[Paper Review] Classicality via hydrodynamics in quantum field theory

Charis Anastopoulos|ArXiv.org|May 19, 1998

Theoretical and Computational Physics3 references3 citations

TL;DR

This paper proposes a hydrodynamic coarse-graining approach to derive classical behavior from quantum field theory by averaging a scalar field over spatial regions of size L. Using the consistent histories framework, it derives effective hydrodynamic equations that include dissipation and noise, demonstrating how classical dynamics emerges from quantum foundations through coarse-graining at finite scales.

ABSTRACT

Motivated by the consistent histories approach to quantum mechanics, we examine a simple model of hydrodynamic coarse-graining for a scalar field. It consists in averaging the field over spatial regions of size L and constructing the evolution equation for the coarse grained quantities, thus identifying dissipation and noise.

Motivation & Objective

• To understand how classical behavior emerges from quantum field theory through coarse-graining.
• To apply the consistent histories approach to a hydrodynamic model of field averaging.
• To identify the emergence of dissipation and noise in coarse-grained field dynamics.
• To establish a bridge between quantum field theory and classical hydrodynamics via spatial averaging.
• To analyze the role of scale L in determining the classical limit of quantum fields.

Proposed method

• A scalar quantum field is spatially coarse-grained by averaging over regions of size L.
• The coarse-grained field variables are evolved using effective equations derived from the underlying quantum dynamics.
• The method introduces noise and dissipation terms in the effective hydrodynamic equations through the coarse-graining process.
• The consistent histories framework is used to justify the coarse-graining procedure and interpret the resulting dynamics.
• The approach relies on a perturbative or systematic expansion in the coarse-graining scale L to derive the effective dynamics.
• The resulting equations resemble stochastic hydrodynamics, with noise and damping terms arising naturally from quantum fluctuations.

Experimental results

Research questions

• RQ1 How does coarse-graining a quantum scalar field over spatial regions of size L lead to classical-like behavior?
• RQ2 What are the effective dynamical equations governing the coarse-grained field, and what physical features (e.g., dissipation, noise) do they exhibit?
• RQ3 In what sense does this hydrodynamic coarse-graining reproduce classical hydrodynamics from quantum field theory?
• RQ4 How does the scale L influence the emergence of classicality in the effective dynamics?
• RQ5 Can the consistent histories framework be used to justify the emergence of classical behavior in this coarse-grained setting?

Key findings

• The coarse-grained field dynamics are governed by effective equations that include both dissipation and noise terms.
• The noise and dissipation arise naturally from the averaging procedure and the quantum fluctuations of the underlying field.
• The effective dynamics resemble stochastic hydrodynamics, suggesting a natural emergence of classical behavior at macroscopic scales.
• The scale L determines the strength of the dissipative and noisy contributions, with larger L leading to stronger classical features.
• The consistent histories framework provides a foundation for interpreting the coarse-grained variables as classical-like observables.
• The model demonstrates that classicality is not a fundamental property but emerges from coarse-graining in quantum field theory.