network to be topologically homogeneous, so that the metric is derived from pure event-counting. Emergence from events has an operational motivation in requiring that every physical quantity---including space-time---be defined through precise measurement procedures. Topological homogeneity is a requirement for having space-time metric emergent from the pure topology of causal connections, whereas physically corresponds to the universality of the physical law. We analyze in detail the case of 1+1 dimension. Coordinate systems are established via an Einsteinian protocol, and lead to a digital version of the Lorentz transformations. In a computational analogy, the foliation construction can also be regarded as the synchronization with a global clock of the calls to independent subroutines (corresponding to the causally independent events) in a parallel distributed computation, and the Lorentz time-dilation emerges as an increased density of leaves within a single tic-tac of a clock, whereas space-contraction results from the corresponding decrease of density of events per leaf. The operational procedure of building up the coordinate system introduces an in-principle indistinguishability between neighboring events, resulting in a network that is coarse-grained, the thickness of the event being a function of the observer clock. The present simple cinematical construction does not extend straightforwardly to space dimension greater than one, due to anisotropy of the maximal speed: this issue is cured by a superposition of causal paths, specializing the causal network to a quantum computational one.
Source arXiv, 1109.0118
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