Quantum Space-Time and Reference Frames in ADM Canonical Gravity

TL;DR

This paper explores how quantum effects of material reference frames influence space-time structure and transformations in ADM canonical gravity, integrating quantum uncertainties into relativistic and quantum gravity models.

Contribution

It introduces quantum corrections to Lorentz transformations and space-time structure within the ADM canonical gravity framework, accounting for quantum reference frame effects.

Findings

Quantum corrections modify Lorentz transformations between reference frames.

Quantum fluctuations affect proper time and space-time observables.

Framework allows calculation of quantum gravity metrics fluctuations.

Abstract

The quantum space-time model which accounts material Reference Frames (RF) quantum effects considered for flat space-time and ADM canonical gravity. As was shown by Aharonov for RF - free material object its c.m. nonrelativistic motion in vacuum described by Schrodinger wave packet evolution which modify space coordinate operator of test particle in this RF and changes its Heisenberg uncertainty relations. In the relativistic case we show that Lorentz transformations between two RFs include the quantum corrections for RFs momentum uncertainty and in general can be formulated as the quantum space-time transformations. As the result for moving RF its Lorentz time boost acquires quantum fluctuations which calculated solving relativistic Heisenberg equations for the quantum clocks models. It permits to calculate RF proper time for the arbitrary RF quantum motion including quantum gravity metrics fluctuations. Space-time structure of canonical Quantum Gravity and its observables evolution for RF proper time discussed in this quantum space-time transformations framework.