Bøger i Fundamental Theories of Physics serien

This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual.

This book provides a captivating journey through the realms of classical and quantum systems as it unravels the profound influence that noise may have on their static and dynamic properties. The first part of the book offers succinct yet enlightening discussions on foundational topics related to noise. The second part focuses on a variety of applications, where a diverse spectrum of noise effects in physical systems comes to life, meticulously presented and thoughtfully analyzed. Whether you are a curious student or a dedicated researcher, this book is your key to gaining invaluable insights into noise effects in physical systems. ¿The book has the merit of presenting several topics scattered in the literature and could become a very useful reference.¿ Giovanni Jona-Lasinio, Sapienza ¿ Università di Roma, Italy

This volume commemorates the scientific contributions of Detlef Dürr (1951¿2021) to foundational questions of physics. It presents new contributions from his former students, collaborators, and colleagues about their current research on topics inspired or influenced by Dürr. These topics are drawn from physics, mathematics, and philosophy of nature, and concern interpretations of quantum theory, new developments of Bohmian mechanics, the role of typicality, quantum physics in relativistic space-time, classical and quantum electrodynamics, and statistical mechanics. The volume thus also gives a snapshot of present research in the foundations of physics.

This book addresses research challenges in the rapidly developing area of nonequilibrium thermodynamics and fluctuation kinetics. This cross-disciplinary field comprises various topics, ranging from fundamental problems of nonequilibrium statistical mechanics and thermodynamics to multiple applications in plasma, fluid mechanics, nonlinear science, systems of dissipative particles, and high-Q resonators. The purpose of this book is to bring together world-leading experts in the above fields to initiate a cross-fertilization among these active research areas. The book is dedicated to and honours the memory of Professor Slava Belyi who passed away unexpectedly on May 20, 2020. He was pioneering the theory of nonequilibrium fluctuations, in particular the application of the Callen-Welton fluctuation-dissipation theorem to nonequilibrium systems and its generalization. This and related problems also feature in the book.

Our vast Universe is filled with an enormous amount of matter and energy, which are the source of large gravitational potentials affecting all physical phenomena. Because this fact about the size and contents of the Universe was not known when our fundamental theories of dynamics and relativity were completed by the 1920s, the current theories - based as they are in empty space - fail to incorporate cosmic gravity. Though the current theories are consistent with the majority of empirical facts, there are some crucial discrepancies, which demand a drastic shift to a cosmic gravitational paradigm for the theories of relativity and dynamics. The book is a detailed and widely accessible account of this paradigm, called Cosmic Relativity, supported by ample empirical evidence. It is established that all motional relativistic effects are cosmic gravitational effects. The new theory of Cosmic Relativity solves and answers all outstanding questions and puzzles about dynamics and relativity.

To understand phenomena in nature, it is important to focus not only on properties of stationary states, but also their changes in time, that is, the dynamics between bistable states. This book reviews the mechanics of first-order phase transitions and discusses relaxation and collapses of metastable states from various viewpoints, including Kramers' method for the lifetime of metastability, Langer's analysis on the singularity, effects of thermal fluctuation studied by Neel and Brown, and eigenvalue structures of the transfer-matrix for the phase transitions. The book also goes into the mechanics of metastability in quantum systems from the viewpoints of the eigenvalue problem of the Hamiltonian and the Liouvillian for a dynamical process and discusses relations between quantum tunneling processes and metastability therein. Lastly, the coercivity of magnets consisting of an ensemble of grains is reviewed.The book is beneficial for those new in the field as a primer on first-order phase transition from modern perspectives. The comprehensive content offers overviews of related topics and allows readers to quickly catch up with developments in the field.

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.

This book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics. Namely, the book is devoted to a review of a "covariant approach" to Quantum Mechanics, along with several improvements and new results with respect to the previous related literature. The first part of the book deals with a covariant formulation of Galilean Classical Mechanics, which stands as a suitable background for covariant Quantum Mechanics. The second part deals with an introduction to covariant Quantum Mechanics. Further, in order to show how the presented covariant approach works in the framework of standard Classical Mechanics and standard Quantum Mechanics, the third part provides a detailed analysis of the standard Galilean space-time, along with three dynamical classical and quantum examples. The appendix accounts for several non-standard mathematical methods widely used in the body of the book.

This book presents a comprehensive account of the renormalization-group (RG) method and its extension, the doublet scheme, in a geometrical point of view. It extract long timescale macroscopic/mesoscopic dynamics from microscopic equations in an intuitively understandable way rather than in a mathematically rigorous manner and introduces readers to a mathematically elementary, but useful and widely applicable technique for analyzing asymptotic solutions in mathematical models of nature. The book begins with the basic notion of the RG theory, including its connection with the separation of scales. Then it formulates the RG method as a construction method of envelopes of the naive perturbative solutions containing secular terms, and then demonstrates the formulation in various types of evolution equations. Lastly, it describes successful physical examples, such as stochastic and transport phenomena including second-order relativistic as well as nonrelativistic fluid dynamics with causality and transport phenomena in cold atoms, with extensive numerical expositions of transport coefficients and relaxation times. Requiring only an undergraduate-level understanding of physics and mathematics, the book clearly describes the notions and mathematical techniques with a wealth of examples. It is a unique and can be enlightening resource for readers who feel mystified by renormalization theory in quantum field theory.

This self-contained monograph provides a mathematically simple and physically meaningful model which unifies gravity, electromagnetism, optics and even some quantum behavior. The simplicity of the model is achieved by working in the frame of an inertial observer and by using a physically meaningful least action principle.The authors introduce an extension of the Principle of Inertia. This gives rise to a simple, physically meaningful action function. Visualizations of the geometryare obtained by plotting the action function. These visualizations may be used to compare the geometries of different types of fields. Moreover, a new understanding of the energy-momentum of a field emerges.The relativistic dynamics derived here properly describes motion of massive and massless objects under the influence of a gravitational and/or an electromagnetic field, and under the influence of isotropic media.The reader will learn how to compute theprecession of Mercury, the deflection of light, and the Shapiro time delay. Also covered is the relativistic motion of binary stars, including the generation of gravitational waves, a derivation of Snell's Law and a relativistic description of spin. We derive a complex-valued prepotential of an electromagnetic field. The prepotential is similar to the wave function in quantum mechanics. The mathematics is accessible to students after standard courses in multivariable calculus and linear algebra. For those unfamiliar with tensors and the calculus of variations, these topics are developed rigorously in the opening chapters. The unifying model presented here should prove useful to upper undergraduate and graduate students, as well as to seasoned researchers.

This book presents a collection of novel contributions and reviews by renowned researchers in the foundations of quantum physics, quantum optics, and neutron physics. It is published in honor of Michael Horne, whose exceptionally clear and groundbreaking work in the foundations of quantum mechanics and interferometry, both of photons and of neutrons, has provided penetrating insight into the implications of modern physics for our understanding of the physical world. He is perhaps best known for the Clauser-Horne-Shimony-Holt (CHSH) inequality. This collection includes an oral history of Michael Horne's contributions to the foundations of physics and his connections to other eminent figures in the history of the subject, among them Clifford Shull and Abner Shimony.

This book presents the fundamentals of stochastic thermodynamics, one of the most central subjects in non-equilibrium statistical mechanics. It also explores many recent advances, e.g., in information thermodynamics, the thermodynamic uncertainty relation, and the trade-off relation between efficiency and power.The content is divided into three main parts, the first of which introduces readers to fundamental topics in stochastic thermodynamics, e.g., the basics of stochastic processes, the fluctuation theorem and its variants, information thermodynamics, and large deviation theory. In turn, parts two and three explore advanced topics such as autonomous engines (engines not controlled externally) and finite speed engines, while also explaining the key concepts from recent stochastic thermodynamics theory that are involved.To fully benefit from the book, readers only need an undergraduate-level background in statistical mechanics and quantum mechanics; no backgroundin information theory or stochastic processes is needed. Accordingly, the book offers a valuable resource for early graduate or higher-level readers who are unfamiliar with this subject but want to keep up with the cutting-edge research in this field. In addition, the author¿s vivid descriptions interspersed throughout the book will help readers grasp ¿living¿ research developments and begin their own research in this field.

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, physicist and astronomer (1564-1642) This book is a second edition of "e;Classical Electromagnetic Theory"e; which derived from a set of lecture notes compiled over a number of years of teaching elect- magnetic theory to fourth year physics and electrical engineering students. These students had a previous exposure to electricity and magnetism, and the material from the ?rst four and a half chapters was presented as a review. I believe that the book makes a reasonable transition between the many excellent elementary books such as Gri?th's Introduction to Electrodynamics and the obviously graduate level books such as Jackson's Classical Electrodynamics or Landau and Lifshitz' Elect- dynamics of Continuous Media. If the students have had a previous exposure to Electromagnetictheory, allthematerialcanbereasonablycoveredintwosemesters. Neophytes should probable spend a semester on the ?rst four or ?ve chapters as well as, depending on their mathematical background, the Appendices B to F. For a shorter or more elementary course, the material on spherical waves, waveguides, and waves in anisotropic media may be omitted without loss of continuity.

This monograph is planned to provide the application of the soliton theory to solve certain practical problems selected from the fields of solid mechanics, fluid mechanics and biomechanics. The work is based mainly on the authors' research carried out at their home institutes, and on some specified, significant results existing in the published literature. The methodology to study a given evolution equation is to seek the waves of permanent form, to test whether it possesses any symmetry properties, and whether it is stable and solitonic in nature. Students of physics, applied mathematics, and engineering are usually exposed to various branches of nonlinear mechanics, especially to the soliton theory. The soliton is regarded as an entity, a quasi-particle, which conserves its character and interacts with the surroundings and other solitons as a particle. It is related to a strange phenomenon, which consists in the propagation of certain waves without attenuation in dissipative media. This phenomenon has been known for about 200 years (it was described, for example, by the Joule Verne's novel Les histoires de Jean Marie Cabidoulin, Ed. Hetzel), but its detailed quantitative description became possible only in the last 30 years due to the exceptional development of computers. The discovery of the physical soliton is attributed to John Scott Russell. In 1834, Russell was observing a boat being drawn along a narrow channel by a pair of horses.

From a historical point of view, the theory we submit to the present study has its origins in the famous dissertation of P. Finsler from 1918 ([Fi]). In a the classical notion also conventional classification, Finsler geometry has besides a number of generalizations, which use the same work technique and which can be considered self-geometries: Lagrange and Hamilton spaces. Finsler geometry had a period of incubation long enough, so that few math- ematicians (E. Cartan, L. Berwald, S.S. Chem, H. Rund) had the patience to penetrate into a universe of tensors, which made them compare it to a jungle. To aU of us, who study nowadays Finsler geometry, it is obvious that the qualitative leap was made in the 1970's by the crystallization of the nonlinear connection notion (a notion which is almost as old as Finsler space, [SZ4]) and by work-skills into its adapted frame fields. The results obtained by M. Matsumoto (coUected later, in 1986, in a monograph, [Ma3]) aroused interest not only in Japan, but also in other countries such as Romania, Hungary, Canada and the USA, where schools of Finsler geometry are founded and are presently widely recognized.

Old and new problems of the foundations of quantum mechanics are viewed from the new perspective provided by a generalization of the mathematical formalism encompassing positive operator-valued measures. One objective is to demonstrate the crucial role the generalized formalism plays in fundamental issues as well as in practical applications, and to contribute to the development of the operational approach. A second objective is the development of an empiricist interpretation of this approach, duly taking into account the role played by the measuring instrument in quantum mechanical measurements. Copenhagen and anti-Copenhagen interpretations are critically assessed, and found to be wanting due to insufficiently taking into account the measurement interaction. The Einstein-Podolsky-Rosen problem and the problem of the Bell inequalities are discussed, starting from this new perspective. An explanation of violation of the Bell inequalities is developed, providing an alternative to the usual explanation on the basis of non-locality. This treatise is based on lecture notes of an advanced course on the foundations of quantum mechanics.

Despite a long history of almost 180 years stretching back to the times of Carnot and, later, Clausius and Lord Kelvin, amongst others following him, the subject of thermodynamics has not as yet seen its full maturity, in the sense that the theory of irreversible processes has remained incomplete. The works of L. Onsager, J. Meixner, I. Prigogine on the thermodyn- ics of linear irreversible processes are, in effect, the early efforts toward the desired goal of giving an adequate description of irreversible processes, but their theory is confined to near-equilibrium phenomena. The works in recent years by various research workers on the extension of the aforem- tioned thermodynamic theory of linear irreversible processes are further efforts toward the goal mentioned. The present work is another of such efforts and a contribution to the subject of generalizing the thermodyn- ics of reversible processes, namely, equilibrium thermodynamics, to that of irreversible processes-non-equilibrium thermodynamics, without being restricted to linear irreversible processes. In this context the terms 'far - moved from equilibrium' is often used in the literature, and such states of macroscopic systems and non-linear irreversible phenomena in them are the objects of interest in this work. The thermodynamics of processes, either reversible or irreversible, is a continuum mechanical theory of matter and energy and their exchange between different parts of the system, and as such it makes no direct r- erence to the molecules constituting the substance under consideration.

Flux quantization experiments indicate that the carriers, Cooper pairs (pairons), in the supercurrent have charge magnitude 2e, and that they move independently. Josephson interference in a Superconducting Quantum Int- ference Device (SQUID) shows that the centers of masses (CM) of pairons move as bosons with a linear dispersion relation. Based on this evidence we develop a theory of superconductivity in conventional and mate- als from a unified point of view. Following Bardeen, Cooper and Schrieffer (BCS) we regard the phonon exchange attraction as the cause of superc- ductivity. For cuprate superconductors, however, we take account of both optical- and acoustic-phonon exchange. BCS started with a Hamiltonian containing "e;electron"e; and "e;hole"e; kinetic energies and a pairing interaction with the phonon variables eliminated. These "e;electrons"e; and "e;holes"e; were introduced formally in terms of a free-electron model, which we consider unsatisfactory. We define "e;electrons"e; and "e;holes"e; in terms of the cur- tures of the Fermi surface. "e;Electrons"e; (1) and "e;holes"e; (2) are different and so they are assigned with different effective masses: Blatt, Schafroth and Butler proposed to explain superconductivity in terms of a Bose-Einstein Condensation (BEC) of electron pairs, each having mass M and a size. The system of free massive bosons, having a quadratic dispersion relation: and moving in three dimensions (3D) undergoes a BEC transition at where is the pair density.

The problem of irreversibility is ubiquitous in physics and chemistry. The present book attempts to present a unified theoretical and conceptual framework for the description of various irreversible phenomena in quantum mechanics. In a sense, this book supplements conventional textbooks on quantum mechanics by including the theory of irreversibilities. However, the content and style of this book are more appropriate for a monograph than a textbook. We have tried to arrange the material so that, as far as possible, the reader need not continually refer elsewhere. The references to the literature make no pretense of completeness. The book is by no means a survey of present theoretical work. We have tried to highlight the basic principles and their results, while the attention has been mainly paid to the problems in which the author himself has been involved. The book as a whole is designed for the reader with knowledge of theoretical physics (especially quantum mechanics) at university level. This book is based on the courses of lectures given at the Chemistry Department of Tel-Aviv University.