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Why No PlaneWaves of Macroscopic Bodies? A Micro-Macro Threshold?

L. Bányai

Published Jul 10, 2024• 0 citations

Abstract

According to Quantum Mechanics a narrow wave-package of the center of mass of macroscopic objects, due to their heavy mass, remains stable over astronomical times. However Quantum Mechanics allows and energetically even prefers largely smeared out c.m. states that never been seen. Why is this the real state of the world we know? Does it suggest a micro-macro threshold with different theoretical descriptions?

DOI: 10.20944/preprints202307.0731.v2

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According to Quantum Mechanics a narrow wave-package of the center of mass of macroscopic objects, due to their heavy mass, remains stable over astronomical times. However Quantum Mechanics allows and energetically even prefers largely smeared out c.m. states that never been seen. Why is this the real state of the world we know? Does it suggest a micro-macro threshold with different theoretical descriptions?

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According to Quantum Mechanics a narrow wave-packet of the center of mass of any macroscopic object should smear out after some time. The problem is usually waved out by assuming that due to their heavy masses this occurs over astronomical times. Without a clear definition of macroscopic objects this remains ambiguous. On the other hand, Quantum Mechanics allows and energetically even prefers largely smeared out c.m. states that never been seen. Why is this the real state of the world we know? Does it suggest a micro-macro threshold with different theoretical descriptions? Does offer micro-miniaturization a hope for answering these questions?

Harmonizing classical and quantum worlds is a major challenge for modern physics. A significant portion of the scientific community supports the notion that classical mechanics is an effective theory that arises from quantum mechanics. Recently, the present authors have argued that this should not be the case, as quantum mechanics is not trustworthy for describing the center of mass of systems with masses

m

much larger than the Planck mass

M_\text{P}

. In this vein, a simple gravitational self-decoherence model was proposed, describing how the center of mass of quantum systems would classicalize for

m \sim M_\text{P}

. Here, we show that our model does not prevent macroscopic systems (with classical centers of mass) from harboring quantum internal vibrations (as has been observed in the laboratory).

Using very general and well established ideas of the statistical physics of macroscopic bodies, that is, of those composed of many degrees of freedom, we show how classical behavior of the center of mass motion arises from a fully quantum mechanical description of the dynamics of the whole body. We do not attempt to provide a rigorous proof of the latter statement, but rather, we show or, at least, indicate the hypotheses needed to obtain the purported result. Moreover, we neither attempt to deal with the "most general" physical situation and, instead, we concentrate on a stylized model of a small solid, yet macroscopic, that we shall call a "little stone". The main hypothesis is that a macroscopic body can be decomposed into several smaller pieces, still macroscopic, that become statistically independent due to the short-range interaction nature of their constituent atoms. The ensuing main result is that the quantum distributions of extensive variables of the body become sharply-peaked. The center of mass variables are of this type and hence their dynamics is essentially classical. We point out the crucial role played by the external potential, in which the motion occurs, as the macroscopic agent that executes the "measurement" process of the center of mass.

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.