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arXiv:2410.17298

Does quantum mechanics apply to macroscopic objects? How to define macro?

L. Bányai

Published Oct 22, 2024• 0 citations
arXivHTMLPDF

Abstract

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?

DOI
10.48550/arxiv.2410.17298

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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?
What is quantum mechanics and what does it do ? In very general terms, the basic problem that both classical Newtonian mechanics and quantum mechanics seek to address can be stated very simply: if the state of a dynamic system is known initially and something is done to it, how will the state of the system change with time in response ? In this chapter, we will give a brief overview of, first, how Newtonian mechanics goes about solving the problem for systems in the macroscopic world and, then, how quantum mechanics does it for systems on the atomic and subatomic scale. We will see qualitatively what the differences and similarities of the two schemes are and what the domain of applicability of each is. Brief overview of classical mechanics To answer the question posed above systematically, we must first give a more rigorous formulation of the problem and introduce the special language and terminology (in double quotation marks) that will be used in subsequent discussions. For the macroscopic world, common sense tells us that, to begin with, we should identify the “system” that we are dealing with in terms of a set of “static properties” that do not change with time in the context of the problem. For example, the mass of an object might be a static property. The change in the “state” of the system is characterized by a set of “dynamic variables.
We argue that correct account of the quantum properties of macroscopic objects which form reference frames (RF) demand the change of the standard space-time picture accepted in Quantum Mechanics. The presence of RF free quantum motion in the form of wave packet smearing results in formal nonapplicability of Galilean or Lorentz space-time transformations in this case. For the description of the particles states transformations between different quantum RF the special quantum space-time transformations are formulated. Consequently it results in corrections to Schrodinger or Klein- Gordon equations which depends on the RF mass. RF proper time becomes the operator depending of momentums spread in RF wave packet ,from the point of view of other observer. The experiments with macroscopic coherent states are proposed in which this effects can be tested.}
The question as to whether quantum mechanics can be applied to a macroscopic system, which has recently been raised through discussions of the problem of how to interpret the so-called “reduction of a wave packet”, is discussed. It is shown by a detailed analysis of the destruction of interference which brings about the reduction, that a supplementary assumption on the preciseness of measurements must at least be introduced in order to interpret the reduction process as an objective process, and it does not, however, necessarily imply inapplicability of quantum mechanics to a macroscopic system.
Classical mechanics is usually valid at the macro scale. The changes in the position and the momentum of the object over time are described by the Hamiltonian equation of motion. The wave function in quantum mechanics, if unobserved, evolves in a smooth and continuous way according to the Schrodinger equation, which is related to the Hamiltonian equation of motion. This equation describes a linear superposition of different states at time. A quantum mechanical description of a physical system is related to a probabilistic representation; it is described by a vector in Hilbert space. This description extends the two- or three-dimensional Euclidean space into spaces that have any finite or infinite number of dimensions. The state of a compound system is projected to the subspace that corresponds to the observed state and the vector representing the state is renormalized to the unit length. An observable describes a subspace for some dimensions with a special case of one dimension.