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Mysteries, Puzzles, and Paradoxes in Quantum Mechanics

Quantum space-time and physical reference frames

Sergey Nikolaevich Mayburov

Published Jan 1, 1999• 1 citation
Publisher

Abstract

Aharonov-Kaufherr model of quantum space-time which accounts Reference Frames quantum effects is considered in Relativistic Quantum Mechanics framework. Due to this effect the quantum corrections to Galilean or Lorentz transformations appears. In particular the Lorentz time boost corrections calculated solving relativistic Heisenberg equations for the quantum clocks model.

DOI
10.1063/1.57879

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Aharonov-Kaufherr model of quantum space-time which accounts Reference Frames quantum effects is considered in Relativistic Quantum Mechanics framework. Due to this effect the quantum corrections to Galilean or Lorentz transformations appears. In particular the Lorentz time boost corrections calculated solving relativistic Heisenberg equations for the quantum clocks model.
Aharonov-Kaufherr model of quantum space-time which accounts Reference Frames (RF) quantum effects is considered in Relativistic Quantum Mechanics framework. For RF connected with some macroscopic object its free quantum motion - wave packet smearing results in additional uncertainty of test particle coordinate. Due to the same effects the use of Galilean or Lorentz transformations for this RFs becomes incorrect and the special quantum space-time transformations are introduced. In particular for any RF the proper time becomes the operator in other RF. This time operator calculated solving relativistic Heisenberg equations for some quantum clocks models. Generalized Klein- Gordon equation proposed which depends on both the particle and RF masses.
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.
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.
We argue that correct account of the quantum properties of macroscopic objects which form reference frames (RF) demand the change of the standard space-time picture accepted in Quantum Mechanics. Galilean or Lorentz space-time transformations are shown to become incorrect in this case and for the description of transformations between different RF the special quantum space-time transformations are introduced. Consequently it results in the generalised Schrodinger equation which depends on the observer mass. The experiments with macroscopic coherent states are proposed in which this effects can be tested.
We argue that correct account of the quantum properties of macroscopic objects which form reference frames (RF) demand the change of the standard space-time picture accepted in Quantum Mechanics. The presence of RF free quantum motion in the form of wave packet smearing results in formal nonapplicability of Galilean or Lorentz space-time transformations in this case. For the description of the particles states transformations between different quantum RF the special quantum space-time transformations are formulated. Consequently it results in corrections to Schrodinger or Klein- Gordon equations which depends on the RF mass. RF proper time becomes the operator depending of momentums spread in RF wave packet ,from the point of view of other observer. The experiments with macroscopic coherent states are proposed in which this effects can be tested.}
Since their first introduction, Quantum Reference Frame (QRF) transformations have been extensively discussed, generalising the covariance of physical laws to the quantum domain. Despite important progress, a formulation of QRF transformations for Lorentz symmetry is still lacking. The present work aims to fill this gap. We first introduce a reformulation of relativistic quantum mechanics independent of any notion of preferred temporal slicing. Based on this, we define transformations that switch between the perspectives of different relativistic QRFs. We introduce a notion of ''quantum Lorentz transformations'' and ''superposition of Lorentz boosts'', acting on the external degrees of freedom of a quantum particle. We analyse two effects, superposition of time dilations and superposition of length contractions, that arise only if the reference frames exhibit both relativistic and quantum-mechanical features. Finally, we discuss how the effects could be observed by measuring the wave-packet extensions from relativistic QRFs.