Janina Marciak-Kozłowska
Institute of Electron Technology, Warsaw, Poland

Miroslaw Kozlowski
Warsaw University, Warsaw, Poland

Series: Physics Research and Technology

The use of mathematics in modern physics can be rather daunting. In classical mechanics, the representation of the position of a particle by a cuclidean three-vector can be directly related to our immediate impressions of the world around us. However, quantum theory is distinguished by a striking gap between the mathematical structure and the physical objects it seeks to represent: a gap that can become an unbridgeable chasm for engineers encountering the subject for the first few times. For this reason, it is worth being clear in advance what the main goals are in the material that follows.

A theoretical structure in modern physics typically has the following, axiomatic, features:
1. A specified domain of applicability that limits the class of physical systems to which the theory should be applied;
2. An identification of certain physical concepts that relate to the class of systems in this domain;
3. A specification of the general mathematical framework within which the theory is to be presented;
4. A collection of rules that relate the physical concepts to elements of the mathematical structure;
5. An overall conceptual scheme for analysing the meaning of funda¬mental terms employed in the statement of the rules;
6. A set of techniques for applying the rules to specific physical systems within the class admitted by the domain of applicability.

The book begins with a short summary of some of the key ideas in modern physics, presented in a way that is adapted to the later discussion. Chapters 2 and 3 then introduce the basic ideas of classical and quantum systems. This material is kept to the mini¬mum necessary for the task in hand: in particular, no attempt is made to deal rigorously with the mathematical problems
One of the main goals of the book is to explore some of the deep conceptual issues that arise in quantum theory. Of the many ways in which this topic can be approached, I have chosen to focus on the notion of a physical property and the extent to which it is, or is not, meaningful to talk about a quantum system ‘possessing’ such properties. Analogous situation in classical physics: in particular, the way in which a certain philosophical view about the physical world is reflected m the mathematical framework used to describe it. In classical physics, the ‘realist’ and ‘instrumentalist’ views of science fit together seamlessly, whereas in quantum physics they differ sharply, especially in their atti¬tudes towards the idea of physical properties. (Imprint: Nova)