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Time, space and entanglement are the main characters in this book. Their nature is still a great mystery in physics and we study here the possibility that these three phenomena are closely connected, showing how entanglement can be at the basis of the emergence of time and space within closed quantum systems. We revisit and extend the Page and Wootters theory that was originally introduced in order to describe the emergence of time through entanglement between subsystems in a globally static, quantum Universe. In the book, after providing a complete review of the salient aspects of the theory, we establish a connection with recent research on the foundations of statistical mechanics and we provide a new understanding of the thermalization process. Furthermore, we generalize the framework in order describe the spatial degree of freedom and we provide a model of 3+1 dimensional, quantum spacetime emerging from entanglement among different subsystems in a globally "timeless" and "positionless" Universe. Finally, via the Page and Wootters theory, the evolution of quantum clocks within a gravitational field is treated and a time dilation effect is obtained in agreement with the Schwarzschild solution.
List of contents
Introduction.- Page and Wootters theory.- Complement of the Hamiltonian.- Time Observables in a Timeless Universe.- Thermal Equilibrium and Emergence of Time.- Quantum Spacetime.- Quantum Clocks in a Gravitational Field.- Conclusions.
About the author
Tommaso Favalli was born in Florence in 1987. He received his master's degree in physical and astrophysical sciences from the University of Florence and his Ph.D. in Quantum Technologies from the University of Naples Federico II. His research activity focuses mainly on the foundations of quantum mechanics and in particular on the concepts of time and space. He is currently a researcher at the University of Trieste.
