An Axiomatic Basis For Quantum Mechanics Derivation Of Hilbert Space Structure

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An Axiomatic Basis for Quantum Mechanics

Author : G. Ludwig
Publisher : Springer Science & Business Media
ISBN 13 : 3642700292
Total Pages : 255 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis An Axiomatic Basis for Quantum Mechanics by : G. Ludwig

Download or read book An Axiomatic Basis for Quantum Mechanics written by G. Ludwig and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first volume of a two-volume work, which is an improved version of a preprint [47] published in German. We seek to deduce the funda mental concepts of quantum mechanics solely from a description of macroscopic devices. The microscopic systems such as electrons, atoms, etc. must be detected on the basis of the macroscopic behavior of the devices. This detection resembles the detection of the dinosaurs on the basis offossils. In this first volume we develop a general description of macroscopic systems by trajectories in state spaces. This general description is a basis for the special de scription of devices consisting of two parts, where the first part is acting on the second. The microsystems are discovered as systems transmitting the action. Axioms which describe general empirical structures of the interactions between the two parts of each device, give rise to a derivation of the Hilbert space structure of quantum mechanics. Possibly, these axioms (and consequently the Hilbert space structure) may fail to describe other realms than the structure of atoms and mole cules, for instance the "elementary particles". This book supplements ref. [2]. Both together not only give an extensive foundation of quantum mechanics but also a solution in principle of the measuring problem.

An Axiomatic Basis for Quantum Mechanics

Author : G. Ludwig
Publisher : Springer
ISBN 13 : 9783642700316
Total Pages : 0 pages
Book Rating : 4.7/5 (3 download)

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Book Synopsis An Axiomatic Basis for Quantum Mechanics by : G. Ludwig

Download or read book An Axiomatic Basis for Quantum Mechanics written by G. Ludwig and published by Springer. This book was released on 2011-11-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first volume of a two-volume work, which is an improved version of a preprint [47] published in German. We seek to deduce the funda mental concepts of quantum mechanics solely from a description of macroscopic devices. The microscopic systems such as electrons, atoms, etc. must be detected on the basis of the macroscopic behavior of the devices. This detection resembles the detection of the dinosaurs on the basis offossils. In this first volume we develop a general description of macroscopic systems by trajectories in state spaces. This general description is a basis for the special de scription of devices consisting of two parts, where the first part is acting on the second. The microsystems are discovered as systems transmitting the action. Axioms which describe general empirical structures of the interactions between the two parts of each device, give rise to a derivation of the Hilbert space structure of quantum mechanics. Possibly, these axioms (and consequently the Hilbert space structure) may fail to describe other realms than the structure of atoms and mole cules, for instance the "elementary particles". This book supplements ref. [2]. Both together not only give an extensive foundation of quantum mechanics but also a solution in principle of the measuring problem.

An Axiomatic Basis for Quantum Mechanics

Author : Günther Ludwig
Publisher : Springer Science & Business Media
ISBN 13 : 3642718973
Total Pages : 252 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis An Axiomatic Basis for Quantum Mechanics by : Günther Ludwig

Download or read book An Axiomatic Basis for Quantum Mechanics written by Günther Ludwig and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first volume we based quantum mechanics on the objective description of macroscopic devices. The further development of the quantum mechanics of atoms, molecules, and collision processes has been described in [2]. In this context also the usual description of composite systems by tensor products of Hilbert spaces has been introduced. This method can be formally extrapolated to systems composed of "many" ele mentary systems, even arbitrarily many. One formerly had the opinion that this "extrapolated quantum mechanics" is a more comprehensive theory than the objec tive description of macrosystems, an opinion which generated unsurmountable diffi culties for explaining the measuring process. With respect to our foundation of quan tum mechanics on macroscopic objectivity, this opinion would mean that our founda tion is no foundation at all. The task of this second volume is to attain a compatibility between the objective description of macrosystems and an extrapolated quantum mechanics. Thus in X we establish the "statistical mechanics" of macrosystems as a theory more compre hensive than an extrapolated quantum mechanics. On this basis we solve the problem of the measuring process in quantum mechan ics, in XI developing a theory which describes the measuring process as an interaction between microsystems and a macroscopic device. This theory also allows to calculate "in principle" the observable measured by a device. Neither an incorporation of consciousness nor a mysterious imagination such as "collapsing" wave packets are necessary.

Handbook of Quantum Logic and Quantum Structures

Author : Kurt Engesser
Publisher : Elsevier
ISBN 13 : 008055038X
Total Pages : 821 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Quantum Logic and Quantum Structures by : Kurt Engesser

Download or read book Handbook of Quantum Logic and Quantum Structures written by Kurt Engesser and published by Elsevier. This book was released on 2011-08-11 with total page 821 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled "The logic of quantum mechanics quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results.Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate. The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject. The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability.- Written by eminent scholars in the field of logic- A comprehensive presentation of the theory, approaches and results in the field of quantum logic- Volume focuses on quantum structures

Hilbert Space Operators in Quantum Physics

Author : Jirí Blank
Publisher : Springer Science & Business Media
ISBN 13 : 9781563961427
Total Pages : 626 pages
Book Rating : 4.9/5 (614 download)

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Book Synopsis Hilbert Space Operators in Quantum Physics by : Jirí Blank

Download or read book Hilbert Space Operators in Quantum Physics written by Jirí Blank and published by Springer Science & Business Media. This book was released on 1999-04-23 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Market: Mathematicians, researchers, teachers, and graduate students specializing in quantum physics, mathematical physics, and applied mathematics. "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone....The translation is remarkably good." John R. Taylor, University of Colorado Based on lectures delivered over the past two decades, this book explains in detail the theory of linear Hilbert-space operators and its uses in quantum physics. The central mathematical tool of this book is the spectral theory of self-adjoint operators, which together with functional analysis and an introduction to the theory of operator sets and algebras, is used in a systematic analysis of the operator aspect of quantum theory. In addition, the theory of Hilbert-space operators is discussed in conjunction with various applications such as Schrodinger operators and scattering theory.

Quantum Theory and Pictures of Reality

Author : Wolfram Schommers
Publisher : Springer Science & Business Media
ISBN 13 : 3642955703
Total Pages : 352 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Quantum Theory and Pictures of Reality by : Wolfram Schommers

Download or read book Quantum Theory and Pictures of Reality written by Wolfram Schommers and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schommers introduces the foundations, mostly from a histori- cal point of view. Eberhard gives an introductory account of the Einstein-Podolsky-Rosen paradox and Bell's celebrated inequalities. D'Espagnat discusses realism andseparability and concludes that contemporary physics does not lead to a definite conception of the world. Eberhard shows how a model consistent with Bell's theorem can be constructed by ad- mitting faster-than-light action at a distance. Schommers discusses the structure ofspace-time and argues that physi- cally real processes do not take place in but are projected on space-time. Selleri discusses the idea that objectively real quantum waves exist and could in principle be detected.

Information Complexity and Control in Quantum Physics

Author : A. Blaquiere
Publisher : Springer
ISBN 13 : 3709129710
Total Pages : 356 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Information Complexity and Control in Quantum Physics by : A. Blaquiere

Download or read book Information Complexity and Control in Quantum Physics written by A. Blaquiere and published by Springer. This book was released on 2014-05-04 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Beyond the Quantum

Author : Theo M. Nieuwenhuizen
Publisher : World Scientific
ISBN 13 : 9812771182
Total Pages : 399 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Beyond the Quantum by : Theo M. Nieuwenhuizen

Download or read book Beyond the Quantum written by Theo M. Nieuwenhuizen and published by World Scientific. This book was released on 2007 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Already Einstein could never see quantum mechanics as a complete theory. Nowadays, many researchers, including 't Hooft, view quantum mechanics as a statistical description of some underlying reality. The workshop Beyond the Quantum, organized in Spring 2006 at the Lorentz Center in Leiden, The Netherlands, was one of the first meetings completely devoted to physics that may need an explanation beyond quantum mechanics. A broad variety of subjects was covered. The present book reflects this. Sample Chapter(s). Chapter 1: The Mathematical Basis for Deterministic Quantum Mechanics (267 KB). Contents: Introductions: The Mathematical Basis for Deterministic Quantum Mechanics (G 't Hooft); What Did We Learn from Quantum Gravity? (A Ashtekar); BoseOCoEinstein Condensates and EPR Quantum Non-Locality (F Lalo1/2); The Quantum Measurement Process: Lessons from an Exactly Solvable Model (A E Allahverdyan et al.); Quantum Mechanics and Quantum Information: POVMs: A Small but Important Step Beyond Standard Quantum Mechanics (W M de Muynck); State Reduction by Measurements with a Null Result (G Nienhuis); Solving Open Questions in the BoseOCoEinstein Condensation of an Ideal Gas via a Hybrid Mixture of Laser and Statistical Physics (M Kim et al.); Long Distance Correlations and Bell Inequalities: Fair Sampling vs No-Signalling Principle in EPR Experiments (G Adenier & A Yu Khrennikov); Mathematical Foundations: Where the Mathematical Structure of Quantum Mechanics Comes From (G M D'Ariano); Phase Space Description of Quantum Mechanics and Non-Commutative Geometry: Wigner-Moyal and Bohm in a Wider Context (B J Hiley); Quantum Mechanics as Simple Algorithm for Approximation of Classical Integrals (A Yu Khrennikov); Stochastic Electrodynamics: Some Quantum Experiments from the Point of View of Stochastic Electrodynamics (V apicka et al.); Models for the Electron: Rotating Hopf-Kinks: Oscillators in the Sense of de Broglie (U Enz); The Electron and the Neutrino as Solitos in Classical Electromagnetism (Th M Nieuwenhuizen); Philosophical Considerations; Round Table; and other papers. Readership: Postgraduates and researchers in quantum physics."

Algorithms and Complexity in Mathematics, Epistemology, and Science

Author : Nicolas Fillion
Publisher : Springer
ISBN 13 : 1493990519
Total Pages : 300 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Algorithms and Complexity in Mathematics, Epistemology, and Science by : Nicolas Fillion

Download or read book Algorithms and Complexity in Mathematics, Epistemology, and Science written by Nicolas Fillion and published by Springer. This book was released on 2019-02-07 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: ACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including numerical analysis and its underlying philosophy, computer algebra, reliability and uncertainty quantification, computation and complexity theory, combinatorics, error analysis, perturbation theory, experimental mathematics, scientific epistemology, and foundations of mathematics. By bringing together contributions from researchers who approach the mathematical sciences from different perspectives, the volume will further readers' understanding of the multifaceted role of mathematics in modern science, informed by the state of the art in mathematics, scientific computing, and current modeling techniques.

Quantum Theory without Reduction,

Author : Cini
Publisher : Routledge
ISBN 13 : 1351420348
Total Pages : 188 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Quantum Theory without Reduction, by : Cini

Download or read book Quantum Theory without Reduction, written by Cini and published by Routledge. This book was released on 2017-10-19 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum theory offers a strange, and perhaps unique, case in the history of science. Although research into its roots has provided important results in recent years, the debate goes on. Some theorists argue that quantum theory is weakened by the inclusion of the so called "reduction of the state vector" in its foundations. Quantum Theory without Reduction presents arguments in favor of quantum theory as a consistent and complete theory without this reduction and as a theory capable of explaining all known features of the measurement problem. This collection of invited contributions defines and explores different aspects of this issue, bringing an old debate into a new perspective and leading to a more satisfying consensus about quantum theory. The book will be of interest to researchers in theoretical physics and mathematical physics involved in the foundations of quantum theory. Scientists, engineers, and philosophers interested in the conceptual problems of quantum theory will also find this work stimulating.

The Space of Mathematics

Author : Javier Echeverria
Publisher : Walter de Gruyter
ISBN 13 : 3110870290
Total Pages : 440 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis The Space of Mathematics by : Javier Echeverria

Download or read book The Space of Mathematics written by Javier Echeverria and published by Walter de Gruyter. This book was released on 2012-10-25 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Topics Between Classical and Quantum Mechanics

Author : Nicholas P. Landsman
Publisher : Springer Science & Business Media
ISBN 13 : 146121680X
Total Pages : 547 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Mathematical Topics Between Classical and Quantum Mechanics by : Nicholas P. Landsman

Download or read book Mathematical Topics Between Classical and Quantum Mechanics written by Nicholas P. Landsman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph draws on two traditions: the algebraic formulation of quantum mechanics as well as quantum field theory, and the geometric theory of classical mechanics. These are combined in a unified treatment of the theory of Poisson algebras of observables and pure state spaces with a transition probability, which leads on to a discussion of the theory of quantization and the classical limit from this perspective. A prototype of quantization comes from the analogy between the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel between reduction of symplectic manifolds in classical mechanics and induced representations of groups and C*- algebras in quantum mechanics plays an equally important role. Examples from physics include constrained quantization, curved spaces, magnetic monopoles, gauge theories, massless particles, and $theta$- vacua. Accessible to mathematicians with some prior knowledge of classical and quantum mechanics, and to mathematical physicists and theoretical physicists with some background in functional analysis.

Knowledge and Time

Author : Hans Primas
Publisher : Springer
ISBN 13 : 3319473700
Total Pages : 431 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Knowledge and Time by : Hans Primas

Download or read book Knowledge and Time written by Hans Primas and published by Springer. This book was released on 2017-05-23 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique volume by a unique scientist, which combines conceptual, formal, and engineering approaches in a way that is rarely seen. Its core is the relation between ways of learning and knowing on the one hand and different modes of time on the other. Partial Boolean logic and the associated notion of complementarity are used to express this relation, and mathematical tools of fundamental physics are used to formalize it. Along the way many central philosophical problems are touched and addressed, above all the mind-body problem. Completed only shortly before the death of the author, the text has been edited and annotated by the author's close collaborator Harald Atmanspacher.

Erhard Scheibe's Structuralism

Author : Johannes Mierau
Publisher : Springer Nature
ISBN 13 : 3031253477
Total Pages : 183 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Erhard Scheibe's Structuralism by : Johannes Mierau

Download or read book Erhard Scheibe's Structuralism written by Johannes Mierau and published by Springer Nature. This book was released on 2023-04-20 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers the first systematic review of the structuralism of physical theories. Particular emphasis is placed on the inclusion of empirical imprecision into formal reconstructions of theories. The proposed measure of imprecision allows for a topological comparison of theories. Considering the ongoing debates on the nature of the thermodynamic limit in statistical mechanics, as well as on limit relations between classical and quantum mechanics, the author asserts that the Bourbaki-style structuralism, together with E. Scheibe's theory of reduction, is the best choice for reconstructing and analyzing the related questions of reduction and emergence. Readers will appreciate the critical overview of the main positions in philosophy of science, examined with particular attention to their applicability to current problems of fundamental theories of physics.

Fundamental Aspects of Quantum Theory

Author : Vittorio Gorini
Publisher : Springer Science & Business Media
ISBN 13 : 1468452215
Total Pages : 455 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Fundamental Aspects of Quantum Theory by : Vittorio Gorini

Download or read book Fundamental Aspects of Quantum Theory written by Vittorio Gorini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thi's book collects the contributions to the NATO Advanced Research WJrkshop on "FundaIrental Aspects of Quantum 'Iheory," held at the Centro di Cultura Scientifica "Alessandro Volta," Villa Olma, Carro, Italy, 2-7 September 1985. The rreeting was dedicated to the rremory of the late pro fessor Piero Caldirola, a prominent member of the Physics Departrrent of the University of r1ilan and a native of Como. The aim of the workshop has been to present several recent experi rrental results and theoretical developrrents concerning the various fa cets of quantum physics. The breadth of scope of the rreeting was in accordance with Professor Caldirola's vast scientific interests, and fostered communication among experirrental physicists, theoretical and mathematical physicists, and nEthematicians, working in different but related fields. Indeed, lectu rers endeavoured to make their contributions understandable to people acquainted with the problem but not necessarily familiar with the tech nical details; and these efforts were successful, as indicated by the frequent private discussions which took place among participants belon ging to different breeds and brands. 1ne rreeting was made up of six one-day sessions, each of them addres sing to a specific aspect of quantum theory: 1. General Problems and Crucial Experinents; with emphasis on sin gle-particle interference eh rirrents of neutrons and of photons, and on the rreasurerrent problem. 2. Quantization and Stochastic Processes; including stochastic quan tization of gauge fields, stochastic description of supersyrnmetric fields, quantum stochastic calculus and stochastic mechanics."

Quantum Computation

Author : American Mathematical Society. Short Course
Publisher : American Mathematical Soc.
ISBN 13 : 0821820842
Total Pages : 377 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quantum Computation by : American Mathematical Society. Short Course

Download or read book Quantum Computation written by American Mathematical Society. Short Course and published by American Mathematical Soc.. This book was released on 2002 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents written versions of the eight lectures given during the AMS Short Course held at the Joint Mathematics Meetings in Washington, D.C. The objective of this course was to share with the scientific community the many exciting mathematical challenges arising from the new field of quantum computation and quantum information science. The course was geared toward demonstrating the great breadth and depth of this mathematically rich research field. Interrelationships withexisting mathematical research areas were emphasized as much as possible. Moreover, the course was designed so that participants with little background in quantum mechanics would, upon completion, be prepared to begin reading the research literature on quantum computation and quantum informationscience. Based on audience feedback and questions, the written versions of the lectures have been greatly expanded, and supplementary material has been added. The book features an overview of relevant parts of quantum mechanics with an introduction to quantum computation, including many potential quantum mechanical computing devices; introduction to quantum algorithms and quantum complexity theory; in-depth discussion on quantum error correcting codes and quantum cryptography; and finally,exploration into diverse connections between quantum computation and various areas of mathematics and physics.

Philosophy of Physics

Author : Jeremy Butterfield
Publisher : Elsevier
ISBN 13 : 0444515607
Total Pages : 1481 pages
Book Rating : 4.4/5 (445 download)

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Book Synopsis Philosophy of Physics by : Jeremy Butterfield

Download or read book Philosophy of Physics written by Jeremy Butterfield and published by Elsevier. This book was released on 2007 with total page 1481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ambition of this volume is twofold: to provide a comprehensive overview of the field and to serve as an indispensable reference work for anyone who wants to work in it. For example, any philosopher who hopes to make a contribution to the topic of the classical-quantum correspondence will have to begin by consulting Klaas Landsman's chapter. The organization of this volume, as well as the choice of topics, is based on the conviction that the important problems in the philosophy of physics arise from studying the foundations of the fundamental theories of physics. It follows that there is no sharp line to be drawn between philosophy of physics and physics itself. Some of the best work in the philosophy of physics is being done by physicists, as witnessed by the fact that several of the contributors to the volume are theoretical physicists: viz., Ellis, Emch, Harvey, Landsman, Rovelli, 't Hooft, the last of whom is a Nobel laureate. Key features - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences that have grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers