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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zlib/Biology and other natural sciences/K Svozil/Randomness And Undecidability In Physics_3373135.djvu

Mathematical Methods In Electromagnetism: Linear Theory And Applications Linear Theory and Applications

Svozil, Karl

World Scientific Publishing Co Pte Ltd

Forgotten Books

World Scientific Publishing Company, River Edge, N.J., 1993

United Kingdom and Ireland, United Kingdom

River Edge, N.J, New Jersey, 1993

River Edge, N.J, 1992

Singapore, Singapore

Singapore, ©1993

1, 19931005

kolxoz -- 81

lg2131431

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Includes bibliographical references (p. 271-289) and index.

Algorithmic physics: the universe as a computer. 1. Algorithmics and recursive function theory -- 2. Mechanism and determinism -- 3. Discrete physics -- 4. Source coding -- 5. Lattice theory -- 6. Extrinsic-intrinsic concept -- 7. Algorithmic information -- 8. Computational complexity -- Undecidability. 9. Classical results -- 10. Complementarity -- 11. Extrinsic indeterminism -- 12. Intrinsic indeterminism -- 13. Weak physical chaos -- Randomness. 14. Randomness in mathematics -- 15. Random fractals and 1/f noise -- 16. Chaotic systems are optimal analogues of themselves -- 17. Quantum chaos -- 18. Algorithmic entropy -- Epilogue: Afterthoughts, speculations & metaphysics

Algorithmic physics is the field in which physical systems are identified with computation processes. Several mathematical concepts of randomness are then discussed with respect to their applicability for a characterization of chaotic, physical motion.

2017-10-15