[Paper Review] Quasiclassical Realms in a Quantum Universe

James B. Hartle|ArXiv.org|Apr 11, 1994

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper proposes that classical, deterministic laws emerge from quantum mechanics in a closed quantum universe through decoherence and coarse-graining. It shows that quasiclassical realms—consistent with everyday experience—arise from the initial condition and Hamiltonian of the universe, with only a small fraction of initial states reproducing our specific classical reality.

ABSTRACT

In this universe, governed fundamentally by quantum mechanical laws, characterized by indeterminism and distributed probabilities, classical deterministic laws are applicable over a wide range of time, place, and scale. We review the origin of these laws in the context of the quantum mechanics of closed systems, most generally, the universe as a whole. There probabilities are predicted for members of decoherent sets of alternative histories of the universe, ie ones for which the interference between pairs in the set is negligible as measured by a decoherence functional. An expansion of the decoherence functional in the separation between histories allows the form of the deterministic equations of motion to be derived for suitable coarse grainings of a class of non-relativistic systems, including ones with general non-linear interactions. More coarse graining is needed to achieve classical predictability than naive arguments based on the uncertainty principle would suggest. Coarse graining is needed for decoherence, and coarse graining beyond that for the inertia necessary to resist the noise that mechanisms of decoherence produce. Sets of histories governed largely by deterministic laws constitute the quasiclassical realm of everyday experience which is an emergent feature of the closed system's initial condition and Hamiltonian. We analyse the sensitivity of the existence of a quasiclassical realm to the particular form of the initial condition. We find that almost any initial condition will exhibit a quasiclassical realm of some sort, but only a small fraction of the total number of possible initial states could reproduce the everyday quasiclassical realm of our universe. (Talk given at the Lanczos Centenary Conference, North Carolina State University, December 15, 1993.)

Motivation & Objective

• To explain how classical, deterministic laws emerge from fundamentally quantum mechanical laws in a closed quantum system.
• To investigate the role of decoherence and coarse-graining in the emergence of quasiclassical realms.
• To analyze the sensitivity of quasiclassical realm existence to the initial quantum state of the universe.
• To clarify why more coarse graining is required for classical predictability than suggested by the uncertainty principle.
• To determine under what conditions the universe's initial state leads to a quasiclassical realm resembling our everyday experience.

Proposed method

• Uses the consistent histories framework to define probabilities for alternative histories in a closed quantum system.
• Applies a perturbative expansion of the decoherence functional in the separation between histories to derive deterministic equations of motion.
• Introduces coarse-graining to suppress quantum interference and achieve decoherence.
• Demonstrates that additional coarse graining is necessary to stabilize dynamics against quantum noise from decoherence.
• Analyzes the dependence of quasiclassical realm emergence on the form of the initial quantum state.
• Employs a non-relativistic model with general nonlinear interactions to illustrate the emergence of classical behavior.

Experimental results

Research questions

• RQ1 How do deterministic classical laws emerge from the fundamentally probabilistic and indeterministic laws of quantum mechanics?
• RQ2 What role does coarse-graining play in achieving both decoherence and classical predictability?
• RQ3 Why is more coarse graining required for classical behavior than implied by the uncertainty principle?
• RQ4 How sensitive is the existence of a quasiclassical realm to the specific form of the universe's initial quantum state?
• RQ5 What fraction of possible initial conditions lead to a quasiclassical realm resembling our observed universe?

Key findings

• Quasiclassical realms emerge from the initial condition and Hamiltonian of the universe, not from fundamental laws.
• Decoherence alone is insufficient for classical predictability; additional coarse graining is required to suppress noise from the decoherence mechanism.
• Almost any initial condition leads to some form of quasiclassical realm, but only a small fraction reproduce the specific quasiclassical realm of our universe.
• The deterministic equations of motion can be derived from a perturbative expansion of the decoherence functional for suitable coarse-grainings.
• The emergence of classical behavior is contingent on the structure of the initial quantum state, with only a small subset yielding the familiar classical world.
• The framework supports the idea that classicality is an emergent feature of quantum mechanics in a closed system, not a fundamental property.