Randomness And Undecidability In Physics

Randomness And Undecidability In Physics
Author: Karl Svozil
Publsiher: World Scientific
Total Pages: 310
Release: 1993-10-05
Genre: Science
ISBN: 9789814522922

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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.

Undecidability Uncomputability and Unpredictability

Undecidability  Uncomputability  and Unpredictability
Author: Anthony Aguirre,Zeeya Merali,David Sloan
Publsiher: Springer Nature
Total Pages: 181
Release: 2021-08-20
Genre: Science
ISBN: 9783030703547

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For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Gödel’s undecidability results (the incompleteness theorems), Turing’s proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world? This book, based on the winning essays from the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigation of the meaning of these constraints for the physical world, and for us as humans.​

Randomness Through Computation

Randomness Through Computation
Author: Hector Zenil
Publsiher: World Scientific
Total Pages: 439
Release: 2011
Genre: Computers
ISBN: 9789814327749

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This review volume consists of an indispensable set of chapters written by leading scholars, scientists and researchers in the field of Randomness, including related subfields specially but not limited to the strong developed connections to the Computability and Recursion Theory. Highly respected, indeed renowned in their areas of specialization, many of these contributors are the founders of their fields. The scope of Randomness Through Computation is novel. Each contributor shares his personal views and anecdotes on the various reasons and motivations which led him to the study of the subject. They share their visions from their vantage and distinctive viewpoints. In summary, this is an opportunity to learn about the topic and its various angles from the leading thinkers.

Information and Randomness

Information and Randomness
Author: Cristian Calude
Publsiher: Springer Science & Business Media
Total Pages: 252
Release: 2013-03-09
Genre: Mathematics
ISBN: 9783662030493

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"Algorithmic information theory (AIT) is the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously", says G.J. Chaitin, one of the fathers of this theory of complexity and randomness, which is also known as Kolmogorov complexity. It is relevant for logic (new light is shed on Gödel's incompleteness results), physics (chaotic motion), biology (how likely is life to appear and evolve?), and metaphysics (how ordered is the universe?). This book, benefiting from the author's research and teaching experience in Algorithmic Information Theory (AIT), should help to make the detailed mathematical techniques of AIT accessible to a much wider audience.

Introduction to Random Time and Quantum Randomness

Introduction to Random Time and Quantum Randomness
Author: Kai Lai Chung,Jean-Claude Zambrini
Publsiher: World Scientific
Total Pages: 228
Release: 2003
Genre: Science
ISBN: 9812384154

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This book is made up of two essays on the role of time in probability and quantum physics. In the first one, K L Chung explains why, in his view, probability theory starts where random time appears. This idea is illustrated in various probability schemes and the deep impact of those random times on the theory of the stochastic process is shown. In the second essay J-C Zambrini shows why quantum physics is not a regular probabilistic theory, but also why stochastic analysis provides new tools for analyzing further the meaning of Feynman's path integral approach and a number of foundational issues of quantum physics far beyond what is generally considered. The role of the time parameter, in this theory, is critically re-examined and a fresh way to approach the long-standing problem of the quantum time observable is suggested.

Between Chance and Choice

Between Chance and Choice
Author: Harald Atmanspacher,Robert Bishop
Publsiher: Imprint Academic
Total Pages: 548
Release: 2002
Genre: Philosophy
ISBN: 0907845215

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Chance and choice are two leading actors on stage whenever issues of determinism are under discussion. This volume collects essays by scientists and philosophers presenting a discussion of determinism, randomness and freewill from the viewpoint of philosophy, maths and psychology.

Machines Computations and Universality

Machines  Computations  and Universality
Author: Maurice Margenstern
Publsiher: Springer
Total Pages: 328
Release: 2005-02-25
Genre: Computers
ISBN: 9783540318347

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This book constitutes the thoroughly refereed postproceedings of the 4th International Conference on Machines, Computations, and Universality, MCU 2004, held in St. Petersburg, Russia in September 2004. The 21 revised full papers presented together with 5 invited papers went through two rounds of reviewing, selection, and improvement. A broad variety of foundational aspects in theoretical computer science are addressed, such as cellular automata, molecular computing, quantum computing, formal languages, automata theory, Turing machines, P systems, etc.

Information Randomness Incompleteness

Information  Randomness   Incompleteness
Author: Gregory J. Chaitin
Publsiher: World Scientific
Total Pages: 332
Release: 1990-01-01
Genre: Mathematics
ISBN: 9810201710

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This book contains in easily accessible form all the main ideas of the creator and principal architect of algorithmic information theory. This expanded second edition has added thirteen abstracts, a 1988 Scientific American Article, a transcript of a EUROPALIA 89 lecture, an essay on biology, and an extensive bibliography. Its new larger format makes it easier to read. Chaitin's ideas are a fundamental extension of those of G”del and Turning and have exploded some basic assumptions of mathematics and thrown new light on the scientific method, epistemology, probability theory, and of course computer science and information theory.