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A beloved introductory physics textbook, now including exercises and an answer key, explains the concepts essential for thorough scientific understanding.

\"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) \"-- Provided by publisher.

Relativity is a set of remarkable insights into the way space and time work. The basic notion of relativity, first articulated by Galileo, explains why we do not feel Earth moving as it orbits the Sun and was successful for hundreds of years. We present thinking tools that elucidate Galilean relativity and prepare us for the more modern understanding. We then show how Galilean relativity breaks down at speeds near the speed of light, and follow Einstein’s steps in working out the unexpected relationships between space and time that we now call special relativity. These relationships give rise to time dilation, length contraction, and the twin “paradox” which we explain in detail. Throughout, we emphasize how these effects are tightly interwoven logically and graphically. Our graphical understanding leads to viewing space and time as a unified entity called spacetime whose geometry differs from that of space alone, giving rise to these remarkable effects. The same geometry gives rise to the energy?momentum relation that yields the famous equation E = mc2, which we explore in detail. We then show that this geometric model can explain gravity better than traditional models of the “force” of gravity. This gives rise to general relativity, which unites relativity and gravity in a coherent whole that spawns new insights into the dynamic nature of spacetime. We examine experimental tests and startling predictions of general relativity, from everyday applications (GPS) to exotic phenomena such as gravitomagnetism, gravitational waves, Big Bang cosmology, and especially black holes.

This book is a compilation of the lectures for a one-semester course on gravitation at the University of Rochester. Starting from a simple description of geometry, the topics are systematically developed to the big bang theory with a simple derivation of the cosmic background temperature. Several informative examples are worked out in detail as well.

This book is an introduction to Einstein's general theory of relativity, suitable for advanced undergraduate or beginning graduate courses. The content is structured so that interesting applications, such as gravitational lensing, black holes and cosmology, can be presented without the readers having to first learn the difficult mathematics of tensor calculus. The mathematical accessibility and the presentation of the book make it practical for readers to study the subject on their. own. - ;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's field equation and cosmology. The author presents the subject from the very beginning with an emphasis on physical examples and simple applications without the full tensor apparatus. One 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, as well as 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 and 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, gravitation and cosmology on their own. - ;This is a great time to have published a fresh new undergraduate text on relativity and cosmology...this is an excellent textbook which this reviewer would rate as the text of choice for a course on relativity and cosmology aimed at physics and astronomy undergraduates. American Journal of Physics, October 2005. -.

A bstract Standard textbooks will state that hydrodynamics requires near-equilibrium to be applicable. Recently, however, out-of-equilibrium attractor solutions for hydrodynamics have been found in kinetic theory and holography in systems with a high degree of symmetry, suggesting the possibility of a genuine out-of-equilibrium formulation of hydrodynamics. This work demonstrates that attractor solutions also occur in non-conformal kinetic theory and spatially non-homogeneous systems, potentially having important implications for the interpretation of experimental data in heavy-ion and proton-proton collisions and relativistic fluid dynamics as a whole.

The Paper highlights discovery from 2000 of two Errors (ERM81/87) by Michelson in analysis of his experiments ME81/87. ERM81/87 has also been addressed in series of previous articles by the authors. ERM81/87 consisted of assuming the transverse path of light ray 2 or of SW2 swimmer, to be an isosceles triangle (Error 1) inclined with angle β’ in referential frame (RF) ether/water (E/W), or a double orthogonal path (in RF device/bank (D/B)), thus calculating the wrong result, t 2 < t 1 , or Δt = t 1 -t 2 > 0, (Error 2), states SW2 wins the contest. In ERM81/87 it is proven firstly, by Demonstration 1, based on logic, starting from the non-observance in Michelson’s analysis, of rules of correctness and fair play, in development of the two swimmers contest (TSC). Rresulted in correct transversal path as a right triangle, with t 2 = t 1 (in RF, E/W), the correct contest result is a draw. Demonstration 2 consists, in correction of SW2 route, resulting under fair play conditions, for transversal path, a right triangle with hypotenuse inclined at angle 2β (in RF, E/W) and t 2 = t 1 or Δt = 0, with the contest result in a tie. Demonstration 3 is based on a new Generalised Case (GC) of the TSC where the orientation of the starting path of SW1 can be inclined at any angle α, always one obtains, t 1 = t 2 , the correct result. Evidence provided shows Michelson designed his interferometer by analogy with TSC, Michelson considered SW2 the winner. Evidence provided in 1892 by Lorenz expressed doubts about the correctness of Michelson’s analysis of ME81/87, without finding errors. We show, an initial error (ERM81) was committed by Michelson in ME81analysis, erroneously superposing paths for SW2 (in RF, D/B), and in incorrect calculations of t 2 and Δt obtaining t 2 < t 1 , an error communicated to him by Potier, which also mentioned the correct result Δt = 0, without any demonstration. In analysis of ME87, Michelson acknowledged the error, modified the path of SW2 to isosceles triangle (in RF, E/W), and made new t 2 calculation. But he reduced by only half, the Δt compared to Δt in ME81, meaning the basic error in Δt (ERM87) has persisted, until today. We emphasize that errors ERM81/87 in TSC are repeatedly printed, and appear in all college physics textbooks around the world, exemplifying by presenting four such excerpts from college textbooks from the US and Canada. Thus, a correction of ERM81/87 is required, starting with the correction of the TSC, by admitting the correct result of equality of SW1 and SW2, in all college physics textbooks. As result the ether can be reintroduced into physics with multiple consequences including re-evaluation of the Special Relativity Theory.

A bstract The theory of modular flow has proved extremely useful for applying thermodynamic reasoning to out-of-equilibrium states in quantum field theory. However, the standard proofs of the fundamental theorems of modular flow use machinery from Fourier analysis on Banach spaces, and as such are not especially transparent to an audience of physicists. In this article, I present a construction of modular flow that differs from existing treatments. The main pedagogical contribution is that I start with thermal physics via the KMS condition, and derive the modular operator as the only operator that could generate a thermal time-evolution map, rather than starting with the modular operator as the fundamental object of the theory. The main technical contribution is a new proof of the fundamental theorem stating that modular flow is a symmetry. The new proof circumvents the delicate issues of Fourier analysis that appear in previous treatments, but is still mathematically rigorous.

Because of its abstract nature, Albert Einstein's theory of general relativity is rarely present in school physics curricula. Although the educational community has started to investigate ways of bringing general relativity to classrooms, field-tested educational material is rare. Employing the model of educational reconstruction, we present a collaborative online learning environment that was introduced to final year students (18-19 years old) in six Norwegian upper secondary physics classrooms. Design-based research methods guided the development of the learning resources, which were based on a sociocultural view of learning and a historical-philosophical approach to teaching general relativity. To characterize students' learning from and interaction with the learning environment we analyzed focus group interviews and students' oral and written responses to assigned problems and discussion tasks. Our findings show how design choices on different levels can support or hinder understanding of general relativity, leading to the formulation of design principles that help to foster qualitative understanding and encourage collaborative learning. The results indicate that upper secondary students can obtain a qualitative understanding of general relativity when provided with appropriately designed learning resources and sufficient scaffolding of learning through interaction with teacher and peers.