Origin and measurement of time in quantum cosmology

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Abstract
The notion of probabilistic time is used to explain the origin and possible measurement of time in the Unruh-Wald formulation of quantum gravity. It is shown how ideal and real clocks measure probabilistic time and how we can extract from the Universe a real clock. Afterward, it is also shown how probabilistic time can be endowed with the two fundamental properties of time: it is an ordering parameter and it is ‘‘Heraclitian.’’ We discuss the correlation between the different arrows of time with the quantum arrows defined by the real clock.