Randomness And Undecidability In Physics - Hardcover

Svozil, K

9789810208097: Randomness And Undecidability In Physics

Hardcover

ISBN 10: 981020809X ISBN 13: 9789810208097

Publisher: Wspc, 1993

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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.

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Review

"The interaction between computer science and physics has become more and more visible. Indeed, physical systems may be perceived as computational processes (according to some authors, physical systems exactly correspond to specific computations), and, conversely, computers are physical systems, not only in the crude sense of their hardware, but as a medium to virtual realities. Svozil's text is the first monograph devoted, in a technical sense, to this topic, and in the reviewer's opinion the author has succeeded excellently in his project. The book represents a valuable contribution toward a global understanding of computers and physics; the topic presented in its entirely and placed in perspective for researchers, students, and practitioners alike." Cristian Calude

Synopsis

Algorithmic physics is the field in which physical systems are identified with computation processes. This book contains a brief outline of algorithmic physics, in particular of algorithmics, automata theory coding and information theory, as well as algorithmic information theory. The author relates physical entities to concepts in computer science, logic and mathematics, and introduces the concept of a theoretical model "from within" an artificial computer world and "from the outside". Chaos is characterized by both algorithmic undecidability and randomness. Godel incompleteness is translated into physical undecidability and unpredictability. It is shown that the behaviour of deterministic processes is generally impossible to predict even if their evolution law and initial states are exactly known. Several mathematical concepts of randomness are discussed with respect to their applicability for a characterization of chaotic, physical motion.

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