Clasical Mechanics

Mastering Mechanics: Solving Real-World Problems to Understand Fundamental Equations

Mastering Mechanics: Solving Real-World Problems to Understand Fundamental Equations

In the first volume we based quantum mechanics on the objective description of macroscopic devices. The further development of the quantum mechanics of atoms, molecules, and collision processes has been described in [2]. In this context also the usual description of composite systems by tensor products of Hilbert spaces has been introduced. This method can be formally extrapolated to systems composed of "many" ele­ mentary systems, even arbitrarily many. One formerly had the opinion that this "extrapolated quantum mechanics" is a more comprehensive theory than the objec­ tive description of macrosystems, an opinion which generated unsurmountable diffi­ culties for explaining the measuring process. With respect to our foundation of quan­ tum mechanics on macroscopic objectivity, this opinion would mean that our founda­ tion is no foundation at all. The task of this second volume is to attain a compatibility between the objective description of macrosystems and an extrapolated quantum mechanics. Thus in X we establish the "statistical mechanics" of macrosystems as a theory more compre­ hensive than an extrapolated quantum mechanics. On this basis we solve the problem of the measuring process in quantum mechan­ ics, in XI developing a theory which describes the measuring process as an interaction between microsystems and a macroscopic device. This theory also allows to calculate "in principle" the observable measured by a device. Neither an incorporation of consciousness nor a mysterious imagination such as "collapsing" wave packets are necessary.

The aim of this book is to explain the basic concepts and phenomena of quantum mechanics by means of visualization. Computer-generated illustrations in color are used extensively throughout the text, helping to establish the relation between quantum mechanics—wave functions, interference, atomic structure, and so forth—and classical physics—point mechanics, statistical mechanics, and wave optics. Even more important, by studying the pictures in parallel with the text, readers develop an intuition for such notoriously abstract phenomena as

Stochastic mechanics is a theory that holds great promise in resolving the mathematical and interpretational issues encountered in the canonical and path integral formulations of quantum theories. It provides an equivalent formulation of quantum theories, but substantiates it with a mathematically rigorous stochastic interpretation by means of a stochastic quantization prescription.

Purpose and Emphasis. Mechanics not only is the oldest branch of physics but was and still is the basis for all of theoretical physics. Quantum mechanics can hardly be understood, perhaps cannot even be formulated, without a good knowledge of general mechanics. Field theories such as electrodynamics borrow their formal framework and many of their building principles from mechanics. In short, throughout the many modem developments of physics where one fre­ quently turns back to the principles of c1assical mechanics its model character is feIt. For this reason it is not surprising that the presentation of mechanics reflects to some extent the development of modem physics and that today this c1assical branch of theoretical physics is taught rather differently than at the time of Arnold Sommerfeld, in the 1920s, or even in the 1950s, when more emphasis was put on the theory and the applications of partial-differential equations. Today, symme­ tries and invariance principles, the structure ofthespace-time continuum, and the geometrical structure of mechanics play an important role. The beginner should realize that mechanics is not primarily the art of describing block-and-tackles, coIIisions of billiard balls, constrained motions of the cylinder in a washing ma­ chine, or bicycle riding.

Mechanics Over Micro and Nano Scales covers the recent developments in the fields of mechanics in all forms over micro, meso and nano scales. Special emphasis is given to related novel applications and includes fundamental aspects of fluid and solid mechanics, soft matters, scaling laws, and synthetic biology. At the micro and nano scales, realization of many technologically viable ideas relies on the skillful integration of mechanics at macroscopic and molecular levels, both for solids as well as fluids. Research in the related areas is no longer confined to the understanding of the governing the physics of the system, but is also responsible for triggering a technological revolution at small scales.