Quantum Space-Time and Reference Frames in Gravity and Flat Space-Time

TL;DR

This paper explores quantum effects on space-time and reference frames in flat space-time and gravity, introducing quantum corrections to Lorentz transformations and analyzing quantum fluctuations of proper time and space-time structure.

Contribution

It develops a framework for quantum space-time transformations incorporating quantum corrections to reference frames and relativistic effects, advancing understanding of quantum gravity and reference frame dynamics.

Findings

Quantum corrections modify Lorentz transformations between reference frames.

Quantum fluctuations of proper time are calculable for moving quantum reference frames.

The structure of quantum gravity and observable evolution are described within this quantum space-time framework.

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.