Publication: Reducing space-time to binary information
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2014-03-07
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IOP Publishing Ltd
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Abstract
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 EinsteinHilbert 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.
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© 2014 IOP Publishing Ltd. We acknowledge support by the Spanish MICINN grant FIS2009-10061, the CAM research consortium QUITEMADS 2009-ESP-1594, the European Commission PICC: FP7 2007-2013, Grant No. 249958, the UCMBS grant GICC-910758, and the Austrian Science Fund (FWF) through project F04012. SW was supported by Marie Curie Actions – Career Integration Grant (CIG); Project acronym: MULTI-QG-2011 and the FQXi Minigrant “Physics without borders”. SW would like to thank Matt Visser, Piyush Jain, and Thomas Sotiriou for enlightening comments and discussions. GDLC acknowledges support from the Alexander von Humboldt foundation.