Quantum mechanics: Is the theory applicable to macroscopic objects?

A. J. Leggett

Kevin F. Brennan

Quantum mechanics forms the basis of modern physics. In a sense it is the parent theory about which we construct our view of the physical world. Briefly, quantum mechanics is the theory by which we describe the behaviors of subatomic and atomic particles, such as electrons, of which the macroscopic world is made. Although it is not necessary to treat macroscopic objects by use of quantum mechanics, the laws of quantum mechanics and their implications are completely consistent with Newton's Laws of Motion, which we know are applicable to most macroscopic objects. As we will see below, Newton's Laws of Motion are a special subset of quantum mechanics; quantum mechanics reduces to Newton's Laws at macroscopic dimensions. Before we begin our study of quantum mechanics, it is of interest to explain why quantum mechanics is of importance in the study of modern electrical engineering. Many new areas of electrical engineering are based on developments that can be understood only through the use of quantum mechanics. Among these are the broad areas of semiconductors and solid-state electronic devices, electro-optics and lasers, superconductors. It would be fair to say that in the study of each of the above areas some knowledge of quantum mechanics is essential. In this book, some basic concepts in quantum mechanics are presented that are necessary in the study of the above-mentioned disciplines. Introduction The concept most basic toward the understanding of quantum mechanics is the concept of measurement.

Anthony J. Leggett

Christian Ngô, J. B. Natowitz

The motion of macroscopic objects such as soccer balls, vehicles and planets can be well described using classical mechanics. However, classical mechanics is inadequate to describe the movements or the structure of microscopic objects such as atoms, molecules or nuclei. To properly describe the properties of microscopic objects, the theory of quantum mechanics was developed. While quantum mechanics can be applied to macroscopic objects, it turns out that for objects of large dimensions the quantum mechanical laws evolve naturally into classical mechanics. In general, solving a problem in quantum mechanics is far more difficult than solving it in classical mechanics. Therefore, the laws of classical mechanics are employed when they can be applied safely.

Yanbei Chen

Rapid experimental progress has recently allowed the use of light to prepare macroscopic mechanical objects into nearly pure quantum states. This research field of quantum optomechanics opens new doors toward testing quantum mechanics, and possibly other laws of physics, in new regimes. In the first part of this paper, I will review a set of techniques of quantum measurement theory that are often used to analyze quantum optomechanical systems. Some of these techniques were originally designed to analyze how a classical driving force passes through a quantum system, and can eventually be detected with optimal signal-to-noise ratio --- while others focus more on the quantum state evolution of a mechanical object under continuous monitoring. In the second part of this paper, I will review a set of experimental concepts that will demonstrate quantum mechanical behavior of macroscopic objects --- quantum entanglement, quantum teleportation, and the quantum Zeno effect. Taking the interplay between gravity and quantum mechanics as an example, I will review a set of speculations on how quantum mechanics can be modified for macroscopic objects, and how these speculations --- and their generalizations --- might be tested by optomechanics.

Günther Ludwig