Quantum Theory (or Quantum Mechanics or Quantum Physics - the terms are interchangeable) is an extension of physics in order to cover the behaviour of microscopic objects. Physics as it was before Quantum Theory is called Classical Physics. On some versions Quantum Theory includes Classical Physics as a special case. From the start the theory was subject to controversy and developed into a wealth of different forms, mostly agreeing at the level of practical calculation but disagreeing wildly as to the interpretation. The question "what is quantum theory" is therefore a difficult one.
Both Classical and Quantum Physics describe how the observable properties of a system change with time. The "system" (which here means "thing") can be anything from an atom to the universe; its properties are quantities like position, momentum, energy, the internal arrangements of its parts and so on.
In Classical Physics there is a set of properties for any given system (namely the positions and velocities of all its parts) which completely determines its time-development and the properties at any later time. In Quantum Physics there is no such complete set of properties. Instead
1. At any given time there are many different possible sets of properties, any one of which sets can be observed; but it is not possible to observe all the properties simultaneously. For instance, position and velocity cannot be observed simultaneously; the first gives a particle-picture the second a wave-picture.
2. Any properties at a later time cannot (except in special circumstances) be determined by observing properties at an earlier time. Only their probabilities are fixed by the earlier observation.
The term observed means different things in different versions: e.g. "manifested," "recorded by a macroscopic instrument," "brought to (human?) consciousness" and so on. The last possibility links quantum theory with theories of mind. At any given time there is a well defined specification of the probability of observing any given property. This collection of probabilities is fixed by (or in some versions is identical with) the quantum state, but this state is not itself observable. Interpretations differ as to whether the state is real or a mathematical abstraction, with profound consequences for the whole notion of reality in physics.
The earliest interpretations, dating from workers in Copenhagen, used a two-tier world: a small system obeying non-Classical Physics and an observing laboratory obeying Classical Physics. The many pre-1965 theories tend to call themselves "The Copenhagen Interpretation." Later interpretations tried to achieve a more unified view. This history introduced a succession of alternative structures: the collapse of the state, many worlds, environmental diffusion and so on. These have almost all been superseded.
Systems with infinitely many degrees of freedom (in particular, fields such as the electromagnetic field) are described by quantum field theory whose states can all be constructed out of a special state of the field in question called the vacuum for that field. The vacuum has zero energy (except in Dirac's theory which enjoyed brief popularity).
Prof. Chris Clarke is visiting Professor in the Faculty of Mathematical Studies, University of Southampton. He is the author of 'Reality Through the Looking Glass' (1995).
Gribbin, John (1995). Schrödinger's Kittens. London: Weidenfeld and Nicholson. ISBN 1-85799-4027.
Perhaps the best popular exposition of the mainstream physicists' approach. Well written, very readable and reliable as far as it goes.
Stapp, Henry P (1993). Mind, Matter, and Quantum Mechanics. New York: Springer-Verlag Berlin Heidelberg New York. ISBN 3-540-56289-3.
A collection of non-mathematical essays, forming a good compromise between rigour, scope and imaginative extension. Surveys with philosophical care the history and main versions of the subject as well as the author's own personal approach. Not the easiest text, but the most reliable.
Zohar, Danah (1990). The Quantum Self. London: Bloomsbury. ISBN 0-7475-0271-4.
Highly readable and inspiring account of why quantum theory is important for the way we live. Conveys the inner spirit of quantum theory, though a lot of the details would be contested by the mainstream.
Omnès, Roland (1999) Quantum Philosophy Princeton, NJ: Princeton University Press. ISBN 0-691-02787-0.
I think this is the only non-mathematical account of the consistent histories approach to quantum theory, which has now taken over from older versions as the most promising candidate for a generally applicable interpretation. He takes a very individual philosophical and interpretative position, however, which should be allowed for.
Wheeler, John A and Zurek, Wojciech H (1983) eds. Quantum Theory and Measurement. Princeton, NJ: Princeton University Press. ISBN 0-691-08316-9.
A collection of 49 classic papers with commentaries and a guide to further literature, including Schrödinger (the cat!), Bohr, Heisenberg, Einstein, . Many of the papers are non-mathematical and provide an invaluable source for those who want to know what these people really said.
Home, Dipankar (1997) Conceptual Foundations of Quantum Physics. New York: Plenum Press. ISBN 0-306-45660-5.
An excellent critical survey and summary of the main interpretations and their key features, plus Bell's theorem, non-locality etc. But it is mathematical.
Bohm, David and Hiley, Basil J (1993) The Undivided Universe. London: Routledge. ISBN 0-415-06588-7.
The definitive presentation of David Bohm's approach, which is the most important philosophically realist alternative to quantum theory. This book, Bohm's physical work, conveys an essentially different slant from the philosophical material given in his Implicate Order book, but it does contain quite a lot of mathematics.
Feynman, Paul and Hibbs A. R. (1965) Quantum Mechanics and Path Integrals.
New York: McGraw-Hill Book Company; ISBN 0-070-20650-3.
The approach that has had a profound influence on both interpretation and practice. A text book, but still quite readable - the maths is avoidable!
Peskin, Michael E. (1995) An Introduction to Quantum Field Theory. New York: Addison Wesley Publishing Company; ISBN: 0-201-50397-2.
There is unfortunately no popular account of quantum field theory. I have included a standard modern text book for those who have some maths, in order to underline the fact that the quantum vacuum is not, in modern physics, the "infinite sea of energy" that is claimed by some journalists.