03358nam a22005175i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001000172072001700182072002300199072001600222100008600238245011100324250001800435264006900453300006300522336002600585337002600611338003600637347002400673490007200697505024600769520122001015650001702235650001302252650002802265650002602293650004202319650004902361650002802410650006402438710003402502773002602536776003602562776003602598776003602634830007902670856004602749912001402795912001402809999001702823978-3-031-52352-6DE-He21320251030111421.0cr nn 008mamaa240209s2024    sz |    s    |||| 0|eng d  a97830315235269978-3-031-52352-67 a10.1007/978-3-031-52352-62doi 4aQC178 7aPHDV2bicssc 7aSCI0330002bisacsh 7aPHDV2thema1 aFavalli, Tommaso.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97082610aOn the Emergence of Time and Space in Closed Quantum Systemsh[electronic resource] /cby Tommaso Favalli.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXXI, 163 p. 8 illus., 6 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Theses, Recognizing Outstanding Ph.D. Research,x2190-50610 aIntroduction -- 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.  aTime, 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. 0aGravitation. 0aScience. 0aQuantum physics.966608 0aMathematical physics.14aClassical and Quantum Gravity.96940924aFoundations of Physics and Cosmology.97051624aQuantum Physics.96660824aTheoretical, Mathematical and Computational Physics.9655632 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303152351908iPrinted edition:z978303152353308iPrinted edition:z9783031523540 0aSpringer Theses, Recognizing Outstanding Ph.D. Research,x2190-506196637040uhttps://doi.org/10.1007/978-3-031-52352-6  aZDB-2-PHA  aZDB-2-SXP  c57558d57558