Abstract
I exploit the close connection between the tessellation of space-time in the Regge calculus and an Eilenberg homology to investigate the deep quantum nature of space-time in a simple bubble universe of a size consistent with the Planck regime. Following the mathematics allows me to define this granulated space-time as the embedding space of the skeleton of a computational spin network inside a quantum computer. This approach can be regarded as a quantum simulation of the equivalent physics. I can, therefore, define a fundamental characterisation of any high-energy physical process at the Planck scale as equivalent to a quantum simulation inside a quantum computer.
Highlights
I define a bubble universe to be a possibly unique simple bubble of space-time developing within the Planck regime over a few atto-seconds after the big bang
A simpler quantum-based theory, based on the elegant idea of small finite increments of space-time, is adequate to the task, as we will show. The point of these quantum assumptions is to impose a granularity on space-time at the Planck scale; as is implied by most theories of quantum gravity; see for example [8] (Chapter 2)
I start this discussion from the reasonable assumption that space-time is granular in a bubble universe of a size consistent with the Planck regime
Summary
The mathematics of this black box theory of reality are best expressed in the language of linear operators as first pointed out by Born, Jordan and Heisenberg. An abstract W*-algebra A is a C*-algebra which is (isomorphic to) the dual space of a Banach space [3]; Observations/measurements of a quantum system such as the total energy in a GNS representation correspond to discrete eigenvalues of the corresponding matrix operator. This implies that the set of observables corresponds to the subset of selfadjoint operators (with real eigenvalues)
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