Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 006, 33 pages      arXiv:1605.03942      https://doi.org/10.3842/SIGMA.2017.006

Spacetime-Free Approach to Quantum Theory and Effective Spacetime Structure

Matti Raasakka
Näyttelijänkatu 25, 33720 Tampere, Finland

Received May 13, 2016, in final form January 17, 2017; Published online January 24, 2017

Abstract
Motivated by hints of the effective emergent nature of spacetime structure, we formulate a spacetime-free algebraic framework for quantum theory, in which no a priori background geometric structure is required. Such a framework is necessary in order to study the emergence of effective spacetime structure in a consistent manner, without assuming a background geometry from the outset. Instead, the background geometry is conjectured to arise as an effective structure of the algebraic and dynamical relations between observables that are imposed by the background statistics of the system. Namely, we suggest that quantum reference states on an extended observable algebra, the free algebra generated by the observables, may give rise to effective spacetime structures. Accordingly, perturbations of the reference state lead to perturbations of the induced effective spacetime geometry. We initiate the study of these perturbations, and their relation to gravitational phenomena.

Key words: algebraic quantum theory; quantum gravity; emergent spacetime.

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