[Paper Review] Macroscopic Body Motion in Terms of Quantum Evolution

Alexey Yur'evich Samarin|arXiv (Cornell University)|Aug 2, 2014

Quantum Mechanics and Applications20 references3 citations

TL;DR

This paper proposes that the classical motion of a macroscopic body's center of mass emerges purely from unitary quantum evolution, without collapse or decoherence, by showing that in the limit of large particle numbers, the path integral for the center of mass selects the classical trajectory via the principle of least action. The key result is that the wave function of the center of mass becomes a delta function in position, corresponding to deterministic classical motion, derived from the Feynman path integral in Euclidean time with ℏ → 0.

ABSTRACT

Macroscopic body is considered as a system, consisting of an infinite number of quantum particles. Mechanical motion of the system center of mass in physical space is described, using Feynman's representation of the quantum evolution. It is shown that the center of mass of the system moves accordingly with the minimum action principle if action functional is much higher then Plank's constant.

Motivation & Objective

• To provide a rigorous mathematical description of macroscopic body motion within standard quantum mechanics, without invoking collapse or decoherence.
• To resolve the foundational problem of how classical mechanics emerges from quantum theory, particularly for systems with a large number of particles.
• To establish a causal, unitary framework for quantum measurement by modeling the measuring apparatus as a macroscopic system governed by quantum evolution.
• To enable the consistent description of processes involving both quantum and macroscopic systems, especially in quantum measurement scenarios.
• To lay a foundation for spacetime structure in quantum mechanics, relevant for quantum gravity.

Proposed method

• Uses Feynman’s path integral formulation of quantum mechanics to describe the time evolution of a many-particle quantum system.
• Focuses on the center of mass degree of freedom, treating it as a collective variable distinct from internal relative coordinates.
• Applies analytic continuation to Euclidean time (t → −iτ), transforming the oscillatory quantum amplitude into a decaying exponential form.
• Derives the transition amplitude for the center of mass using the path integral over all possible trajectories in Euclidean time.
• Shows that in the limit ℏ → 0, only the path with minimal Euclidean action contributes significantly, leading to a delta-function wave function.
• Demonstrates that the classical path emerges naturally from the quantum evolution of the system’s center of mass, without additional postulates.

Experimental results

Research questions

• RQ1 Can classical mechanical motion of a macroscopic body be derived solely from unitary quantum evolution, without wave function collapse or decoherence?
• RQ2 How does the center-of-mass motion of a large quantum system approach the classical trajectory in the limit of many particles?
• RQ3 What is the role of the path integral and the principle of least action in the emergence of classical behavior from quantum theory?
• RQ4 Can the wave function collapse in quantum measurement be understood as a consequence of macroscopic processes in the measuring apparatus, rather than a fundamental postulate?
• RQ5 How can a consistent description of both quantum and macroscopic systems be achieved within a single quantum framework?

Key findings

• The center-of-mass wave function becomes a delta function δ(X2 − X_min₂) in position space, indicating deterministic classical motion, in the limit ℏ → 0.
• The classical path corresponds to the trajectory that minimizes the Euclidean action, derived from the path integral in imaginary time.
• The contribution of all non-classical paths vanishes in the ℏ → 0 limit due to the exponential suppression of paths with non-zero action deviation.
• Decoherence does not affect the center-of-mass motion, so it cannot be the mechanism that defines a system as macroscopic.
• The emergence of classicality is a consequence of the system’s size and the scaling of action with mass, not environmental interaction or wave function collapse.
• The framework allows for a causal, unitary description of quantum measurement, where the collapse is a result of macroscopic dynamics in the measuring device.