Semiclassical Length Measure from a Quantum-Gravity Wave Function

TL;DR

This paper develops a semiclassical length measure derived from a quantum-gravity wave function, enabling the distinction between classical and quantum gravitational effects across cosmological and present times.

Contribution

It introduces a novel length measurement approach based on semiclassical wave-function states, linking quantum gravity effects to observable length variations over cosmic history.

Findings

Length measurements can differentiate quantum effects from classical spacetime features.

Comparisons of length measures reveal potential Lorentz-violating phenomena at high energies.

Analysis of metric tensor components shows how quantum features influence classical spacetime structure.

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 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.