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 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.
Highlights
We address this question and present a binary description of space-time in 1+1 dimensions
We will translate the Pachner moves to operations on the integer string encoding
We show how to map a foliated triangulation to a bit array
Summary
Operations (i)-(iii) introduce an equivalence class on the space of all integer strings, and there exists a straightforward algorithm to single out its representatives. This can be illustrated with the help of a simple example, evaluating all unique histories for triangulations with 3 spatial slices from 3 to 5 forks. Starting from all possible strings, one can apply operations (i)-(iii) to single out one representative Sof every equivalence class: (1, 2, 3), (1, 2, 3, 3), (1, 2, 2, 3), (1, 2, 3, 2), (1, 1, 2, 3), (1, 2, 3, 3, 3), 1+1 dimensional triangulations [18], suffices to evaluate the discretized path integral (Eq (4)). We compare the degeneracies in the configuration space in the binary with the integer encoding
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