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Article overview
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Emergence of Space-Time from Topologically Homogeneous Causal Networks | Giacomo Mauro D'Ariano
; Alessandro Tosini
; | Date: |
1 Sep 2011 | Abstract: | In 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 | Services: | Forum | Review | PDF | Favorites |
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