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Tidsrummet mellem to begivenheder er afhængigt af, hvor hurtigt en observatør bevæger sig. Det er en af de besynderlige konsekvenser af Albert Einsteins specielle relativitetsteori fra 1905, der er en grundsten i den moderne fysik. I Speciel Relativitetsteori forklarer Ulrik Uggerhøj tid og rum. Han udleder bl.a. fundamentet for fænomener som tidsforlængelse, længdeforkortning og Lorentz-transformationerne, undersøger tyngdens indflydelse på tidens gang, sorte huller og gravitationsbølger og præsenterer løsninger på flere af teoriens tilsyneladende paradokser. Bogen indeholder forslag til læseforløb fra gymnasiale studieretningsprojekter til det avancerede universitetsniveau.
About the BookThe use of the principles of relativity began in the mid-seventeenth century with Galileo, which is known as classical relativity or Newtonian relativity. but these equations faced difficulties when applied to Maxwell's equations in electromagnetism, and they failed in certain astronomical measurements. Therefore, Lorentz transformations were formulated at the end of the nineteenth century. Einstein adopted the Lorentz transformations and considered Newton's relativity as outdated and insufficient, leading him to develop his theory of relativity as an alternative.Critiques and objections to Einstein's theory of relativity have indeed persisted over time. Some have argued that it goes against common sense and appears unrealistic. Additionally, there have been debates about its compatibility with the principle of relativity concerning the constancy of physical laws when observed by moving observers and its application to objects moving according to the law of self-relativity.Many physicists published numerous books and research papers attempting to refute Einstein's theory of relativity. However, all were neglected as they did not provide an alternative and could not prove the failure of Einstein's relativity theory. Einstein was assured that his theory could not be refuted with a practical experiment as it is impossible to achieve a speed close to the speed of light.Today, the remarkable advancement of artificial intelligence in accessing scientific information has given us a rare opportunity that was not available to Einstein. I am not alone in seeing the rapid development of technology and new horizons arising daily. Artificial intelligence feeds us information and ideas, from articles and evidence to online symposiums and deep learning. That being said, we no longer need to put much effort into seeking the truth since we can recognise the tools used by everyone, be inspired by fascinating projects, and search for experts' help. That makes what we introduce of immense importance, which I discovered in Relativity, after seven years of concentrated study to provide evidence of the failure of Einstein's relativity, modify Newton's relativity, and establish the third relativity theory.
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.
A mesmerizing trip to the strange new world of white holes, from Carlo Rovelli, the bestselling author of Seven Brief Lessons on PhysicsLet us journey into the heart of a black hole. Let us slip beyond its boundary, the horizon, and tumble - on and on - down this crack in the universe. As we plunge, we'll see geometry fold, we'll feel the equations draw tight around us. Eventually, we'll pass it: the remains of a star, deep and dense and falling further far. And then - the bottom. Where time and space end, and the white hole is born . . . With lightness and magic, here Carlo Rovelli traces the ongoing adventure of his own cutting-edge research, of the uncertainty and joy of going where we've not yet been. Guiding us to the edge of theory and experiment, he invites us to go beyond, to experience the fever and the disquiet of science. Here is the extraordinary life of a white hole.
This book deals with theoretical mechanics. Newton published the "Philosophiæ Naturalis Principia Mathematica" in 1687. In it, he sets out the basic principles of physics that are required to understand the motion of the planets, their moons, and the comets in the solar system. It includes the gravitational (inverse square) law, the inertial principle, and the basic elements of mechanics. Since its publication, a large number of refinements and reformulations have been introduced, thereby adding enormous insight into the structure of mechanics, which is commonly known as ¿classical mechanics¿. All these have in common that by taking a suitable limit, Newton's original principles re-appear. Thus, physicists and mathematicians who work on the subject always have a notion that if their theories do not return to Newton's foundations, then there is something wrong. Newton himself acknowledged that 'if I have seen further (than others), it is by standing on the shoulders of giants'. One of these giants was undoubtedly Galileo who died in the year Newton was born. So, Newton himself adhered to the 'classical limit'.
This book continues the applications of mathematics, more specifically of theta, eta, and zeta functions, and modular forms, to various areas of theoretical physics. It is a follow-up and extension in some sense of the author¿s earlier book entitled A window into zeta and modular physics. Some of the main topics are1. A new approach to logarithmic corrections to black hole entropy2. My recent work that provides for an explicit cold plasma-black hole connection3. Generalization of work of physicists on certain asymptotic problems relating to string theory, for example, by way of the general theory of modular forms of non-positive weight4. A construction of the E8 root lattice, its theta function, and its relevance for heterotic string theory5. Applications of elliptic functions to KdV, nonlinear Schrödinger, and Duffing equations, for example, including a discussion of Lax pairs and the Miura transformation6. Finite temperature zeta functions and partition functions for quantum fields in thermal equilibrium on various curved background spacetimes7. Exact solutions of the Einstein gravitational field equations for Lemaitre and inhomogeneous cosmological models, with a special focus on the Szekeres¿Szafron exact solutions by way of the Weierstrass elliptic function8. Elementary particles and my zeta function formula for higher spin fermionic particles; this covers, in particular, the gravitino particle (of spin 3/2) and bosons with integral spin s = 2, 3, 4, 5.These are some sample topics. Others include the continuous Heisenberg model, reaction diffusion systems, Dirichlet and Hecke L-functions, the modular j-invariant, the computation of the one-loop effective potential for non-compact symmetric spaces, the BTZ black hole, Jacobi inversion formulas, etc.Thus, there is a very large range of material with the first 9 chapters of preliminary, expositional background for mathematicians and physicists.
Ce livre présente la dérivation de l'équation de Dewitt-Wheeler dans laquelle l'équation indépendante du temps décrit la quantification du champ gravitationnel dans une configuration à trois géomètres. Cette équation peut être appelée équation de Schrodinger-Einstein. Cette approche de la quantification de la gravité a été initiée par Dewitt selon l'interprétation d'Everett de la mécanique quantique qui donne lieu à l'idée du multivers, et ainsi, l'équation WDW a introduit une fonction appelée fonction lapse dans laquelle chaque fonction lapse différente selon Dewitt donne une séquence différente de 3 géométries qui indique le multivers. D'autre part, selon l'interprétation du potentiel quantique de Bohm, l'univers est considéré comme un système mécanique quantique de taille zéro, et donc, l'univers peut creuser un tunnel avec une probabilité bien définie et non nulle, ce qui exprime la création à partir d'une non-chose. Cette idée de la création à partir d'une non-chose est soutenue par Hawking dans son articulation en 1988, selon laquelle, en fait, il n'y avait pas de singularité au début de l'univers "elle peut disparaître une fois que les effets quantiques sont pris en compte". Penrose est d'accord.
This book provides a concise introduction to the physics of gravitational waves. It is aimed at graduate-level students and PhD scholars. Ever since the discovery of gravitational waves in 2016, gravitational wave astronomy has been adding to our understanding of the universe.Gravitational waves have been detected in the past few years from several transient events such as merging stellar-mass black holes, binary neutron stars, etc. These waves have frequencies in a band ranging from a few hundred hertz to around a kilohertz to which LIGO type instruments are sensitive. LISA will be sensitive to much lower range of frequencies from SMBH mergers. Apart from these cataclysmic burst events, there are innumerable sources of radiation which are continuously emitting gravitational waves of all frequencies. These include a whole mass range of compact binary and isolated compact objects and close planetary stellar entities. This book discusses the gravitational wave background produced in typical frequency ranges from such sources emitting over a Hubble time and the fluctuations in the h values measured in the usual devices. Also discussed are the high-frequency thermal background gravitational radiation from hot stellar interiors and newly formed compact objects. The reader will also learn how gravitational waves provide a testing tool for various theories of gravity, i.e. general relativity and extended theories of gravity, and will be the definitive test for general relativity.
The thesis tackles two distinct problems of great interest in gravitational mechanics ¿ one relativistic and one Newtonian. The relativistic one is concerned with the "first law of binary mechanics", a remarkably simple variational relation that plays a crucial role in the modern understanding of the gravitational two-body problem, thereby contributing to the effort to detect gravitational-wave signals from binary systems of black holes and neutron stars. The work reported in the thesis provides a mathematically elegant extension of previous results to compact objects that carry spin angular momentum and quadrupolar deformations, which more accurately represent astrophysical bodies than mere point particles. The Newtonian problem is concerned with the isochrone problem of celestial mechanics, namely the determination of the set of radial potentials whose bounded orbits have a radial period independent of the angular momentum. The thesis solves this problem completely in a geometrical way and explores its consequence on a variety of levels, in particular with a complete characterisation of isochrone orbits. The thesis is exceptional in the breadth of its scope and achievements. It is clearly and eloquently written, makes excellent use of images, provides careful explanations of the concepts and calculations, and it conveys the author¿s personality in a way that is rare in scientific writing, while never sacrificing academic rigor.
This book systematically develops the mathematical foundations of the theory of relativity and links them to physical relations. For this purpose, differential geometry on manifolds is introduced first, including differentiation and integration, and special relativity is presented as tensor calculus on tangential spaces. Using Einstein's field equations relating curvature to matter, the relativistic effects in the solar system including black holes are discussed in detail. The text is aimed at students of physics and mathematics and assumes only basic knowledge of classical differential and integral calculus and linear algebra.
This book examines the topics of magnetohydrodynamics and plasma oscillations, in addition to the standard topics discussed to cover courses in electromagnestism, electrodynamics, and fundamentals of physics, to name a few. This textbook on electricity and magnetism is primarily targeted at graduate students of physics. The undergraduate students of physics also find the treatment of the subject useful. The treatment of the special theory of relativity clearly emphasises the Lorentz covariance of Maxwell's equations. The rather abstruse topic of radiation reaction is covered at an elementary level, and the Wheeler-Feynman absorber theory has been dwelt upon briefly in the book.
This book is an English translation from a Hungarian book designed for graduate and postgraduate students about the use of variational principles in theoretical physics. Unlike many academic textbooks, it dashes across several lecture disciplines taught in physics courses. It emphasizes and demonstrates the use of the variational technique and philosophy behind the basic laws in mechanics, relativity theory, electromagnetism, and quantum mechanics. The book is meant for advanced students and young researchers in theoretical physics but, also, more experienced researchers can benefit from its reading.
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.
No entanto, o que não investigámos é o que realmente acontece no instante t = 0? desta vez é normalmente referido como o ponto do tempo do Big Bang. Alguns dos modelos da evolução do universo não têm claramente nenhuma singularidade, como por exemplo o modelo k = 1 de Sitter. Outros modelos têm uma singularidade. Neste artigo, seremos dedicados às singularidades cosmológicas. Começaremos com as equações de campo de Einstein, a fim de determinar o que precisamos para introduzir alguns conceitos técnicos que conduzam à investigação da existência das singularidades.
This book investigates Lorentzian structures in the four-dimensional space-time, supplemented either by a covector field of the time-direction or by a scalar field of the global time. Furthermore, it proposes a new metrizable model of gravity. In contrast to the usual General Relativity theory, where all ten components of the symmetric pseudo-metric are independent variables, the gravity model presented here essentially depends only on a single four-covector field, and is restricted to have only three-independent components. However, the author proves that the gravitational field, governed by the proposed model and generated by some massive body, resting and spherically symmetric in some coordinate system, is given by a pseudo-metric that coincides with the well known Schwarzschild metric from General Relativity. The Maxwell equations and electrodynamics are also investigated in the framework of the proposed model. In particular, the covariant formulation of electrodynamics of moving dielectrics and para/diamagnetic media is derived.
Soglasno älektricheskomu zarqdu i koäfficientu uprugosti ob#ekta, ne zawisqschim ot dwizheniq ob#ekta, i ishodq iz analogichnyh swojstw grawitacionnogo polq i älektrostaticheskogo polq, delaetsq wywod, chto grawitacionnaq massa ob#ekta qwlqetsq konstantoj, ne zawisqschej ot dwizheniq ob#ekta. Odnako äxperimental'nye rezul'taty pokazywaüt, chto inercionnaq massa ob#ekta swqzana s dwizheniem ob#ekta. Poätomu schitaetsq, chto princip äkwiwalentnosti ne wypolnqetsq. Kogda ob#ekt dwizhetsq s maloj skorost'ü, princip äkwiwalentnosti priblizitel'no weren, poätomu delaetsq wywod, chto obschaq teoriq otnositel'nosti primenima ko wsem kosmicheskim nebesnym telam. Kogda ob#ekt dwizhetsq s bol'shoj skorost'ü, princip äkwiwalentnosti ne wypolnqetsq, poätomu obschaq teoriq otnositel'nosti ne qwlqetsq istinoj. Soglasno principu balansa sil, delaetsq wywod, chto skorost' V chernoj dyry dolzhna byt' rawna nulü. Pri neobhodimyh uslowiqh V = 0, suschestwowanie chernoj dyry ne mozhet byt' wywedeno soglasno obschej teorii otnositel'nosti.
This paper puts forward the force equilibrium invariance axiom and derives the force transformation formula of the special relativity; puts forward the correlation analysis law and eliminates some problems resulted from the improper application of relativity; puts forward the principle of absolute velocity, determines the running speed of any moving object in real time, and solves the problem of twin paradox; puts forward the corresponding principle and determines the relationship between the rest mass and the reference frame; puts forward the concept of absolute transformation and relative transformation and clarifies two different natures of Lorentz transformation; puts forward the field similarity principle and determines the gravitational mass as a constant that has nothing to do with the velocity; infers that the equivalence principle is false and that the general relativity is only applicable to low speed moving objects; puts forward the gravity double equilibrium principle and concludes that Black Hole could not exist. It also analyzes the limiting speed of manned spaceship, and concludes that human beings cannot realize time travel of practical significance.
This book addresses supergravity and supergravity-motivated effective field theories in the context of cosmological model building. Extracting information about quintessence from string theory has attracted much attention in the past few years. The question became more urgent very recently after the possibility of obtaining de Sitter space was called into question. Therefore, there is an interesting debate as to whether de Sitter space or, even, quintessence can be derived from a fundamental theory, string theory or otherwise. This is a very active field of research, and the topics covered in the book render this work very timely.Throughout the book, special care has been taken in demonstrating historical relevance of the field and describing the set of open questions motivating the state-of-the-art research. The first few chapters in each part provide a detailed review of standard perturbative and non-perturbative techniques in supergravity model building, as a way to prepare the reader for the more technical and original subsequent chapters. These early chapters also represent a self-contained review that would be useful for anyone planning to enter this challenging area of study. The subsequent chapters detail research in supergravity-motivated effective field theories, in the first part, and supergravity models, in the second part. One of the important conclusions in this book is that modelling quintessence in perturbative string theory is at least as challenging as modelling de Sitter, placing the wider programme on a collision course with observations.
Despite successes of modern physics, the existence of dark energy and matter is indicative that conventional mechanical accounting is lacking. The most basic of all mechanical principles is Newton's second law, and conventionally, energy is just energy whether particle or wave energy. In this monograph, Louis de Broglie's idea of simultaneous existence of both particle and associated wave is developed, with a novel proposal to account for mass and energy through a combined particle-wave theory. Newton's second law of motion is replaced by a fully Lorentz invariant reformulation inclusive of both particles and waves. The model springs from continuum mechanics and forms a natural extension of special relativistic mechanics. It involves the notion of "e;force in the direction of time"e; and every particle has both particle and wave energies, arising as characteristics of space and time respectively. Dark matter and energy then emerge as special or privileged states occurring for alignments of spatial forces with the force in the direction of time. Dark matter is essentially a backward wave and dark energy a forward wave, both propagating at the speed of light. The model includes special relativistic mechanics and Schrodinger's quantum mechanics, and the major achievements of mechanics and quantum physics. Our ideas of particles and waves are not yet properly formulated, and are bound up with the speed of light as an extreme limit and particle-wave demarcation. Sub-luminal particles have an associated superluminal wave, so if sub-luminal waves have an associated superluminal particle, then there emerges the prospect for faster than light travel with all the implications for future humanity. Carefully structured over special relativity and quantum mechanics, Mathematics of Particle-Wave Mechanical Systems is not a completed story, but perhaps the first mechanical model within which such exalted notions might be realistically and soberly examined. If ultimately the distant universe become accessible, this will necessitate thinking differently about particles, waves and the role imposed by the speed of light. The text constitutes a single proposal in that direction and a depository for mathematically related results. It will appeal to researchers and students of mathematical physics, applied mathematics and engineering mechanics.
This proceedings volume gathers selected, revised papers presented at the X International Meeting on Lorentzian Geometry (GeLoCor 2021), virtually held at the University of Cordoba, Spain, on February 1-5, 2021. It includes surveys describing the state-of-the-art in specific areas, and a selection of the most relevant results presented at the conference. Taken together, the papers offer an invaluable introduction to key topics discussed at the conference and an overview of the main techniques in use today.This volume also gathers extended revisions of key studies in this field. Bringing new results and examples, these unique contributions offer new perspectives to the original problems and, in most cases, extend and reinforce the robustness of previous findings.Hosted every two years since 2001, the International Meeting on Lorentzian Geometry has become one of the main events bringing together the leading experts on Lorentzian geometry. In this volume, the reader will find studies on spatial and null hypersurfaces, low regularity in general relativity, conformal structures, Lorentz-Finsler spacetimes, and more.Given its scope, the book will be of interest to both young and experienced mathematicians and physicists whose research involves general relativity and semi-Riemannian geometry.
The purpose of this book is to illustrate some of the most important techniques which are helpful in combinatorial problems when computing quantum effects in covariant theories, like general relativity. In fact, most of the techniques find application also in broader contexts, such as low energy effective (chiral) Lagrangians or even in specific problems in condensed matter. Some of the topics covered are: the background field approach and the heat kernel ideas. The arguments are explained in some detail and the presentation is meant for young researchers and advanced students who are starting working in the field. As prerequisite the reader should have attended a course in quantum field theory including Feynman's path integral. In the Appendix a nontrivial calculation of one-loop divergences in Einstein-Hilbert gravity is explained step-by-step.
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