Four previous editions of this book were published in 1989, 1992, 1999, and 2001. They were preceded by a German version (Zeh 1984) that was based on lectures I had given at the University of Heidelberg. My interest in this subject arose originally from the endeavor to better - derstand all aspects of irreversibility that might be relevant for the statistical natureandinterpretationofquantumtheory. Thequantummeasurementp- cess is often claimed to represent an ampli?cation of microscopic properties to the macroscopic scale in close analogy to the origin of classical ?uctuations, whichmayleadtothelocalonsetofaphasetransition,forexample. Thisclaim can hardly be upheld under the assumption of universal unitary dynamics, as is well known from the example of Schr odingers cat. However, the classical theoryofstatisticalmechanicso?ersmanyproblemsandmisinterpretationsof its own, which are in turn related to the oft-debated retardation of radiation, irreversible black holes with their thermodynamical aspects, and last but not least the expansion of the Universe. So the subject o?ered a great and exciting interdisciplinary challenge. My interest was also stimulated by Paul Davies (1977) book that I used successfully for my early lectures. Quantum gravity, that for consistency has to be taken into account in cosmology, even requires a complete revision of the concept of time, which leads to entirely novel and fundamental questions of interpretation (Sect. 6. 2). Many of these interesting ?elds and applications have seen considerable progress since the last edition came out.

H. Dieter Zeh studied physics in Brunswick and Heidelberg, where he began work on theoretical nuclear physics. After a year of research at the California Institute of Technology, he moved to the University of California in San Diego to work on the synthesis of the heavy elements, before returning to the University of Heidelberg, where he later became professor of theoretical physics. His studies of collective motion in nuclei led him to address the quantum-to-classical transition in general, and in particular the quantum measurement problem, which is in turn related to many aspects of irreversibility (arrows of time). During this work, Zeh recognized and formulated the universal and unavoidable role of uncontrollable quantum entanglement, thus becoming a founder of the area now known as decoherence.

The Physical Concept of Time.- The Time Arrow of Radiation.- The Thermodynamical Arrow of Time.- The Quantum Mechanical Arrow of Time.- The Time Arrow of Spacetime Geometry.- The Time Arrow in Quantum Cosmology.- Epilog.