1985/11/15 by S. W. Hawking · 192 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Arrow #Arrow of time #Black Holes and Theoretical Physics #Classical mechanics #Cosmology #Cosmology and Gravitation Theories #Dark energy #Entropy (arrow of time) #Metric expansion of space #Particle horizon #Physics #Quantum #Quantum cosmology #Quantum gravity #Quantum mechanics #Theoretical physics #Universe
paper · doi:10.1103/physrevd.32.2489
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 32(10), 2489-2495 (American Physical Society)
openalex publication_date 1985/11/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The usual proof of the CPT theorem does not apply to theories which include the gravitational field. Nevertheless, it is shown that CPT invariance still holds in these cases provided that, as has recently been proposed, the quantum state of the Universe is defined by a path integral over metrics that are compact without boundary. The observed asymmetry or arrow of time defined by the direction of time in which entropy increases is shown to be related to the cosmological arrow of time defined by the direction of time in which the Universe is expanding. It arises because in the proposed quantum state the Universe would have been smooth and homogeneous when it was small but irregular and inhomogeneous when it was large. The thermodynamic arrow would reverse during a contracting phase of the Universe or inside black holes. Possible observational tests of this prediction are discussed.