Recent findings in the computer sciences, discrete mathematics, formal logics and metamathematics have opened up a royal road for the investigation of undecidability and randomness in physics. A translation of these formal concepts yields a fresh look into diverse features of physical modelling such as quantum complementarity and the measurement problem, but also stipulates questions related to the necessity of the assumption of continua.Conversely, any computer may be perceived as a physical system: not only in the immediate sense of the physical properties of its hardware. Computers are a medium to virtual realities. The foreseeable importance of such virtual realities stimulates the investigation of an "inner description", a "virtual physics" of these universes of computation. Indeed, one may consider our own universe as just one particular realisation of an enormous number of virtual realities, most of them awaiting discovery.One motive of this book is the recognition that what is often referred to as "randomness" in physics might actually be a signature of undecidability for systems whose evolution is computable on a step-by-step basis. To give a flavour of the type of questions envisaged: Consider an arbitrary algorithmic system which is computable on a step-by-step basis. Then it is in general impossible to specify a second algorithmic procedure, including itself, which, by experimental input-output analysis, is capable of finding the deterministic law of the first system. But even if such a law is specified beforehand, it is in general impossible to predict the system behaviour in the "distant future". In other words: no "speedup" or "computational shortcut" is available. In this approach, classical paradoxes can be formally translated into no-go theorems concerning intrinsic physical perception.It is suggested that complementarity can be modelled by experiments on finite automata, where measurements of one observable of the automaton destroys the possibility to measure another observable of the same automaton and it vice versa.Besides undecidability, a great part of the book is dedicated to a formal definition of randomness and entropy measures based on algorithmic information theory.

'This book could serve either as a good reference to remind students about what they have seen in their completed courses or as a starting point to show what needs more investigation. Svozil (Vienna Univ. of Technology) offers a very thorough text that leaves no mathematical area out, but it is best described as giving a synopsis of each application and how it relates to other areas ... The text is organized well and provides a good reference list. Summing Up: Recommended. Upper-division undergraduates and graduate students.'CHOICEThis book contains very explicit proofs and demonstrations through examples for a comprehensive introduction to the mathematical methods of theoretical physics. It also combines and unifies many expositions of this subject, suitable for readers with interest in experimental and applied physics.

Quantum Logic deals with the foundations of quantum mechanics and, related to it, the behaviour of finite, discrete deterministic systems. The quantum logical approach is particulalry suitable for the investigation and exclusion of certain hidden parameter models of quantum mechanics. Conversely, it can be used to embed quantum universes into classical ones. It is also highly relevant for the characterization of finite automation. This book has been written with a broad readership in mind. Great care has been given to the motivation of the concepts and to the explicit and detailed discussions of examples.

Unidentified phenomena in space, in the Earth's atmosphere, and in waters are too important to leave their exploration to the military and scientific laypersons. Their proper scientific study is important for a variety of reasons; in particular, scientists and the public at large need to know the basic facts, to be informed about the way evidence is recorded, and to understand the difference been reliable evidence and fiction, as well as between plausible explanations and fantasy. With this objective, the book surveys the history of UFO observations, the variety of recorded phenomena, and recounts the efforts of investigative commissions and their published findings. Although wild rumors are demystified in the process, this is not an exercise in rumor-bashing. An open and at the same time critical mindset is the key. Many narratives and hypothesis appear implausible relative to our present state of knowledge; but this alone should not lead to their outright exclusion. Thus the author also pays attention to UFO sightings that have so far eluded explanation in terms of known physics or meteorology. Here the reader will encounter some of the more speculative but scientifically tenable proposals, for example, relating to sudden zigzag motion without apparent inertia or recognizable propulsion, yet always with a clear guide to their plausibility. Last but not least, the book outlines plans and suggestions for future research capable of revealing the existence and intentions of extraterrestrial intelligences, outer-space engineers, or technologies so far known only from science fiction.