Discrete Causal Theory
Discrete Causal Theory

Author: Benjamin F. Dribus

Publisher: Springer

Published: 2017-04-26

Total Pages: 577

ISBN-13: 331950083X

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This book evaluates and suggests potentially critical improvements to causal set theory, one of the best-motivated approaches to the outstanding problems of fundamental physics. Spacetime structure is of central importance to physics beyond general relativity and the standard model. The causal metric hypothesis treats causal relations as the basis of this structure. The book develops the consequences of this hypothesis under the assumption of a fundamental scale, with smooth spacetime geometry viewed as emergent. This approach resembles causal set theory, but differs in important ways; for example, the relative viewpoint, emphasizing relations between pairs of events, and relationships between pairs of histories, is central. The book culminates in a dynamical law for quantum spacetime, derived via generalized path summation.

Quantum Information and Foundations
Quantum Information and Foundations

Author: Giacomo Mauro D’Ariano

Publisher: MDPI

Published: 2020-03-23

Total Pages: 508

ISBN-13: 3039283804

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Quantum information has dramatically changed information science and technology, looking at the quantum nature of the information carrier as a resource for building new information protocols, designing radically new communication and computation algorithms, and ultra-sensitive measurements in metrology, with a wealth of applications. From a fundamental perspective, this new discipline has led us to regard quantum theory itself as a special theory of information, and has opened routes for exploring solutions to the tension with general relativity, based, for example, on the holographic principle, on non-causal variations of the theory, or else on the powerful algorithm of the quantum cellular automaton, which has revealed new routes for exploring quantum fields theory, both as a new microscopic mechanism on the fundamental side, and as a tool for efficient physical quantum simulations for practical purposes. In this golden age of foundations, an astonishing number of new ideas, frameworks, and results, spawned by the quantum information theory experience, have revolutionized the way we think about the subject, with a new research community emerging worldwide, including scientists from computer science and mathematics.

THEORY OF CAUSAL DIFFERENTIAL EQUATIONS
THEORY OF CAUSAL DIFFERENTIAL EQUATIONS

Author: S. Leela

Publisher: Springer Science & Business Media

Published: 2010-01-01

Total Pages: 218

ISBN-13: 9491216252

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The problems of modern society are both complex and inter-disciplinary. Despite the - parent diversity of problems, however, often tools developed in one context are adaptable to an entirely different situation. For example, consider the well known Lyapunov’s second method. This interesting and fruitful technique has gained increasing signi?cance and has given decisive impetus for modern development of stability theory of discrete and dynamic system. It is now recognized that the concept of Lyapunov function and theory of diff- ential inequalities can be utilized to investigate qualitative and quantitative properties of a variety of nonlinear problems. Lyapunov function serves as a vehicle to transform a given complicated system into a simpler comparison system. Therefore, it is enough to study the properties of the simpler system to analyze the properties of the complicated system via an appropriate Lyapunov function and the comparison principle. It is in this perspective, the present monograph is dedicated to the investigation of the theory of causal differential equations or differential equations with causal operators, which are nonanticipative or abstract Volterra operators. As we shall see in the ?rst chapter, causal differential equations include a variety of dynamic systems and consequently, the theory developed for CDEs (Causal Differential Equations) in general, covers the theory of several dynamic systems in a single framework.

Discrete or Continuous?
Discrete or Continuous?

Author: Amit Hagar

Publisher: Cambridge University Press

Published: 2014-05

Total Pages: 281

ISBN-13: 1107062802

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Novel conceptual analysis, fresh historical perspectives, and concrete physical examples illuminate one of the most thought-provoking topics in physics.

Free Will, Causality, and Neuroscience
Free Will, Causality, and Neuroscience

Author:

Publisher: BRILL

Published: 2019-10-21

Total Pages: 191

ISBN-13: 9004409963

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Neuroscientists often consider free will to be an illusion. Contrary to this hypothesis, the contributions to this volume show that recent developments in neuroscience can also support the existence of free will. Firstly, the possibility of intentional consciousness is studied. Secondly, Libet’s experiments are discussed from this new perspective. Thirdly, the relationship between free will, causality and language is analyzed. This approach suggests that language grants the human brain a possibility to articulate a meaningful personal life. Therefore, human beings can escape strict biological determinism. Contributing author Sofia Bonicalzi has received funding from the European Union’s Framework Programme for Research and Innovation Horizon 2020 (2014-2020) under the Marie Skłodowska-Curie Grant Agreement No. 754388 (LMUResearchFellows) and from LMUexcellent, funded by the Federal Ministry of Education and Research (BMBF) and the Free State of Bavaria under the Excellence Strategy of the German Federal Government and the Länder.

Questioning the Foundations of Physics
Questioning the Foundations of Physics

Author: Anthony Aguirre

Publisher: Springer

Published: 2015-01-24

Total Pages: 279

ISBN-13: 3319130455

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The essays in this book look at way in which the fundaments of physics might need to be changed in order to make progress towards a unified theory. They are based on the prize-winning essays submitted to the FQXi essay competition “Which of Our Basic Physical Assumptions Are Wrong?”, which drew over 270 entries. As Nobel Laureate physicist Philip W. Anderson realized, the key to understanding nature’s reality is not anything “magical”, but the right attitude, “the focus on asking the right questions, the willingness to try (and to discard) unconventional answers, the sensitive ear for phoniness, self-deception, bombast, and conventional but unproven assumptions.” The authors of the eighteen prize-winning essays have, where necessary, adapted their essays for the present volume so as to (a) incorporate the community feedback generated in the online discussion of the essays, (b) add new material that has come to light since their completion and (c) to ensure accessibility to a broad audience of readers with a basic grounding in physics. The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.

New Foundations for Physical Geometry
New Foundations for Physical Geometry

Author: Tim Maudlin

Publisher:

Published: 2014-02

Total Pages: 374

ISBN-13: 0198701306

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Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.

Progress in Group Field Theory and Related Quantum Gravity Formalisms
Progress in Group Field Theory and Related Quantum Gravity Formalisms

Author: Steffen Gielen

Publisher: MDPI

Published: 2020-07-01

Total Pages: 338

ISBN-13: 3039361783

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Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research.