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Technologies 2017, 5(3), 56; doi:10.3390/technologies5030056

Semiclassical Length Measure from a Quantum-Gravity Wave Function

DIAEE—Department for Astronautics Engineering, Electrical and Energetics, Sapienza University of Rome, Via Eudossiana, 18, 00184 Rome, Italy
Received: 7 July 2017 / Revised: 15 August 2017 / Accepted: 23 August 2017 / Published: 8 September 2017
(This article belongs to the Special Issue Quantum Gravity Phenomenology and Experimental Implications)
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Abstract

The definition of a length operator in quantum cosmology is usually influenced by a quantum theory for gravity considered. The semiclassical limit at the Planck age must meet the requirements implied in present observations. The features of a semiclassical wave-functional state are investigated, for which the modern measure(ment)s is consistent. The results of a length measurement at present times are compared with the same measurement operation at cosmological times. By this measure, it is possible to discriminate, within the same Planck-length expansion, the corrections to a Minkowski flat space possibly due to classicalization of quantum phenomena at the Planck time and those due to possible quantum-gravitational manifestations of present times. This analysis and the comparison with the previous literature can be framed as a test for the verification of the time at which anomalies at present related to the gravitational field, and, in particular, whether they are ascribed to the classicalization epoch. Indeed, it allows to discriminate not only within the possible quantum features of the quasi (Minkowski) flat spacetime, but also from (possibly Lorentz violating) phenomena detectable at high-energy astrophysical scales. The results of two different (coordinate) length measures have been compared both at cosmological time and as a perturbation element on flat Minkowski spacetime. The differences for the components of the corresponding classical(ized) metric tensor have been analyzed at different orders of expansions. The results of the expectation values of a length operator in the universe at the Planck time must be comparable with the same length measurements at present times, as far as the metric tensor is concerned. The comparison of the results of (straight) length measures in two different directions, in particular, can encode the pertinent information about the parameters defining the semiclassical wavefunctional for (semiclassicalized) gravitational field. View Full-Text
Keywords: 04.60.-m quantum gravity; 03.65.Vf phases: geometric; dynamic or topological; 04.40.Nr Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields; 42.50.Xa optical tests of quantum theory; 04.80.Cc experimental tests of gravitational theories; 03.65.Sq semiclassical theories and applications; 98.80.Jk mathematical and relativistic aspects of cosmology; 98.80.Qc quantum cosmology; 04. general relativity and gravitation general relativity and gravitation; 03.65.Ta foundations of quantum mechanics, measurement theory 04.60.-m quantum gravity; 03.65.Vf phases: geometric; dynamic or topological; 04.40.Nr Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields; 42.50.Xa optical tests of quantum theory; 04.80.Cc experimental tests of gravitational theories; 03.65.Sq semiclassical theories and applications; 98.80.Jk mathematical and relativistic aspects of cosmology; 98.80.Qc quantum cosmology; 04. general relativity and gravitation general relativity and gravitation; 03.65.Ta foundations of quantum mechanics, measurement theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Lecian, O.M. Semiclassical Length Measure from a Quantum-Gravity Wave Function. Technologies 2017, 5, 56.

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