As we navigate through life we instinctively model time as having a flowing present that divides a fixed past from open future. This model develops in childhood and is deeply saturated within our language, thought and behavior, affecting our conceptions of the universe, freedom and the self. Yet as central as it is to our lives, physics seems to have no room for this flowing present. What Makes Time Special? demonstrates this claim in detail and then turns to two novel positive tasks. First, by looking at the world "sideways" - in the spatial directions - it shows that physics is not "spatializing time" as is commonly alleged. Even relativity theory makes significant distinctions between the spacelike and timelike directions, often with surprising consequences. Second, if the flowing present is an illusion, it is a deep one worthy of explanation. The author develops a picture whereby the temporal flow arises as an interaction effect between an observer and the physics of the world. Using insights from philosophy, cognitive science, biology, psychology and physics, the theory claims that the flowing present model of time is the natural reaction to the perceptual and evolutionary challenges thrown at us. Modeling time as flowing makes sense even if it misrepresents it.

Covariant Physics: From Classical Mechanics to General Relativity and Beyond endeavours to provide undergraduate students as well as self-learners with training in the fundamentals of the modern theories of spacetime, most notably the general theory of relativity as well as physics in curved spacetime backgrounds in general. This text does so with the barest of mathematical preparation. In fact, very little beyond multivariable calculus and a bit of linear algebra is assumed. Throughout this textbook, the main theme tying the various topics is the so-called principle of covariance - a fundamental symmetry of physics that one rarely encounters in undergraduate texts. The material is introduced very gradually, starting with the simplest of high school mathematics, and moving through the more intense notions of tensor calculus, geometry, and differential forms with ease. Familiar notions from classical mechanics and electrodynamics are used to increase familiarity with the advanced mathematical ideas, and to emphasize the unity of all of physics under the single principle of covariance. The mathematical and physical techniques developed in this book should allow students to perform research in various fields of theoretical physics as early as their sophomore year in college. The language the reader will learn in this book is the foundational mathematical language of many modern branches of physics, and as such should allow them to read and generally understand many modern physics papers.

Einstein's general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook. Topics include special relativity, in the formalism of Minkowski's four-dimensional space-time, the principle of equivalence, Riemannian geometry and tensor analysis, Einstein field equation, as well as many modern cosmological subjects, from primordial inflation and cosmic microwave anisotropy to the dark energy that propels an accelerating universe.
The author presents the subject with an emphasis on physical examples and simple applications without the full tensor apparatus. The reader first learns how to describe curved spacetime. At this mathematically more accessible level, the reader can already study the many interesting phenomena such as gravitational lensing, precession of Mercury's perihelion, black holes, and cosmology. The full tensor formulation is presented later, when the Einstein equation is solved for a few symmetric cases. Many modern topics in cosmology are discussed in this book: from inflation, cosmic microwave anisotropy to the "dark energy" that propels an accelerating universe.
Mathematical accessibility, together with the various pedagogical devices (e.g., worked-out solutions of chapter-end problems), make it practical for interested readers to use the book to study general relativity and cosmology on their own.

Ryan Wasserman explores a range of fascinating questions raised by the possibility of time travel. This volume explores a wide-range of puzzles such as the grandfather paradox, the bootstrapping paradox, and the twin paradox of special relativity. Ryan Wasserman draws out their implications for our understanding of time, tense, freedom, fatalism, causation, counterfactuals, laws of nature, persistence, change, and mereology. Paradoxes of Time Travel is written in an accessible style, and filled with entertaining examples from physics, science fiction, and popular culture.

A quirky, funny, and accessible blend of science and art that delves into the heart of Einstein’s theory of relativity

It was a link to Albert Einstein’s 1905 paper―an early attempt at explaining his revolutionary ideas on space, time, and matter―that drew Tanya Bub into his imaginative vision of the world. What particularly struck her was how Einstein interwove words and math to create clear visuals illustrating his theories. As an artist, she naturally started doodling as she worked her way through his concepts, creating drawings that intuitively demonstrated Einstein’s core principles.

In Reimagining Time, Tanya Bub teams up with her father, the distinguished physicist Jeffrey Bub, to create a quirky and accessible take on one of science’s most revolutionary discoveries. Blending original art and text, they guide readers―even nonmathematicians―through Einstein’s theory of special relativity to reveal truths about our universe: time is relative, lengths get shorter with motion, energy and mass are interchangeable, and the universe has a speed limit.

During the last years of his life Einstein tried unsuccessfully to unify electromagnetic force with gravitational force geometrically. The nearest he got was through the ideas of Kaluza and Klein who appended a tiny fifth commuting coordinate to spacetime. Researchers have followed in those footsteps by adding at least six more such minuscule coordinates so as to incorporate the other forces of nature, culminating in string theory - which has unfortunately not met with experimental support. Other proposals have likewise failed or are still waiting to be confirmed experimentally.The author shows that one can successfully unify gravity with electromagnetism geometrically by adding a single complex anticommuting coordinate to spacetime, which can be associated with the property of 'electricity'. By adding extra four anticommuting properties ('chromicity' and 'neutrinicity'), associated with strong and weak interactions, one can get a unified picture of all the natural forces and particles including the 'standard model': The whole construct relies upon the full specification of events and automatically allows for replication of particle families. The monograph traces the history of attempts of unification before explaining the author's 'where-when-what' scheme.

This unique textbook provides an accessible introduction to Einstein's general theory of relativity, a subject of breathtaking beauty and supreme importance in physics. With his trademark blend of wit and incisiveness, A. Zee guides readers from the fundamentals of Newtonian mechanics to the most exciting frontiers of research today, including de Sitter and anti-de Sitter spacetimes, Kaluza-Klein theory, and brane worlds. Unlike other books on Einstein gravity, this book emphasizes the action principle and group theory as guides in constructing physical theories. Zee treats various topics in a spiral style that is easy on beginners, and includes anecdotes from the history of physics that will appeal to students and experts alike. He takes a friendly approach to the required mathematics, yet does not shy away from more advanced mathematical topics such as differential forms. The extensive discussion of black holes includes rotating and extremal black holes and Hawking radiation. The ideal textbook for undergraduate and graduate students, Einstein Gravity in a Nutshell also provides an essential resource for professional physicists and is accessible to anyone familiar with classical mechanics and electromagnetism. It features numerous exercises as well as detailed appendices covering a multitude of topics not readily found elsewhere. * Provides an accessible introduction to Einstein's general theory of relativity * Guides readers from Newtonian mechanics to the frontiers of modern research * Emphasizes symmetry and the Einstein-Hilbert action * Covers topics not found in standard textbooks on Einstein gravity * Includes interesting historical asides * Features numerous exercises and detailed appendices * Ideal for students, physicists, and scientifically minded lay readers * Solutions manual (available only to teachers)

A new title in the Manchester Physics Series, this introductory text emphasises physical principles behind classical mechanics and relativity. It assumes little in the way of prior knowledge, introducing relevant mathematics and carefully developing it within a physics context. Designed to provide a logical development of the subject, the book is divided into four sections, introductory material on dynamics, and special relativity, which is then followed by more advanced coverage of dynamics and special relativity. Each chapter includes problems ranging in difficulty from simple to challenging with solutions for solving problems. Includes solutions for solving problems Numerous worked examples included throughout the book Mathematics is carefully explained and developed within a physics environment Sensitive to topics that can appear daunting or confusing

"Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."--S. Chandrasekhar
"A "tour de force" lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."--L. P. Hughston, "Times Higher Education Supplement"
"Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."--James W. York, "Physics Today"

Cosmic Origins tells the story of how physicists and astronomers have struggled for more than a century to understand the beginnings of our universe, from its origins in the Big Bang to the modern day. The book will introduce the science as a narrative, by telling the story of the scientists who made each major discovery. It will also address and explain aspects of our theories that some cosmologists are still hesitant to accept, as well as gaps in our knowledge and even apparent inconsistencies in our measurements. Clearly written by a master of scientific exposition, this book will fascinate the curious general reader as well as providing essential background reading for college-level courses on physics and astronomy.

Keeping in mind that we can only see the universe from the comfort of our home galaxy, Bascom begins his text by meticulously laying the necessary groundwork to understand the Big Bang's mathematics without using any equations. He then paints a freeze-frame picture of our universe as if we had taken a three-dimensional picture with a giant camera. Within this picture, he traces forces beginning with the smallest (a single atom) to the biggest (the cosmos), keeping in mind that in this frozen moment everything further away from the observer spatially is also further away from the observer in time; that is, older. Soon a very real and very vivid image of the Big Bang appears (especially in things that are loud or hot), echoing down through time and into our everyday lives, reflected in every atom during every measurement. Then, slowly but deliberately, Bascom unfreezes this picture, ratcheting each moment from one to the next, showing us how and why quantum particles are constantly in contact with the Big Bang and why that allows the particles to pop in and out of existence from moment to moment, what a photon is, and what exactly we mean when we say that free space has energy. Whether you're interested in the Big Bang, the weirdness of quantum mechanics, or simply enjoy thinking about the biggest, loudest, and oldest things in our universe, this book will help you question your deepest notions about time and space, while staying firmly rooted in empirical observation. Throughout the text, Bascom sidesteps traditional non-fiction modes, using colorful explanations and vivid imagery to place the reader in simultaneous contact with both the Big Bang and fundamental particles. As a result, Bascom provides the tools and language necessary to contemplate the strangeness of our universe.

Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself.

These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large.

Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.

These conditions are shown to be satisfied in the vicinity of stars of more than twice the solar mass near the endpoint of their nuclear evolution, and in a time-reversed sense for the universe as a whole. In the first case, the singularity in our past. A discussion of the Cauchy problem for General Relativity is also included in the book.

Time magazine's "Man of the Century", Albert Einstein is the founder of modern physics and his theory of relativity is the most important scientific idea of the modern era. In this short book, Einstein explains, using the minimum of mathematical terms, the basic ideas and principles of the theory that has shaped the world we live in today. Unsurpassed by any subsequent books on relativity, this remains the most popular and useful exposition of Einstein's immense contribution to human knowledge. With a new foreword by Derek Raine.

The successes of the standard models of particle physics and cosmology are many, but have proven incapable of explaining all the phenomena that we observe. This book investigates the potentially important role of quantum physics, particularly quantum anomalies, in various aspects of modern cosmology, such as inflation, the dynamical generation of the visible and dark matter in the universe, and gravitational waves. By doing so, the authors demonstrate that exploring the links between cosmology and particle physics is key to helping solve the mysteries of our Universe.

This book consists of contributions from the participants of the Abel Symposium 2019 held in Alesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity. The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.

CHOICE Highly Recommended Title, August 2019 Expertly guided by renowned cosmologist Dr. David Lyth, learn about the pioneering scientists whose work provided the foundation for Einstein's formulation of his theories of relativity, and about Einstein's groundbreaking life and work as well. This highly readable and accessible panorama of the field delicately balances history and science as it takes the reader on an adventure through the centuries. Without complex mathematics or scientific formulae, this book will be of interest to all, even those without a scientific background, who are intrigued to find out more about what paved the way for one of our most famous physicists to push the boundaries of physics to new lengths. Features: Written by an internationally renowned physicist and cosmologist Describes the life and times of Einstein and his important predecessors Focuses on one of the most famous areas of science, Einstein's Relativity Theory

Ross P. Cameron argues that the flow of time is a genuine feature of reality. He suggests that the best version of the A-Theory is a version of the Moving Spotlight view, according to which past and future beings are real, but there is nonetheless an objectively privileged present. Cameron argues that the Moving Spotlight theory should be viewed as having more in common with Presentism (the view that reality is limited to the present) than with the B-Theory (the view that time is just another dimension like space through which things are spread out). The Moving Spotlight view, on this picture, agrees with Presentism that everything is the way it is now, it simply thinks that non-present beings are amongst the things that are now some way. Cameron argues that the Moving Spotlight theory provides the best account of truthmakers for claims about what was or will be the case, and he defends the view against a number of objections, including McTaggart's argument that the A-Theory is inconsistent, and the charge that if the A-Theory is true but presentism false then we could not know that we are present. The Moving Spotlight defends an account of the open future-that what will happen is, as yet, undetermined-Land argues that this is a better account than that available to the Growing Block theory.

Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solution of the equations, and over to the applications in modern physics and astrophysics. Numerous figures, diagrams, and a variety of exercises aid the material in the book. The most obvious applications of this work range from astrophysics (black holes, neutron stars, gamma-ray bursts, and active galaxies) to cosmology (early-universe hydrodynamics and phase transitions) and particle physics (heavy-ion collisions). It is often said that fluids are either seen as solutions of partial differential equations or as "wet". Fluids in this book are definitely wet, but the mathematical beauty of differential equations is not washed out.

This brief approaches General Relativity from a planetary navigation perspective, delving into the unconventional mathematical methods required to produce computer software for space missions. It provides a derivation of the Einstein field equations and describes experiments performed on the Near Earth Asteroid Rendezvous mission, spanning General Relativity Theory from the fundamental assumptions to experimental verification. The software used for planetary missions is derived from mathematics that use matrix notation. An alternative is to use Einstein summation notation, which enables the mathematics to be presented in a compact form but makes the geometry difficult to understand. In this book, the relationship of matrix notation to summation notation is shown. The purpose is to enable the reader to derive the mathematics used in the software in either matrix notation or summation notation. This brief is a useful tool for advanced students and young professionals embarking on careers in planetary navigation.

The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more "utilitarian" treatments of the subject. The book is divided into four parts, entitled respectively "Origins", "Dynamics", "Symmetries", and "Scales". The emphasis is conceptual - the aim is to build the theory up systematically from some clearly stated foundational concepts - and therefore to a large extent anti-historical, but two historical Chapters ("Origins") are included to situate quantum field theory in the larger context of modern physical theories. The three remaining sections of the book follow a step by step reconstruction of this framework beginning with just a few basic assumptions: relativistic invariance, the basic principles of quantum mechanics, and the prohibition of physical action at a distance embodied in the clustering principle. The "Dynamics" section of the book lays out the basic structure of quantum field theory arising from the sequential insertion of quantum-mechanical, relativistic and locality constraints. The central role of symmetries in relativistic quantum field theories is explored in the third section of the book, while in the final section, entitled "Scales", we explore in detail the feature of quantum field theories most critical for their enormous phenomenological success - the scale separation property embodied by the renormalization group properties of a theory defined by an effective local Lagrangian.

A pithy yet deep introduction to Einstein's general theory of relativity Of the four fundamental forces of nature, gravity might be the least understood and yet the one with which we are most intimate. On Gravity combines depth with accessibility to take us on a compelling tour of Einstein's general theory of relativity. A. Zee begins with the discovery of gravity waves, then explains how gravity can be understood in comparison to other classical field theories, presents the idea of curved spacetime, and explores black holes and Hawking radiation. Zee travels as far as the theory reaches, leaving us with tantalizing hints of the unknown, from the intransigence of quantum gravity to the mysteries of dark matter. Infused with Zee's signature warmth and fresh style, On Gravity opens a unique pathway to comprehending relativity, gravity, spacetime, and the workings of the universe.

Following on from a previous volume on Special Relativity, Andrew Steane's second volume on General Relativity and Cosmology is aimed at advanced undergraduate or graduate students undertaking a physics course, and encourages them to expand their knowledge of Special Relativity. Beginning with a survey of the main ideas, the textbook goes on to give the methodological foundations to enable a working understanding of astronomy and gravitational waves (linearized approximation, differential geometry, covariant differentiation, physics in curved spacetime). It covers the generic properties of horizons and black holes, including Hawking radiation, introduces the key concepts in cosmology and gives a grounding in classical field theory, including spinors and the Dirac equation, and a Lagrangian approach to General Relativity. The textbook is designed for self-study and is aimed throughout at clarity, physical insight, and simplicity, presenting explanations and derivations in full, and providing many explicit examples.

An innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum mechanics: Part I is an introduction to analytical mechanics, suitable for a graduate or advanced undergraduate course. Part II presents material designed principally for graduate students. The appendices in Part III summarize the mathematical methods used in the text. The book integrates relativity into the teaching of classical mechanics. Part II introduces special relativity and covariant mechanics. It develops extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics, including an extended definition of canonical transformation that both simplifies the theory and no longer excludes the Lorentz transformation. The book assists students who study classical mechanics as a preparation for quantum mechanics. Analytical mechanics is presented using methods - such as linear vector operators and dyadics - that familiarize the student with similar operator techniques in quantum theory and the dyadic Dirac notation. Comparisons to quantum mechanics appear throughout the text. For example, the chapter on Hamilton-Jacobi theory includes discussions of the closely related Bohm hidden variable model and Feynman path integral method. The chapter on angle-action variables concludes with a section on the old quantum theory. Several of the fundamental problems in physics - the development of quantum information technology, and the problem of quantizing the gravitational field, to name two - require a rethinking of the quantum-classical connection. Graduate students preparing for research careers will find a graduate mechanics course based on this book to be an essential bridge between their undergraduate training and advanced study in analytical mechanics, relativity, and quantum mechanics. New to the Second Edition: Part I contains new chapters on Central Force Motion (Chapter 11) and Scattering (Chapter 12), and new material on time-independent canonical transformations. Part II contains a new chapter (Chapter 22) on Angle-Action Variables. These additions allow a more flexible use of the text. Part I is now a self-contained, introductory analytical mechanics course. The instructor can then select a range of topics from Part II appropriate to the interests of more advanced students.

Ever since its discovery eighty-five years ago, quantum theory has been used to study the physical universe with great profit, both intellectual and financial. Over the last fifty years, however, we have found out more and more about the theory itself, and what it tells us about the universe. It seems we may have to accept non-locality - cause and effect may be light-years apart; loss of realism - nature may be fundamentally probabilistic; and non-determinism - it seems that God does play dice! This book, written by an expert in the field, explains the emergence of our new perspective on quantum theory, but also describes how the ideas involved in this re-evaluation led seamlessly to a totally new discipline -quantum information theory. This discipline includes quantum computation, which is able to perform tasks quite out of the range of other computers; the totally secure algorithms of quantum cryptography; and quantum teleportation - as part of science fact rather than science fiction. The book is the first to combine these elements, and will be of interest to anybody interested in fundamental aspects of science and their application to the real world.

Ross P. Cameron argues that the flow of time is a genuine feature of reality. He suggests that the best version of the A-Theory is a version of the Moving Spotlight view, according to which past and future beings are real, but there is nonetheless an objectively privileged present. Cameron argues that the Moving Spotlight theory should be viewed as having more in common with Presentism (the view that reality is limited to the present) than with the B-Theory (the view that time is just another dimension like space through which things are spread out). The Moving Spotlight view, on this picture, agrees with Presentism that everything is the way it is now, it simply thinks that non-present beings are amongst the things that are now some way. Cameron argues that the Moving Spotlight theory provides the best account of truthmakers for claims about what was or will be the case, and he defends the view against a number of objections, including McTaggart's argument that the A-Theory is inconsistent, and the charge that if the A-Theory is true but presentism false then we could not know that we are present. The Moving Spotlight defends an account of the open future-that what will happen is, as yet, undetermined-and argues that this is a better account than that available to the Growing Block theory.