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CRC Press eBooks

Time in Quantum Cosmology

Michael B. Mensky

Published Oct 19, 2017• 0 citations
Publisher

Abstract

This chapter applies the path-integral approach to the quantum theory of continuous measurements to investigate the quantum Universe, taking into account its self-measurement. It describes the way to apply the path-integral theory of continuous measurements in quantum cosmology in a general form and develops a minisuperspace model. The path-integral approach can be applied to describe the measurement of a quantum field. The measurement of curvature in the framework of quantum gravity has been considered in such a way by Mensky using a functional integral over configurations of the gravitational field. The chapter considers the possible influence of self-measurement on the dynamics of the quantum Universe. The influence could be caused by reduction of the wavefunction of the Universe in the process of continuous measurement. Therefore the time evolution of the quantum Universe makes sense in quantum cosmology provided its self-measurement is correctly taken into account.

DOI
10.1201/9781315140292-8

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This chapter applies the path-integral approach to the quantum theory of continuous measurements to investigate the quantum Universe, taking into account its self-measurement. It describes the way to apply the path-integral theory of continuous measurements in quantum cosmology in a general form and develops a minisuperspace model. The path-integral approach can be applied to describe the measurement of a quantum field. The measurement of curvature in the framework of quantum gravity has been considered in such a way by Mensky using a functional integral over configurations of the gravitational field. The chapter considers the possible influence of self-measurement on the dynamics of the quantum Universe. The influence could be caused by reduction of the wavefunction of the Universe in the process of continuous measurement. Therefore the time evolution of the quantum Universe makes sense in quantum cosmology provided its self-measurement is correctly taken into account.
The dynamics of the quantum universe under self-measurement is investigated in the framework of the path-integral approach to quantum theory of continuous measurements. The corresponding amplitude (propagator) is evaluated explicitly for a simple superspace model. It is shown that the picture of time evolution of the quantum universe naturally emerges as a result of its self-measurement. The Wheeler-DeWitt dynamics holds for small times when the effect of measurement can be neglected and time dependence disappears.
The dynamics of the quantum universe under self-measurement is investigated in the framework of the path-integral approach to quantum theory of continuous measurements. The corresponding amplitude (propagator) is evaluated explicitly for a simple superspace model. It is shown that the picture of time evolution of the quantum universe naturally emerges as a result of its self-measurement. The Wheeler-DeWitt dynamics holds for small times when the effect of measurement can be neglected and time dependence disappears.
Preface INTRODUCTION TO CONTINUOUS QUANTUM MEASUREMENTS Quantum and Classical Systems Amplitudes and Alternatives Paths and Continuous Measurements The Action Uncertainty Principle INSTANTANEOUS AND SEQUENTIAL MEASUREMENTS Measurement of a Quantum System Quantum Zeno Paradox Approximate and Sequential Measurements TECHNIQUE OF PATH INTEGRALS Propagators and Path Integrals Definition of a Path Integral The Path Integral for an Oscillator Gaussian Path Integrals CONTINUOUS MEASUREMENT AND EVOLUTION OF THE MEASURED SYSTEM The Measurement Amplitude Effective Lagrangian Evolution of a Quantum System Subject to Continuous Measurement Scattering by the Measuring Medium CONTINUOUS MEASUREMENTS OF OSCILLATORS Position Monitoring (Path measurement) Estimation of Force Acting on an Oscillator Spectral Measurements of an Oscillator Evolution of a Harmonic Oscillator Subject to Spectral Measurement Measurement of a Path of a Nonlinear Oscillator CONTINUOUS QUANTUM NONDEMOLITION MEASUREMENTS Quantum Nondemolition Measurements Monitoring of Linear Momentum Velocity versus Momentum QND Measurements of Oscillators MEASUREMENT OF AN ELECTROMAGNETIC FIELD Exposition of the Method Measurement Amplitude Analysis of the Results Another Definition of the Field Strength Explicit Model of a Meter TIME IN QUANTUM COSMOLOGY Statement of the Problem Measurements in Quantum Cosmology Minisuperspace without Measurement Minisuperspace under Measurement Analysis of the results Concluding Remarks THE ACTION UNCERTAINTY PRINCIPLE Uncertainties in Continuous Measurements Classical Regime of Measurements Quantum Regime and AUP AUP and Equations of Motion Examples from Quantum Mechanics Quantum Nondemolition Measurements AUP in Quantum Gravity Concluding Remarks GROUP-THEORETICAL STRUCTURE OF QUANTUM CONTINUOUS MEASUREMENTS Evolution under Measurement Transverse Group for Alternatives Longitudinal Semigroup for Evolution Unification of Transverse and Longitudinal Structures Concluding Remarks PATHS AND MEASUREMENTS: FURTHER DEVELOPMENT Quantum and Classical Features in Continuous Measurement The Two-Slit Experiment Wave-Particle Dualism Conceptual Problems References Index
We review the main results that have been obtained in quantum cosmology from the perspective of the de Broglie-Bohm quantum theory. As it is a dynamical theory of assumed objectively real trajectories in the configuration space of the physical system under investigation, this quantum theory is not essentially probabilistic and dispenses the collapse postulate, turning it suitable to be applied to cosmology. In the framework of minisuperspace models, we show how quantum cosmological effects in the de-Broglie-Bohm's approach can avoid the initial singularity, and isotropize the Universe. We then extend minisuperspace in order to include linear cosmological perturbations. We present the main equations which govern the dynamics of quantum cosmological perturbations evolving in non-singular quantum cosmological backgrounds, and calculate some of their observational consequences. These results are not known how to be obtained in other approaches to quantum theory. In the general case of full superspace, we enumerate the possible structures of quantum space and time that emerge from the de Broglie-Bohm picture. Finally, we compare some of the results coming from the de Broglie-Bohm theory with other approaches, and discuss the physical reasons for some discrepancies that occur.
It is demonstrated how classical properties of the intrinsic time variable in minisuperspace of quantum gravity would emerge in the sense of a continuous measurement process solely through interaction with fermionic degrees of freedom. This measurement is much less effective than that by bosons considered in a previous paper. Continuous measurement by fermions would not lead to classical properties for values of intrinsic time near the singularity of a Friedmann universe. It is argued that this result remains true for the full quantum theory of gravity.