The textbook

frontcoverPublisher’s blurb:

An invaluable supplement to standard textbooks on quantum mechanics, this unique introduction to the general theoretical framework of contemporary physics focuses on conceptual, epistemological, and ontological issues. The theory is developed by pursuing the question: what does it take to have material objects that neither collapse nor explode as soon as they are formed? The stability of matter thus emerges as the chief reason why the laws of physics have the particular form that they do.

The first of the book’s three parts familiarizes the reader with the basics through a brief historical survey and by following Feynman’s route to the Schrödinger equation. The necessary mathematics, including the special theory of relativity, is introduced along the way, to the point that all relevant theoretical concepts can be adequately grasped. Part II takes a closer look. As the theory takes shape, it is applied to various experimental arrangements. Several of these are central to the discussion in the final part, which aims at making epistemological and ontological sense of the theory. Pivotal to this task is an understanding of the special status that quantum mechanics attributes to measurements — without dragging in “the consciousness of the observer.” Key to this understanding is a rigorous definition of “macroscopic” which, while rarely even attempted, is provided in this book.

Publisher’s website

Chapter 1: Probability: Basic concepts and theorems [PDF]


From the Preface:

Having explained why interpretations that try to accommodate classical intuitions are impossible, Dieks[1] goes on to say:

However, this is a negative result that only provides us with a starting-point for what really has to be done: something conceptually new has to be found, different from what we are familiar with. It is clear that this constructive task is a particularly difficult one, in which huge barriers (partly of a psychological nature) have to be overcome.

Something conceptually new has been found, and is presented in this book. To make the presentation reasonably self-contained, and to make those already familiar with the subject aware of metaphysical prejudices they may have acquired in the process of studying it, the format is that of a textbook. To make the presentation accessible to a wider audience — not only students of physics and their teachers — the mathematical tools used are introduced along the way, to the point that the theoretical concepts used can be adequately grasped. In doing so, I tried to adhere to a principle that has been dubbed “Einstein’s razor”: everything should be made as simple as possible, but no simpler.

This textbook is based on a philosophically oriented course of contemporary physics I have been teaching for the last ten years at the Sri Aurobindo International Centre of Education (SAICE) in Puducherry (formerly Pondicherry), India. This non-compulsory course is open to higher secondary (standards 10–12) and undergraduate students, including students with negligible prior exposure to classical physics.

(I consider this a plus. In the first section of his brilliant Caltech lectures, Richard Feynman[2] raised a question of concern to every physics teacher:

Should we teach the correct but unfamiliar law with its strange and difficult conceptual ideas…? Or should we first teach the simple … law, which is only approximate, but does not involve such difficult ideas? The first is more exciting, more wonderful, and more fun, but the second is easier to get at first, and is a first step to a real understanding of the second idea.

With all due respect to one of the greatest physicists of the 20th Century, I cannot bring myself to agree. How can the second approach be a step to a real understanding of the correct law if “philosophically we are completely wrong with the approximate law,” as Feynman himself emphasized in the immediately preceding paragraph? To first teach laws that are completely wrong philosophically cannot but impart a conceptual framework that eventually stands in the way of understanding the correct laws. The damage done by imparting philosophically wrong ideas to young students is not easily repaired.)

The text is divided into three parts. After a short introduction to probability, Part 1 (“Overview”) follows two routes that lead to the Schrödinger equation — the historical route and Feynman’s path-integral approach. On the first route we stop once to gather the needed mathematical tools, and on the second route we stop once for an introduction to the special theory of relativity.

The first chapter of Part 2 (“A Closer Look”) derives the mathematical formalism of quantum mechanics from the existence of “ordinary” objects — stable objects that “occupy space” while being composed of objects that do not “occupy space.” The next two chapters are concerned with what happens if the objective fuzziness that “fluffs out” matter is ignored. (What happens is that the quantum-mechanical correlation laws degenerate into the dynamical laws of classical physics.) The remainder of Part 2 covers a number of conceptually challenging experiments and theoretical results, along with more conventional topics.

Part 3 (“Making Sense”) deals with the ontological implications of the formalism of quantum mechanics. The penultimate chapter argues that quantum mechanics — whose validity is required for the existence of “ordinary” objects — in turn requires for its consistency the validity of both the Standard Model and the general theory of relativity, at least as effective theories. The final chapter hazards an answer to the question of why stable objects that “occupy space” are composed of objects that do not “occupy space.” It is followed by an appendix containing solutions or hints for some of the problems provided in the text.

Ulrich Mohrhoff
August 15, 2010

1. [↑] Dieks, D.G.B.J. (1996). The quantum mechanical worldpicture and its popularization. Communication & Cognition 29 (2), pp. 153–168.

2. [↑] Feynman, R.P., Leighton, R.B., and Sands, M. (1963). The Feynman Lectures in Physics I, Addison–Wesley, pp. 1–2.