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Archive for History of Exact Sciences

Classical Behavior of Macroscopic Bodies from Quantum Principles: Early Discussions

Helge Kragh, B. Carazza

Published Aug 1, 2000• 7 citations
Publisher
DOI
10.1007/s004070000018

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arXiv:0809.3764•Sep 22, 2008•1 citation
Newton's second law of motion, F = ma, has long been considered a cornerstone of classical mechanics, providing a fundamental framework for understanding the behavior of macroscopic objects. However, as physics delves into the quantum realm, the applicability of Newton's second law becomes limited, and the principles of quantum mechanics emerge as the dominant description of particle behavior. Beginning with an overview of the historical development of classical mechanics by Newton and the emergence of quantum mechanics in the early 20th century, the article delves into the foundational principles of framework. The classical description of particles as point masses with deterministic trajectories is contrasted with the probabilistic nature of quantum particles described by wave functions and superposition principles. Practical applications and implications of these theories are also discussed, shedding light on their significance in various scientific disciplines. This research article presents a comparative analysis of Newton's second law of motion and quantum physics, examining their fundamental principles and implications through the lens of classical and quantum mechanics. Beginning with an overview of Newton's second law and its significance in classical mechanics, the article delves into the foundational postulates of quantum mechanics and their departure from classical concepts. This explores the inherent limitations of Newton's second law when applied to quantum phenomena, comparing and contrasting its principles with those of quantum physics. Through a comprehensive analysis of evidence and theoretical frameworks, this article elucidates the boundaries of classical mechanics and highlights the need for quantum mechanics to describe phenomena at the atomic and subatomic levels. Through an exploration of key differences and similarities, this aims to provide insights into the behavior of particles at both macroscopic and microscopic scales
We investigate the quantum electrodynamics of many-body systems, and discuss the circumstances under which the results are identical to the results of classical electrodynamics. This classical behavior is shown to occur when the motion of a large number of the particles is correlated. The correlation manifests itself in a form of coherence which is characterized by the many-body quantum state's being very nearly an eigenstate of the current operator. We present several explicit examples of quantum states which exhibit such coherence and show that they give the expected classical results. Nowhere do we assume $h\ensuremath{\rightarrow}0$.
I argue that conventional estimates of the criterion for classical behavior of a macroscopic body are incorrect, because they do not take into account the locality of interactions, which characterizes the behavior of all systems described approximately by local quantum field theory. Black holes are the only localized objects which do not have such a description. The deviations from classical behavior of a macroscopic body, except for those which can be described as classical uncertainties in the initial values of macroscopic variables,are {\it exponentially} small as a function of the volume of the macro-system in microscopic units.