Canonical Quantum Gravity and the Problem of Time

Canonical Quantum Gravity and the Problem of Time

August 1992 | C.J. Isham
This paper provides an introduction to the problem of time in quantum gravity, focusing on the conflict between the concept of time in quantum theory and its role in a diffeomorphism-invariant theory like general relativity. The problem arises because time is treated as an external parameter in quantum theory, while general relativity is invariant under diffeomorphisms, making time a coordinate rather than a fundamental concept. Three main approaches are discussed: (I) identifying time before quantisation, (II) identifying time after quantisation, and (III) timelessness, where time plays no fundamental role. The paper also introduces the canonical decomposition of general relativity and discusses various schemes for resolving the problem of time, including the internal Schrödinger interpretation, matter clocks, unimodular gravity, the Klein-Gordon interpretation, third quantisation, and the semi-classical approximation. It also covers timeless interpretations such as the conditional probability interpretation, consistent histories, and the frozen formalism. The paper highlights the technical challenges in these approaches, including ultraviolet divergences, operator ordering, global time issues, and the multiple-choice problem. It concludes by emphasizing the importance of understanding the role of time in quantum gravity and the need for a consistent framework that reconciles the classical and quantum descriptions of time.This paper provides an introduction to the problem of time in quantum gravity, focusing on the conflict between the concept of time in quantum theory and its role in a diffeomorphism-invariant theory like general relativity. The problem arises because time is treated as an external parameter in quantum theory, while general relativity is invariant under diffeomorphisms, making time a coordinate rather than a fundamental concept. Three main approaches are discussed: (I) identifying time before quantisation, (II) identifying time after quantisation, and (III) timelessness, where time plays no fundamental role. The paper also introduces the canonical decomposition of general relativity and discusses various schemes for resolving the problem of time, including the internal Schrödinger interpretation, matter clocks, unimodular gravity, the Klein-Gordon interpretation, third quantisation, and the semi-classical approximation. It also covers timeless interpretations such as the conditional probability interpretation, consistent histories, and the frozen formalism. The paper highlights the technical challenges in these approaches, including ultraviolet divergences, operator ordering, global time issues, and the multiple-choice problem. It concludes by emphasizing the importance of understanding the role of time in quantum gravity and the need for a consistent framework that reconciles the classical and quantum descriptions of time.
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