REFLECTIONS ON SPACETIME - FOUNDATIONS, PHILOSOPHY AND HISTORY During the academic year 1992/93, an interdisciplinary research group constituted itself at the Zentrum fUr interdisziplinare Forschung (ZiF) in Bielefeld, Germany, under the title 'Semantical Aspects of Spacetime Theories', in which philosophers and physicists worked on topics in the interpretation and history of relativity theory. The present issue consists of contributions resulting from material presented and discussed in the group during the course of that year. The scope of the papers ranges from rather specialised issues arising from general relativity such as the problem of referential indeterminacy, to foundational questions regarding spacetime in the work of Carnap, Weyl and Hilbert. It is well known that the General Theory of Relativity (GTR) admits spacetime models which are 'exotic' in the sense that observers could travel into their own past. This poses a number of problems for the physical interpretation of GTR which are also relevant in the philosophy of spacetime. It is not enough to exclude these exotic models simply by stating that we live in a non-exotic universe, because it might be possible to "operate time machines" by actively changing the topology of the future part of spacetime. In his contribution, Earman first reviews the attempts of physicists to prove "chronology protection theorems" (CPTs) which exclude the operation of time machines under reasonable assumptions.

This contributed volume explores the renaissance of general relativity after World War II, when it transformed from a marginal theory into a cornerstone of modern physics. Chapters explore key historical processes related to the theory of general relativity, in addition to presenting a thorough treatment of the relevant science behind these episodes. A broad historiographical framework is introduced first, thus providing the broad context in which the given computational approaches and case studies occurred. Written by an international and interdisciplinary group of expert authors, these chapters will bring readers to a more complete understanding of Einstein's theory. Specific topics include: Social and citation networks The Fock-Infeld dispute Wheeler's turn to gravitation theory The position of general relativity in theories of fundamental interactions The pursuit of a quantum theory of gravity The emergence of dark matter in relation to cosmological models Institutional frameworks for gravitational wave search in Europe The Renaissance of General Relativity in Context is ideal for historians, philosophers, and sociologists of science. Students and researchers in physics will also be interested in the topics explored.

This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity.
First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory.
The goal of this book is to provide the reader with a sound conceptual understanding of both the special and general theories of relativity, and gain an insight into how the mathematics of the theory can be utilized to calculate relativistic effects.

These documents do nothing less than bear witness to one of the most dramatic changes in the foundations of science. The book has three sections that cover general relativity, epistemological issues, and quantum mechanics. This fascinating work will be a vital text for historians and philosophers of physics, as well as researchers in related physical theories.

This book serves as a textbook for senior undergraduate students who are learning the subject of general relativity and gravitational waves for the first time. Both authors have been teaching the course in various forms for a few decades and have designed the book as a one stop book at basic level including derivations and exercises. A spectacular prediction of general relativity is gravitational waves. Gravitational waves were first detected by the LIGO detectors in 2015, hundred years after their prediction. Both authors are part of the LIGO Science Collaboration and were authors on the discovery paper. Therefore, a strong motivation for this book is to provide the essential concepts of general relativity theory and gravitational waves with their modern applications to students and to researchers who are new to the multi-disciplinary field of gravitational wave astronomy. One of the advanced topics covered in this book is the fundamentals of gravitational wave data analysis, filling a gap in textbooks on general relativity. The topic blends smoothly with other chapters in the book not only because of the common area of research, but it uses similar differential geometric and algebraic tools that are used in general relativity.

This textbook provides an introduction to gravitational lensing, which has become an invaluable tool in modern astrophysics, with applications that range from finding planets orbiting distant stars to understanding how dark matter and dark energy conspired to form the cosmic structures we see today. Principles of Gravitational Lensing begins with Einstein's prediction that gravity bends light, and shows how that fundamental idea has spawned a rich field of study over the past century. The gravitational deflection of light was first detected by Eddington during a solar eclipse in May 1919, launching Einstein and his theory of relativity into public view. Yet the possibility of using the phenomenon to unlock mysteries of the Universe seemed remote, given the technology of the day. Theoretical work was carried out sporadically over the next six decades, but only with the discovery of the system Q0957+561 in 1979 was gravitational lensing transformed from a curiosity of general relativity into a practical observational tool. This book describes how the three subfields known as strong lensing, weak lensing, and microlensing have grown independently but become increasingly intertwined. Drawing on their research experience, Congdon and Keeton begin with the basic physics of light bending, then present the mathematical foundations of gravitational lensing, building up to current research topics in a clear and systematic way. Relevant background material from physics and mathematics is included, making the book self-contained. The derivations and explanations are supplemented by exercises designed to help students master the theoretical concepts as well as the methods that drive current research. An extensive bibliography guides those wishing to delve more deeply into particular areas of interest. Principles of Gravitational Lensing is ideal for advanced students and seasoned researchers looking to penetrate this thriving subject and even contribute research of their own.

The Golden Oldies series of the journal General Relativity and Gravitation reprints important papers in general relativity theory that were published 30 or more years ago and are either hard to get hold of, or were originally printed in a language other than English. They play a key part in making these important papers readily accessible today, in the language that has now become the lingua franca of scientific publication. The value of this reprinting is enhanced by an accompanying editorial note for each paper, which briefly explains the significance of the work and where it has subsequently led to, together with a biographical note about the author or authors. This volume presents a selection of 14 rarities among the Golden Oldies grouped in the three categories "Basic results in differential geometry and general relativity," "Discussion of physical effects" and "Basic exact solutions and their interpretation." Researchers in the field will appreciate having these important papers collected in one book for the first time. Reprinted from the journal General Relativity and Gravitation.

The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

Special and General Relativity are concisely developed together with essential aspects of nuclear and particle physics. Problem sets are provided for many chapters, making the book ideal for a course on the physics of white dwarf and neutron star interiors. Norman K. Glendenning is Senior Scientist Emeritus at the Nuclear Science Division, Institute for Nuclear and Particle Astrophysics, Lawrence Berkeley National Laboratory at the University of California, Berkeley. He is the author of numerous books.

'Everything you wanted to know about physics but were afraid to ask' Priyamvada Natarajan, author of Mapping the Heavens __________________________ When leading theoretical physicist Professor Michael Dine was asked where you could find an accessible book that would teach you about the Big Bang, Dark Matter, the Higgs boson and the cutting edge of physics now, he had nothing he could recommend. So he wrote it himself. In This Way to the Universe, Dine takes us on a fascinating tour through the history of modern physics - from Newtonian mechanics to quantum, from particle to nuclear physics - delving into the wonders of our universe at its largest, smallest, and within our daily lives. If you are looking for the one book to help you understand physics, written in language anyone can follow, this is it. __________________________ 'An extraordinary journey into what we know, what we hope to know, and what we don't know, about the universe and the laws that govern it' Leonard Susskind, author of The Theoretical Minimum series 'This book is a rare event . . . presented by someone who is a true master' Sean Carroll, author of From Eternity to Here 'Dine's enthusiastic storytelling makes the read worth it for those who want to finally wrap their mind around string theory or the Higgs boson' Tess Joosse, Scientific American

Thermal noise from optical coatings is a growing area of concern and overcoming limits to the sensitivity of high precision measurements by thermal noise is one of the greatest challenges faced by experimental physicists. In this timely book, internationally renowned scientists and engineers examine our current theoretical and experimental understanding. Beginning with the theory of thermal noise in mirrors and substrates, subsequent chapters discuss the technology of depositing coatings and state-of-the-art dielectric coating techniques used in precision measurement. Applications and remedies for noise reduction are also covered. Individual chapters are dedicated to specific fields where coating thermal noise is a particular concern, including the areas of quantum optics/optomechanics, gravitational wave detection, precision timing, high-precision laser stabilisation via optical cavities and cavity quantum electrodynamics. While providing full mathematical detail, the text avoids field-specific jargon, making it a valuable resource for readers with varied backgrounds in modern optics.

This book is an elaboration of lecture notes for the graduate course on General Rela tivity given by the author at Boston University in the spring semester of 1972. It is an introduction to the subject only, as the time available for the course was limited. The author of an introduction to General Relativity is faced from the beginning with the difficult task of choosing which material to include. A general criterion as sisting in this choice is provided by the didactic character of the book: Those chapters have to be included in priority, which will be most useful to the reader in enabling him to understand the methods used in General Relativity, the results obtained so far and possibly the problems still to be solved. This criterion is not sufficient to ensure a unique choice. General Relativity has developed to such a degree, that it is impossible to include in an introductory textbook of a reasonable length even a very condensed treatment of all important problems which have been discussed until now and the author is obliged to decide, in a more or less subjective manner, which of the more recent developments to omit. The following lines indicate by means of some examples the kind of choice made in this book."

Our esteemed colleague C. V. Vishveshwara, popularly known as Vishu, turned sixty on 6th March 1998. His colleagues and well wishers felt that it would be appropriate to celebrate the occasion by bringing out a volume in his honour. Those of us who have had the good fortune to know Vishu, know that he is unique, in a class by himself. Having been given the privilege to be the volume's editors, we felt that we should attempt something different in this endeavour. Vishu is one of the well known relativists from India whose pioneer ing contributions to the studies of black holes is universally recognised. He was a student of Charles Misner. His Ph. D. thesis on the stability of the Schwarzschild black hole, coordinate invariant characterisation of the sta tionary limit and event horizon for Kerr black holes and subsequent seminal work on quasi-normal modes of black holes have passed on to become the starting points for detailed mathematical investigations on the nature of black holes. He later worked on other aspects related to black holes and compact objects. Many of these topics have matured over the last thirty years. New facets have also developed and become current areas of vigorous research interest. No longer are black holes, ultracompact objects or event horizons mere idealisations of mathematical physicists but concrete entities that astrophysicists detect, measure and look for. Astrophysical evidence is mounting up steadily for black holes."

This book evolved out of some one hundred lectures given by twenty experts at a special instructional conference sponsored by the University Grants Commis sion, India. It is pedagogical in style and self-contained in several interrelated areas of physics which have become extremely important in present-day theoretical research. The articles begin with an introduction to general relativity and cosmology as well as particle physics and quantum field theory. This is followed by reviews of the standard gauge models of high-energy physics, renormalization group and grand unified theories. The concluding parts of the book comprise discussions in current research topics such as problems of the early universe, quantum cosmology and the new directions towards a unification of gravitation with other forces. In addition, special concise treatments of mathematical topics of direct relevance are also included. The content of the book was carefully worked out for the mutual education of students and research workers in general relativity and particle physics. This ambitious programe consequently necessitated the involvement of a number of different authors. However, care has been taken to ensure that the material meshes into a unified, cogent and readable book. We hope that the book will serve to initiate and guide a student in these different areas of investigation starting from first principles and leading to the exciting current research problems of an interdisciplinary nature in the context of the origin and structure of the universe."

From the international bestselling author of Physics of the Impossible and Physics of the Future.

This is the story of a quest: to find a Theory of Everything. Einstein dedicated his life to seeking this elusive Holy Grail, a single, revolutionary 'god equation' which would tie all the forces in the universe together, yet never found it. Some of the greatest minds in physics took up the search, from Stephen Hawking to Brian Greene. None have yet succeeded.

In The God Equation, renowned theoretical physicist Michio Kaku takes the reader on a mind-bending ride through the twists and turns of this epic journey: a mystery that has fascinated him for most of his life. He guides us through the key debates in modern physics, from Newton's law of gravity via relativity and quantum mechanics to the latest developments in string theory. It is a tale of dazzling breakthroughs and crushing dead ends, illuminated by Kaku's clarity, storytelling flair and infectious enthusiasm.

The object of the quest is now within sight: we are closer than ever to achieving the most ambitious undertaking in the history of science. If successful, the Theory of Everything could simultaneously unlock the deepest mysteries of space and time, and fulfil that most ancient and basic of human desires - to understand the meaning of our lives.

This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. The premise of analogy as a study strategy is to make the unfamiliar familiar. Accordingly, this book introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors. Gyrovectors turn out to be equivalence classes that add according to the gyroparallelogram law just as vectors are equivalence classes that add according to the parallelogram law. In the gyrolanguage of this book, accordingly, one prefixes a gyro to a classical term to mean the analogous term in hyperbolic geometry. As an example, the relativistic gyrotrigonometry of Einstein's special relativity is developed and employed to the study of the stellar aberration phenomenon in astronomy.Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0. It turns out that the invariant mass of the relativistic center of mass of an expanding system (like galaxies) exceeds the sum of the masses of its constituent particles. This excess of mass suggests a viable mechanism for the formation of dark matter in the universe, which has not been detected but is needed to gravitationally 'glue' each galaxy in the universe. The discovery of the relativistic center of mass in this book thus demonstrates once again the usefulness of the study of Einstein's special theory of relativity in terms of its underlying hyperbolic geometry.

In this thesis we discuss the construction of an effective field theory (EFT) for non-relativistic Majorana fermions, show how to use it to calculate observables in a thermal medium, and derive the effects of these thermal particles on the CP asymmetry. The methods described in this thesis allow a systematic and effective description of the non-relativistic dynamics of a heavy Majorana fermion at finite temperature. The CP asymmetry is studied for hierarchical and nearly degenerate heavy-neutrino masses and the analysis includes the treatment of lepton-flavor effects. Heavy Majorana neutrinos are involved in many scenarios of physics beyond the standard model and, in the leptogenesis framework, they are at the root of the baryon asymmetry in the Universe. Besides simplifying exist in g results, the EFT approach provides useful tools for addressing even more involved observables. Indeed, taken together, the approach and the material presented here represent an important step toward a systematic improvement of our knowledge of the CP asymmetry in heavy-neutrino decays at finite temperature.

This volume presents a selection of articles based on inspiring lectures held at the "Capri" Advanced Summer School, an original event conceived and promoted by Leonida Antonio Gizzi and Ralph Assmann that focuses on novel schemes for plasma-based particle acceleration and radiation sources, and which brings together researchers from the conventional accelerator community and from the high-intensity laser-matter interaction research fields. Training in these fields is highly relevant for ultra-intense lasers and applications, which have enjoyed dramatic growth following the development of major European infrastructures like the Extreme Light Infrastructure (ELI) and the EuPRAXIA project. The articles preserve the tutorial character of the lectures and reflect the latest advances in their respective fields. The volume is mainly intended for PhD students and young researchers getting started in this area, but also for scientists from other fields who are interested in the latest developments. The content will also appeal to radiobiologists and medical physicists, as it includes contributions on potential applications of laser-based particle accelerators.

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. General relativity generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations. Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes-regions of space in which space and time are distorted in such a way that nothing, not even light, can escape-as an end-state for massive stars. There is evidence that such stellar black holes as well as more massive varieties of black hole are responsible for the intense radiation emitted by certain types of astronomical objects such as active galactic nuclei or microquasars.

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 the precession 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.

Measuring the masses of galaxies as a function of redshift is perhaps one of the most challenging open issues in current astronomical research. The evolution of the baryonic and dark matter components of galaxies is not only a critical test of the hierarchical formation paradigm, but ultimately also provides new clues on the complex interplay between star formation, the cooling and heating of gas and galaxy merging processes.This book reviews current techniques to measure the baryonic (stellar) and dark masses of nearby galaxies, and focusses on ongoing attempts to measure these same quantities in galaxies at higher and higher redshifts. It also gives room to future perspectives, with special emphasis on new survey projects and satellite missions.

By his theory of relativity, Albert Einstein has provoked a revolution of thought in physical science. The aim of this book is to give an account of Einstein's work without introducing anything very technical in the way of mathematics, physics, or philosophy.

The Mathematical Principles of Scale Relativity Physics: The Concept of Interpretation explores and builds upon the principles of Laurent Nottale's scale relativity. The authors address a variety of problems encountered by researchers studying the dynamics of physical systems. It explores Madelung fluid from a wave mechanics point of view, showing that confinement and asymptotic freedom are the fundamental laws of modern natural philosophy. It then probes Nottale's scale transition description, offering a sound mathematical principle based on continuous group theory. The book provides a comprehensive overview of the matter to the reader via a generalization of relativity, a theory of colors, and classical electrodynamics. Key Features: Develops the concept of scale relativity interpreted according to its initial definition enticed by the birth of wave and quantum mechanics Provides the fundamental equations necessary for interpretation of matter, describing the ensembles of free particles according to the concepts of confinement and asymptotic freedom Establishes a natural connection between the Newtonian forces and the Planck's law from the point of view of space and time scale transition: both are expressions of invariance to scale transition The work will be of great interest to graduate students, doctoral candidates, and academic researchers working in mathematics and physics.