[Paper Review] Macroscopic realism and spatiotemporal continuity

Johannes Kofler, Nikola Burić+1 more|arXiv (Cornell University)|Jun 24, 2009

Quantum Mechanics and Applications2 references3 citations

TL;DR

This paper introduces macrorealism and continuity (MR&C) as a stricter classicality condition than macrorealism alone, showing that while decoherence can restore macrorealism, it fails to ensure continuous spatiotemporal evolution of macroscopic observables under dephasing environments. Thermal environments, however, may support continuous evolution, revealing a fundamental gap between decoherence-induced classicality and the emergence of classical dynamics.

ABSTRACT

Macroscopic realism, as introduced by Leggett and Garg, is the world view in which properties of macroscopic systems exist independent of and are not influenced by measurement. Motivated by classical physical laws such as Newtonian mechanics or Maxwell's electrodynamics, in this work we add the restrictive postulate that the observables of macroscopic objects are evolved continuously through space and time. Quantum theory violates both macroscopic realism and the continuity assumption. While decoherence or collapse models (e.g. due to a universal noise background or gravitational self energy) can restore macroscopic realism, we show that a continuous spatiotemporal description does not become possible in general. This shines new light on the question how the classical world arises out of the quantum realm.

Motivation & Objective

• To formalize a stricter notion of classicality by combining macrorealism with spatiotemporal continuity.
• To investigate whether decoherence mechanisms can restore both macrorealism and continuous evolution of macroscopic observables.
• To clarify the conditions under which classical laws of motion—such as those in Newtonian mechanics or Maxwell’s electrodynamics—can emerge from quantum theory.
• To identify experimental pathways to detect non-classicality even in the presence of decoherence by distinguishing levels of classicality.
• To assess the limitations of collapse models and environmental decoherence in explaining the classical world's emergence.

Proposed method

• Formalizes macrorealism (MR) via Leggett-Garg postulates: definite states, non-invasive measurability, and induction.
• Introduces a fourth postulate—continuity—requiring observables to evolve continuously through space and time.
• Uses the $Q$-distribution of spin-$j$ states to model coarse-grained measurements on macroscopic systems.
• Applies a Lindblad master equation to simulate open quantum dynamics under two environmental models: dephasing and thermal.
• Solves the master equation numerically using quantum state diffusion, a stochastic nonlinear Schrödinger equation, to compute ensemble averages over $10^3$ trajectories.
• Analyzes the time evolution of the $z$-magnetization operator $\hat{m}_z$ under coarse-grained measurements to assess continuity and macrorealism.

Experimental results

Research questions

• RQ1 Can decoherence restore macrorealism while ensuring continuous spatiotemporal evolution of macroscopic observables?
• RQ2 Under which environmental conditions—dephasing versus thermal—can continuous evolution of macroscopic variables emerge?
• RQ3 Is there a physical mechanism that can simultaneously satisfy macrorealism and continuity, even in the presence of environmental interactions?
• RQ4 Can non-classical Hamiltonians lead to violations of MR&C under coarse-grained measurements, despite decoherence?
• RQ5 How do collapse models and decoherence differ in their ability to account for the classical limit of quantum mechanics?

Key findings

• Decoherence via dephasing environments restores macrorealism but fails to ensure continuous spatiotemporal evolution, as intermediate magnetization states remain unpopulated.
• Thermal environments, due to their dissipative nature, can induce continuous evolution of macroscopic observables, enabling a continuous spatiotemporal description.
• Even under strong dephasing, the evolution of the $z$-magnetization remains discontinuous, with populations jumping directly from north to south poles without intermediate values.
• The numerical simulations show that dephasing environments suppress off-diagonal density matrix elements without altering diagonal populations, leading to abrupt transitions.
• Thermal environments with $\bar{n} \gg 1$ and $\gamma_{\text{th}}\bar{n} = 1$ lead to smooth, continuous changes in the diagonal elements of the density matrix, supporting continuous evolution.
• The results demonstrate that macrorealism and continuity (MR&C) are not guaranteed by decoherence alone, highlighting a critical distinction in the quantum-to-classical transition.