Conceptual Problems in Quantum Cosmology The application of quantum theory to cosmology raises a number of conceptual questions, such as the role of the quantum-mechanical notion of “observer” or the absence of a time variable in the Wheeler–DeWitt equation. I point out that a relational formulation of quantum mechanics, and more in general the observation that evolution is always relational, provides a coherent solution to this tangle of problems. A number of confusing issues appear when we try to apply quantum mechanics to cosmology. Quantum mechanics, for instance, is generally formulated in terms of an observer making measurements on a system. In a laboratory experiment, it is easy to identify the system and the observer: but what is the observer in quantum cosmology? Is it part of the same universe described by the cosmological theory, or should we think of it as external to the universe? Furthermore, the basic quantum dynamical equation describing a system including gravity is not the Schrödinger equation, but rather the Wheeler–DeWitt equation, which has no time parameter: is this related to the absence of an observer external to the universe? How do we describe the quantum dynamics of the universe without a time variable in the dynamical equation and without an observer external to the universe? I suggest that clarity on these issues can be obtained by simply recognizing the relational nature of quantum mechanics and more in general the relational nature of physical evolution. In the context of quantum theory, this nature is emphasized by the so-called relational interpretation of quantum mechanics (Rovelli, 1996). The relational nature of evolution, on the other hand, has been pointed out by the partial-observable formulation of general covariant dynamics (Rovelli, 2002). A central observation is that there is a common confusion between two different meanings of the expression “cosmology”. This is discussed below, in Section 15.1.1. A considerable amount of the difficulties mentioned above stems, I argue, from this confusion. The discussion clarifies on the role of the quantum mechanical observer in cosmology, which is considered in Section 15.1.2. In Section 15.2, I briefly describe the relational interpretation of quantum mechanics and some related aspects of quantum theory.Conceptual Problems in Quantum Cosmology The application of quantum theory to cosmology raises a number of conceptual questions, such as the role of the quantum-mechanical notion of “observer” or the absence of a time variable in the Wheeler–DeWitt equation. I point out that a relational formulation of quantum mechanics, and more in general the observation that evolution is always relational, provides a coherent solution to this tangle of problems. A number of confusing issues appear when we try to apply quantum mechanics to cosmology. Quantum mechanics, for instance, is generally formulated in terms of an observer making measurements on a system. In a laboratory experiment, it is easy to identify the system and the observer: but what is the observer in quantum cosmology? Is it part of the same universe described by the cosmological theory, or should we think of it as external to the universe? Furthermore, the basic quantum dynamical equation describing a system including gravity is not the Schrödinger equation, but rather the Wheeler–DeWitt equation, which has no time parameter: is this related to the absence of an observer external to the universe? How do we describe the quantum dynamics of the universe without a time variable in the dynamical equation and without an observer external to the universe? I suggest that clarity on these issues can be obtained by simply recognizing the relational nature of quantum mechanics and more in general the relational nature of physical evolution. In the context of quantum theory, this nature is emphasized by the so-called relational interpretation of quantum mechanics (Rovelli, 1996). The relational nature of evolution, on the other hand, has been pointed out by the partial-observable formulation of general covariant dynamics (Rovelli, 2002). A central observation is that there is a common confusion between two different meanings of the expression “cosmology”. This is discussed below, in Section 15.1.1. A considerable amount of the difficulties mentioned above stems, I argue, from this confusion. The discussion clarifies on the role of the quantum mechanical observer in cosmology, which is considered in Section 15.1.2. In Section 15.2, I briefly describe the relational interpretation of quantum mechanics and some related aspects of quantum theory.

arXiv:1508.05543Cambridge University Press eBooksJan 1, 201714 citations

The interpretation of quantum cosmology and the problem of time.

H. F. Halliwell

Nov 1, 200315 citations

Time and prediction in quantum cosmology.

James B. Hartle

Jan 1, 19917 citations

Time and Evolution in Quantum and Classical Cosmology

Alexander Yu Kamenshchik, Jeinny Nallely Pérez Rodríguez, Tereza Vardanyan

We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators the classical evolution is reproduced. We show that it is neither necessary nor sufficient for the Poisson bracket between the time variable and the super-Hamiltonian to be equal to unity in all of the phase space. We also discuss the question of switching between different internal times as well as the Montevideo interpretation of quantum theory.We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators the classical evolution is reproduced. We show that it is neither necessary nor sufficient for the Poisson bracket between the time variable and the super-Hamiltonian to be equal to unity in all of the phase space. We also discuss the question of switching between different internal times as well as the Montevideo interpretation of quantum theory.

arXiv:2107.00917UniverseJun 30, 20216 citations

The Time Arrow in Quantum Cosmology

H. D. Zeh

Springer eBooksJan 1, 20010 citations

A Non-Critical String Approach to Black Holes, Time and Quantum Dynamics

John R. Ellis, Nick E. Mavromatos, D.V. Nanopoulos

We review our approach to time and quantum dynamics based on non-critical string theory, developing its relationship to previous work on non-equilibrium quantum statistical mechanics and the microscopic arrow of time. We exhibit specific non-factorizing contributions to the ${\nd S}$ matrix associated with topological defects on the world sheet, explaining the rôle that the leakage of ${W_{\infty}}$ charges plays in the loss of quantum coherence. We stress the analogy with the quantum Hall effect, discuss the violation of $CPT$ , and also apply our approach to cosmology.We review our approach to time and quantum dynamics based on non-critical string theory, developing its relationship to previous work on non-equilibrium quantum statistical mechanics and the microscopic arrow of time. We exhibit specific non-factorizing contributions to the ${\nd S}$ matrix associated with topological defects on the world sheet, explaining the rôle that the leakage of ${W_{\infty}}$ charges plays in the loss of quantum coherence. We stress the analogy with the quantum Hall effect, discuss the violation of $CPT$, and also apply our approach to cosmology.

arXiv:hep-th/9403133Mar 22, 19944 citations

{W_{\infty}}

charges plays in the loss of quantum coherence. We stress the analogy with the quantum Hall effect, discuss the violation of

CPT

, and also apply our approach to cosmology.