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Open AccessArticle

Switching Internal Times and a New Perspective on the ‘Wave Function of the Universe’

1
Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
2
Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
Universe 2019, 5(5), 116; https://doi.org/10.3390/universe5050116
Received: 7 March 2019 / Revised: 5 May 2019 / Accepted: 7 May 2019 / Published: 14 May 2019
(This article belongs to the Special Issue Progress in Group Field Theory and Related Quantum Gravity Formalisms)
Despite its importance in general relativity, a quantum notion of general covariance has not yet been established in quantum gravity and cosmology, where, given the a priori absence of coordinates, it is necessary to replace classical frames with dynamical quantum reference systems. As such, quantum general covariance bears on the ability to consistently switch between the descriptions of the same physics relative to arbitrary choices of quantum reference system. Recently, a systematic approach for such switches has been developed. It links the descriptions relative to different choices of quantum reference system, identified as the correspondingly reduced quantum theories, via the reference-system-neutral Dirac quantization, in analogy to coordinate changes on a manifold. In this work, we apply this method to a simple cosmological model to demonstrate how to consistently switch between different internal time choices in quantum cosmology. We substantiate the argument that the conjunction of Dirac and reduced quantized versions of the theory defines a complete relational quantum theory that not only admits a quantum general covariance, but, we argue, also suggests a new perspective on the ‘wave function of the universe’. It assumes the role of a perspective-neutral global state, without immediate physical interpretation that, however, encodes all the descriptions of the universe relative to all possible choices of reference system at once and constitutes the crucial link between these internal perspectives. While, for simplicity, we use the Wheeler-DeWitt formulation, the method and arguments might be also adaptable to loop quantum cosmology. View Full-Text
Keywords: quantum relational dynamics; switching relational clocks; quantum symmetry reduction; quantum cosmology; quantum general covariance; Dirac and reduced quantization; Hamiltonian constraint; wave function of the universe quantum relational dynamics; switching relational clocks; quantum symmetry reduction; quantum cosmology; quantum general covariance; Dirac and reduced quantization; Hamiltonian constraint; wave function of the universe
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Höhn, P.A. Switching Internal Times and a New Perspective on the ‘Wave Function of the Universe’. Universe 2019, 5, 116.

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