Svozil K. Randomness and Undecidability in Physics

World Scientific Publishing Co.Pte.Ltd, 1993. — 296 p. — ISBN10: 981020809XAlgorithmic 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.Algorithmic physics: the Universe as a computer
Algorithmes and recursive function theory
Mechanism and determinism
Discrete physics
Source coding
Lattice theory
Extrinsic-intrinsic concept
Algorithmic information
Computational complexity
Undecidability
Classical results
Complementarity
Extrinsic indeterminism
Intrinsic indeterminism
Weak physical chaos
Randomness
Randomness in mathematics
Random fractals and l/f noise
Chaotic systems are optimal analogues of themselves
Quantum chaos
Algorithmic entropy
Epilogue:Afterthoughts, speculations & metaphysics
Program code
Cellular Automata simulation
log*2&lg*
Automaton analysis