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Atlantis Press eBooks

Introduction and Outline

Theo van Holten

Published Dec 9, 2016• 0 citations

Abstract

Following a short history of quantum mechanics, an outline of the contents of this book is given. A model of an electron is derived by time-averaging the motion of a “zittering” electromagnetic singularity, and by adding an apparent force in the form of surface tension in order to remove false electrostatic effects due to the model simplification. This model of a deformable droplet of charge is adopted as a working hypothesis, to see what are the consequences of such a model. The consequences are mathematically worked out and are shown to lead to a quantitatively correct replica of quantum behaviour. Matter waves are shown to correspond to trains of beats in the pulsation of the droplet, and the correct value of Planck's constant is derived. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI: 10.2991/978-94-6239-234-2_1

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The conclusion of Part I, the non-technical (or somewhat less technical) part of this book, is that a completely convincing model of our universe is lacking. This should be a model that shows how quantum mechanical behaviour, with all its mysteries and paradoxes, can emerge from a local, deterministic theory. Yet we also find that one can assume its existence to arrive at a picture of our quantum mechanical universe that makes perfect sense. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In the previous chapter the motion of the “analogon-machine” was studied in case the torsional spring shown in Fig. 7.3 was removed. Our laboratory set-up thereby became the analogue of a free-flying droplet of charge. In the present chapter the analogue of a potential well will be studied. It is shown that energy quantisation is found, identical to the results of quantum mechanics. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In Part II, we expounded Shale-Stinespring theory and exhibited the abstract charged field as the simplest example of a summable Fredholm module, and thus a source of noncommutative geometry. Having come so far, it would be a pity not to develop fermion quantum dynamics in external fields, which comes straight from the spin representation. As on many occasions in this book, we set to work here on an enterprise of translation; in this case, to render in algebraic terms the quantization of wave equations of the Dirac type. Most of the footwork has already been laid in Section 6.4. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

To begin to describe quantum algorithms, we need an understanding of the physical phenomena that motivate quantum mechanics, a simple mathematical model of a potential quantum storage device and the notation to describe and manipulate such a model. In this chapter we present the context in which we will work, motivate the need for quantum mechanics and provide a quick introduction to the essential mathematical tools and notation to be used throughout the book. As part of the price of brevity, we will work with a static model of quantum mechanics and will defer additional mathematical definitions until they are needed. The reader who is already familiar with this material can easily skip to Chapter 2, giving only a cursory glance at Chapter 1 to identify any idiosyncratic notation. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.