Reducing space-time to binary information

We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is ergodic in the class of space-time manifolds respecting coordina...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2014-03, Vol.47 (9), p.95301-14
Main Authors: Weinfurtner, Silke, Cuevas, Gemma De las, Martin-Delgado, Miguel Angel, Briegel, Hans J
Format: Article
Language:English
Subjects:
Computer simulation
covariant and sum-over-histories quantization
Einstein equations
Encoding
Ergodic processes
Fluctuation
information and communication theory
lattice and discrete methods
Lattices
Mathematical analysis
Mathematical models
Path-integral methods
quantum gravity
quantum information
Tensors
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Summary:We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is ergodic in the class of space-time manifolds respecting coordinate invariance of general relativity. Space-time fluctuations can be represented in a classical lattice gas model whose Boltzmann weights are constructed with the discretized form of the Einstein-Hilbert action. Within this framework, it is possible to compute basic quantities such as the Ricci curvature tensor and the Einstein equations, and to evaluate the path integral of discrete gravity. The description as a lattice gas model also provides a novel way of quantization and, at the same time, to quantum simulation of fluctuating space-time.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/47/9/095301