Quasiclassical Realms
Classical physics is an approximation to quantum mechanics, not valid generally, but only in particular circumstances. A system behaves classically when, in a suitable set of alternative coarse-grained histories, the probability is high for histories exhibiting correlations in time described by classical deterministic laws.
Perhaps the most striking feature of our indeterministic quantum universe is the wide range of time, place, and scale, on which the deterministic laws of classical physics hold to an excellent approximation. What is the origin of this predictable quasiclassical realm in a quantum universe characterized fundamentally by indeterminancy and distributed probabilities. The papers in this section are devoted to answering this question.
The papers are grouped into two parts on two pages. In the first group on this page are papers that assume the quasiclassical realm is defined by familiar quasiclassical variables --- integrals over small volumes of densities of conserved quantities like energy, momentum, and conserved numbers. The next page is devoted to the question of whether these quasiclassical realms are the unique ones with high levels of predictability.
The Quasiclassical Realms of This Quantum Universe [141]
An overview on how the origin of the quasiclassical realm of our universe can be understood from a fundamental quantum theory of the universe --- a quantum cosmology. The essay expresses the importance of classical spacetime as the origin of the quasiclassical behavior of matter in the universe.
Quasiclassical Coarse Grainings and Thermodynamic Entropy [138]
(with Murray Gell-Mann) This paper describes in the most detail the what we mean by a quasiclassical realm (Section V) --- the variables, the coarse graining, branch dependence, narratives, and high probabilities for correlation in time by deterministic classical laws. It also shows how the usual entropy of chemistry and physics is related to the coarse-graining defining classical histories, and how the second law of thermodynamics originates in the initial condition of the universe.
Quasiclassical Realms in a Quantum Universe [102]
A review of the issues involved in understanding classicality in quantum mechanics. The article in particular does two important things: It provides a short summary of the derivation of classical equations of motion in the next paper Classical Equations for Quantum Systems. (Authors advice: read this first.) Second it analyzes the question of whether the existence of our quasiclassical realm is sensitive to the particular form of the quantum state of the universe.
Classical Equations for Quantum Systems [97]
(with Murray Gell-Mann) Among many other things, this paper investigates the derivation of classical equations of motion from the probabilities for histories in a class of simple models. (See especially Section VI.) In suitable coarse grainings the probabilities for correlations in time are shown to have a peak at those described by classical equations. These are not just the equations following from the Lagrangian that defines the model. They include effects such as dissipation that arise from the interactions that produce decoherence. The width of the probability distributions around the classical equations is a measure of the quantum noise produced by these interactions that causes deviations from classical predictability. Generally coarse graining beyond that necessary for decoherence is necessary for classicality. The connections among decoherence, noise, dissipation, and the amount of coarse graining necessary to achieve classical predictability are investigated quantitatively.The connection between quantum-mechanical causality and causality in classical phenomenological equations of motion is demonstrated. (A short review of all this is in Quasiclassical Realms in a Quantum Universe [102]).
Classical Dynamics of the Quantum Harmonic Chain [121]
(with Todd Brun.) This paper analyzed the origin of classical predictability for a very simple, explicitly computable model of a closed quantum system ---- a one-dimensional chain of atoms interacting by harmonic nearest neighbor potentials. Different coarse grainings ranging from local to highly non-local ones were compared with respect to decoherence times and classicality. The local ones were favored for predictability. For realistic parameters the decoherence time for these coarse gainings is very short compared to dynamical time scales. Decoherence and computational complexity favor locality over non-locality for deterministic predictability by classical laws.
The No-Boundary Measure of the Universe [139]
(with Stephen Hawking and Thomas Hertog.) Classical spacetime is the single most important feature of the quasiclassical realm. Its symmetries define the conservation laws that are the basis of the quasiclassical variables. The papers above have assumed classical spacetime. Almost all the papers on the wave function of the universe describe how it predicts probabilities for different classical spacetimes in an ensemble of possible ones. The different classical spacetimes are distinguished by such things as the number of efolds of inflation, the size of density fluctuations, etc. This particular paper is just the simplest example how a quantum state predicts classical spacetime.
Classical Physics and Hamiltonian Quantum Mechanics as Relics of the Big Bang [92]
An early paper arguing that quasiclassicl realm and Hamiltonian quantum mechanics with its preferred notion of time are not general properties of quantum theory but rather approximate features of the universe emergent after the Planck time because of the character of the specific initial conditions and dynamics of our universe.
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